広島大学学位請求論文

Measurement of
low transverse-momentum direct photons
in Cu+Cu collisions at sNN = 200 GeV
核子対あたり重心系衝突エネルギー200GeV
銅+銅原子核衝突における低横運動量直接光子の測定

2021 年
星野 知也

目次
１． 主論文Measurement of low transverse-momentum direct photons in Cu+Cu collisions
at sNN = 200 GeV
核子対あたり重心系エネルギー200GeV 銅+銅原子核衝突における低横運動量直接光子の測定

２． 公表論文

題目：Low-momentum direct-photon measurement in Cu+Cu collisions at sNN= 200 GeV
著者：A. Adare et.al., （別紙、共著者リスト①参照）
Physical Review C 98, 054902 (2018)

３． 参考論文(1) 題目：Azimuthally anisotropic emission of low-momentum direct photons in
Au+Au collisions at sNN = 200 GeV
著者：A. Adare et.al., （別紙、共著者リスト②参照）
Physical Review C 94, 064901 (2016)(2) 題目：Dielectron production in Au+Au collisions at sNN = 200 GeV
著者：A. Adare et.al., （別紙、共著者リスト③参照）
Physical Review C 93, 014904 (2016)

共著者リスト①
A. Adare, S. Afanasiev, C. Aidala,, N. N. Ajitanand, Y. Akiba,,†, H. Al-Bataineh, J. Alexander, M. Alfred,
K. Aoki,,, L. Aphecetche, R. Armendariz, S. H. Aronson, J. Asai, E. T. Atomssa, R. Averbeck, T. C. Awes,
B. Azmoun, V. Babintsev, A. Bagoly, G. Baksay, L. Baksay, A. Baldisseri, K. N. Barish, P. D. Barnes, B.
Bassalleck, S. Bathe, S. Batsouli, V. Baublis, A. Bazilevsky, S. Belikov, R. Belmont, R. Bennett, A.
Berdnikov, Y. Berdnikov, A. A. Bickley, M. Boer, J. G. Boissevain, J. S. Bok, H. Borel, K. Boyle,, M. L.
Brooks, J. Bryslawskyj, H. Buesching, V. Bumazhnov, G. Bunce,, S. Butsyk,, S. Campbell,, V. Canoa
Roman, B. S. Chang, J.-L. Charvet, S. Chernichenko, C. Y. Chi, J. Chiba, M. Chiu, I. J. Choi, T. Chujo,,
P. Chung, A. Churyn, V. Cianciolo, C. R. Cleven, B. A. Cole, M. P. Comets, M. Connors, P. Constantin,
M. Csanád, T. Csörgő, T. Dahms, T. W. Danley, K. Das, G. David, M. B. Deaton, K. Dehmelt,, H.
Delagrange, A. Denisov, D. d'Enterria, A. Deshpande, E. J. Desmond, O. Dietzsch, A. Dion, J. H. Do,
M. Donadelli, O. Drapier, A. Drees, A. K. Dubey, J. M. Durham, A. Durum, V. Dzhordzhadze, Y. V.
Efremenko, J. Egdemir, F. Ellinghaus, W. S. Emam, A. Enokizono, H. En'yo, S. Esumi, K. O. Eyser, W.
Fan, N. Feege, D. E. Fields, M. Finger, M. Finger, Jr., F. Fleuret, S. L. Fokin, Z. Fraenkel, J. E. Frantz,
A. Franz, A. D. Frawley, K. Fujiwara, Y. Fukao, T. Fusayasu, S. Gadrat, P. Gallus, P. Garg, I. Garishvili,
H. Ge, A. Glenn,, H. Gong, M. Gonin, J. Gosset, Y. Goto, R. Granier de Cassagnac, N. Grau, S. V. Greene,
M. Grosse Perdekamp, T. Gunji, H.-Å. Gustafsson, T. Hachiya, A. Hadj Henni, C. Haegemann, J. S.
Haggerty, H. Hamagaki, R. Han, H. Harada, E. P. Hartouni, K. Haruna, S. Hasegawa, T. O. S. Haseler,
E. Haslum, R. Hayano, X. He, M. Heffner, T. K. Hemmick, T. Hester, H. Hiejima, J. C. Hill, K. Hill, R.
Hobbs, A. Hodges, M. Hohlmann, W. Holzmann, K. Homma, B. Hong, T. Horaguchi, D. Hornback, T.
Hoshino, N. Hotvedt, J. Huang, T. Ichihara, H. Iinuma, K. Imai, M. Inaba, Y. Inoue, D. Isenhower, L.
Isenhower, M. Ishihara, T. Isobe, M. Issah, A. Isupov, D. Ivanishchev, B. V. Jacak, Z. Ji, J. Jia, J. Jin,
O. Jinnouchi, B. M. Johnson, K. S. Joo, D. Jouan, F. Kajihara, S. Kametani, N. Kamihara, J. Kamin, M.
Kaneta, J. H. Kang, H. Kanou, D. Kawall, A. V. Kazantsev, V. Khachatryan, A. Khanzadeev, J. Kikuchi,
D. H. Kim, D. J. Kim, E. Kim, E.-J. Kim, M. Kim, D. Kincses, E. Kinney, Á. Kiss, E. Kistenev, A. Kiyomichi,
J. Klay, C. Klein-Boesing, L. Kochenda, V. Kochetkov, B. Komkov, M. Konno, D. Kotchetkov, D. Kotov,
A. Kozlov, A. Král, A. Kravitz, J. Kubart, G. J. Kunde, B. Kurgyis, N. Kurihara, K. Kurita,, M. J. Kweon,
Y. Kwon, G. S. Kyle, R. Lacey, Y. S. Lai, J. G. Lajoie, A. Lebedev, D. M. Lee, M. K. Lee, S. H. Lee, T.
Lee, M. J. Leitch, M. A. L. Leite, B. Lenzi, Y. H. Leung, N. A. Lewis, X. Li, X. Li, S. H. Lim, T. Liška, A.
Litvinenko, M. X. Liu, S. Lökös, B. Love, D. Lynch, C. F. Maguire, T. Majoros, Y. I. Makdisi, A. Malakhov,
M. D. Malik, V. I. Manko, Y. Mao,, L. Mašek, H. Masui, F. Matathias, M. McCumber, P. L. McGaughey,
D. McGlinchey, Y. Miake, A. C. Mignerey, D. E. Mihalik, P. Mikeš, K. Miki, T. E. Miller, A. Milov, S.
Mioduszewski, M. Mishra, J. T. Mitchell, M. Mitrovski, G. Mitsuka,, T. Moon, A. Morreale, D. P. Morrison,
S. I. Morrow, T. V. Moukhanova, D. Mukhopadhyay, J. Murata, S. Nagamiya, K. Nagashima, Y. Nagata,
J. L. Nagle, M. Naglis, I. Nakagawa, Y. Nakamiya, T. Nakamura, K. Nakano,, J. Newby, M. Nguyen, B.
E. Norman, R. Nouicer, T. Novák, N. Novitzky, A. S. Nyanin, E. O'Brien, S. X. Oda, C. A. Ogilvie, H.
Ohnishi, M. Oka, K. Okada, O. O. Omiwade, J. D. Orjuela Koop, J. D. Osborn, A. Oskarsson, M. Ouchida,K. Ozawa, R. Pak, D. Pal, A. P. T. Palounek, V. Pantuev, V. Papavassiliou, J. Park, S. Park, W. J. Park,S. F. Pate, M. Patel, H. Pei, J.-C. Peng, W. Peng, H. Pereira, D. V. Perepelitsa, V. Peresedov, D. Yu.
Peressounko, C. E. PerezLara, C. Pinkenburg, M. L. Purschke, A. K. Purwar, H. Qu, P. V. Radzevich, J.
Rak,, A. Rakotozafindrabe, I. Ravinovich, K. F. Read, S. Rembeczki, M. Reuter, K. Reygers, V. Riabov,
Y. Riabov, D. Richford, T. Rinn, G. Roche, A. Romana, M. Rosati, S. S. E. Rosendahl, P. Rosnet, Z.
Rowan, P. Rukoyatkin, J. Runchey, V. L. Rykov, B. Sahlmueller, N. Saito, T. Sakaguchi, S. Sakai, H.
Sakata, H. Sako, V. Samsonov, M. Sarsour, S. Sato,, S. Sawada, B. K. Schmoll, J. Seele, R. Seidl, V.
Semenov, R. Seto, D. Sharma,, I. Shein, A. Shevel, T.-A. Shibata, K. Shigaki, M. Shimomura, K. Shoji,
A. Sickles, C. L. Silva, D. Silvermyr, C. Silvestre, K. S. Sim, C. P. Singh, V. Singh, M. J. Skoby, S. Skutnik,
M. Slunečka, A. Soldatov, R. A. Soltz, W. E. Sondheim, S. P. Sorensen, I. V. Sourikova, F. Staley, P. W.
Stankus, E. Stenlund, M. Stepanov, A. Ster, S. P. Stoll, T. Sugitate, C. Suire, Z. Sun, J. Sziklai, T. Tabaru,
S. Takagi, E. M. Takagui, A. Taketani, Y. Tanaka, K. Tanida, M. J. Tannenbaum, A. Taranenko, P. Tarján,
T. L. Thomas, R. Tieulent, M. Togawa, A. Toia, J. Tojo, L. Tomášek, H. Torii, R. S. Towell, V.-N. Tram,
I. Tserruya, Y. Tsuchimoto, Y. Ueda, B. Ujvari, C. Vale, H. Valle, H. W. van Hecke, J. Velkovska, R.
Vértesi,, A. A. Vinogradov, M. Virius, V. Vrba,, E. Vznuzdaev, M. Wagner, D. Walker, X. R. Wang, D.
Watanabe, Y. Watanabe, F. Wei, J. Wessels, S. N. White, D. Winter, C. P. Wong, C. L. Woody, M. Wysocki,
W. Xie, C. Xu, Q. Xu, Y. L. Yamaguchi, A. Yanovich, Z. Yasin, J. Ying, S. Yokkaichi, J. H. Yoo, G. R.
Young, I. Younus,, H. Yu, I. E. Yushmanov, W. A. Zajc, O. Zaudtke, C. Zhang, S. Zharko, S. Zhou, J.
Zimamyi, L. Zolin, and L. Zou (PHENIX Collaboration)

共著者リスト②
A. Adare, S. Afanasiev, C. Aidala, N. N. Ajitanand, Y. Akiba, R. Akimoto, H. Al-Bataineh, J. Alexander,
M. Alfred, H. Al-Ta'ani, A. Angerami, K. Aoki, N. Apadula, Y. Aramaki, H. Asano, E. C. Aschenauer, E.
T. Atomssa, R. Averbeck, T. C. Awes, B. Azmoun, V. Babintsev, M. Bai, G. Baksay, L. Baksay, N. S.
Bandara, B. Bannier, K. N. Barish, B. Bassalleck, A. T. Basye, S. Bathe, V. Baublis, C. Baumann, S.
Baumgart, A. Bazilevsky, M. Beaumier, S. Beckman, S. Belikov, R. Belmont, R. Bennett, A. Berdnikov,
Y. Berdnikov, A. A. Bickley, D. S. Blau, J. S. Bok, K. Boyle, M. L. Brooks, J. Bryslawskyj, H. Buesching,
V. Bumazhnov, G. Bunce, S. Butsyk,, C. M. Camacho, S. Campbell, P. Castera, C.-H. Chen, C. Y. Chi,
M. Chiu, I. J. Choi, J. B. Choi, S. Choi, R. K. Choudhury, P. Christiansen, T. Chujo, P. Chung, O. Chvala,
V. Cianciolo, Z. Citron, B. A. Cole, M. Connors, P. Constantin, M. Csanád, T. Csörgő, T. Dahms, S.
Dairaku, I. Danchev, T. W. Danley, K. Das, A. Datta, M. S. Daugherity, G. David, K. DeBlasio, K. Dehmelt,
A. Denisov, A. Deshpande, E. J. Desmond, K. V. Dharmawardane, O. Dietzsch, L. Ding, A. Dion, P. B.
Diss, J. H. Do, M. Donadelli, L. D'Orazio, O. Drapier, A. Drees, K. A. Drees, J. M. Durham, A. Durum,
D. Dutta, S. Edwards,, Y. V. Efremenko, F. Ellinghaus, T. Engelmore, A. Enokizono, H. En'yo, S. Esumi,
K. O. Eyser, B. Fadem, N. Feege, D. E. Fields, M. Finger, M. Finger, Jr., F. Fleuret, S. L. Fokin, Z.
Fraenkel, J. E. Frantz, A. Franz, A. D. Frawley, K. Fujiwara, Y. Fukao, T. Fusayasu, K. Gainey, C. Gal,
P. Gallus, P. Garg,, A. Garishvili, I. Garishvili, H. Ge, F. Giordano, A. Glenn, H. Gong, X. Gong, M.

Gonin, Y. Goto, R. Granier de Cassagnac, N. Grau, S. V. Greene, M. Grosse Perdekamp, T. Gunji, L.
Guo, H.-Å. Gustafsson, T. Hachiya, J. S. Haggerty, K. I. Hahn, H. Hamagaki, J. Hamblen, H. F. Hamilton,
R. Han, S. Y. Han, J. Hanks, E. P. Hartouni, S. Hasegawa, T. O. S. Haseler, K. Hashimoto, E. Haslum,
R. Hayano, X. He, M. Heffner, T. K. Hemmick, T. Hester, J. C. Hill, M. Hohlmann, R. S. Hollis, W.
Holzmann, K. Homma, B. Hong, T. Horaguchi, Y. Hori, D. Hornback, T. Hoshino, N. Hotvedt, J. Huang,
S. Huang, T. Ichihara,, R. Ichimiya, J. Ide, H. Iinuma, Y. Ikeda,, K. Imai, J. Imrek, M. Inaba, A. Iordanova,
D. Isenhower, M. Ishihara, T. Isobe, M. Issah, A. Isupov, D. Ivanishchev, B. V. Jacak, M. Javani, M.
Jezghani, J. Jia, X. Jiang, J. Jin, B. M. Johnson, K. S. Joo, D. Jouan, D. S. Jumper, F. Kajihara, S.
Kametani, N. Kamihara, J. Kamin, S. Kanda, S. Kaneti, B. H. Kang, J. H. Kang, J. S. Kang, J. Kapustinsky,
K. Karatsu, M. Kasai, D. Kawall, M. Kawashima, A. V. Kazantsev, T. Kempel, J. A. Key, V. Khachatryan,
A. Khanzadeev, K. M. Kijima, B. I. Kim, C. Kim, D. H. Kim, D. J. Kim, E. Kim, E.-J. Kim, G. W. Kim, H.
J. Kim, K.-B. Kim, M. Kim, S. H. Kim, Y.-J. Kim, Y. K. Kim, B. Kimelman, E. Kinney, K. Kiriluk, Á. Kiss,
E. Kistenev, R. Kitamura, J. Klatsky, D. Kleinjan, P. Kline, T. Koblesky, L. Kochenda, Y. Komatsu,, B.
Komkov, M. Konno, J. Koster, D. Kotchetkov, D. Kotov, A. Kozlov, A. Král, A. Kravitz, F. Krizek, G. J.
Kunde, K. Kurita, M. Kurosawa, Y. Kwon, G. S. Kyle, R. Lacey, Y. S. Lai, J. G. Lajoie, A. Lebedev, B.
Lee, D. M. Lee, J. Lee, K. Lee, K. B. Lee, K. S. Lee, S. Lee, S. H. Lee, S. R. Lee, M. J. Leitch, M. A. L.
Leite, M. Leitgab, E. Leitner, B. Lenzi, B. Lewis, X. Li, P. Liebing, S. H. Lim, L. A. Linden Levy, T. Liška,
A. Litvinenko, H. Liu, M. X. Liu, B. Love, R. Luechtenborg, D. Lynch, C. F. Maguire, Y. I. Makdisi, M.
Makek, A. Malakhov, M. D. Malik, A. Manion, V. I. Manko, E. Mannel, Y. Mao, H. Masui, S. Masumoto,,
F. Matathias, M. McCumber, P. L. McGaughey, D. McGlinchey, C. McKinney, N. Means, A. Meles, M.
Mendoza, B. Meredith, Y. Miake, T. Mibe, A. C. Mignerey, P. Mikeš,, K. Miki,, A. Milov, D. K. Mishra,
M. Mishra, J. T. Mitchell, Y. Miyachi, S. Miyasaka,, S. Mizuno, A. K. Mohanty, S. Mohapatra, P.
Montuenga, H. J. Moon, T. Moon, Y. Morino, A. Morreale, D. P. Morrison, S. Motschwiller, T. V.
Moukhanova, T. Murakami, J. Murata, A. Mwai, T. Nagae, S. Nagamiya, K. Nagashima, J. L. Nagle, M.
Naglis, M. I. Nagy, I. Nakagawa, H. Nakagomi, Y. Nakamiya, K. R. Nakamura,, T. Nakamura, K. Nakano,
C. Nattrass, A. Nederlof, P. K. Netrakanti, J. Newby, M. Nguyen, M. Nihashi, T. Niida, S. Nishimura, R.
Nouicer, T. Novák, N. Novitzky, A. S. Nyanin, E. O'Brien, S. X. Oda, C. A. Ogilvie, M. Oka, K. Okada,
Y. Onuki, J. D. Orjuela Koop, J. D. Osborn, A. Oskarsson, M. Ouchida, K. Ozawa, R. Pak, V. Pantuev,
V. Papavassiliou, B. H. Park, I. H. Park, J. Park, J. S. Park, S. Park, S. K. Park, W. J. Park, S. F. Pate, L.
Patel, M. Patel, H. Pei, J.-C. Peng, H. Pereira, D. V. Perepelitsa, G. D. N. Perera, V. Peresedov, D.Yu.
Peressounko, J. Perry, R. Petti, C. Pinkenburg, R. Pinson, R. P. Pisani, M. Proissl, M. L. Purschke, A. K.
Purwar, H. Qu, J. Rak, A. Rakotozafindrabe, B. J. Ramson, I. Ravinovich, K. F. Read, K. Reygers, D.
Reynolds, V. Riabov, Y. Riabov,, E. Richardson, T. Rinn, D. Roach, G. Roche, S. D. Rolnick, M. Rosati,
C. A. Rosen, S. S. E. Rosendahl, P. Rosnet, Z. Rowan, J. G. Rubin, P. Rukoyatkin, P. Ružička, B.
Sahlmueller, N. Saito, T. Sakaguchi, K. Sakashita, H. Sako, V. Samsonov, M. Sano, S. Sano,, M. Sarsour,
S. Sato, T. Sato, S. Sawada, B. Schaefer, B. K. Schmoll, K. Sedgwick, J. Seele, R. Seidl, A.Yu. Semenov,
A. Sen, R. Seto, P. Sett, A. Sexton, D. Sharma, I. Shein, T.-A. Shibata, K. Shigaki, M. Shimomura, K.
Shoji, P. Shukla, A. Sickles,, C. L. Silva, D. Silvermyr,, C. Silvestre, K. S. Sim, B. K. Singh, C. P. Singh,

V. Singh, M. Slunečka, M. Snowball, R. A. Soltz, W. E. Sondheim, S. P. Sorensen, I. V. Sourikova, N. A.
Sparks, P. W. Stankus, E. Stenlund, M. Stepanov, A. Ster, S. P. Stoll, T. Sugitate, A. Sukhanov, T. Sumita,
J. Sun, J. Sziklai, E. M. Takagui, A. Takahara, A. Taketani, R. Tanabe, Y. Tanaka, S. Taneja, K. Tanida,
M. J. Tannenbaum, S. Tarafdar, A. Taranenko, P. Tarján, E. Tennant, H. Themann, T. L. Thomas, R.
Tieulent, A. Timilsina, T. Todoroki, M. Togawa, A. Toia, L. Tomášek, M. Tomášek,, H. Torii, C. L. Towell,
R. Towell, R. S. Towell, I. Tserruya, Y. Tsuchimoto, T. Tsuji, C. Vale, H. Valle, H. W. van Hecke, M.
Vargyas, E. Vazquez-Zambrano, A. Veicht, J. Velkovska, R. Vértesi, A. A. Vinogradov, M. Virius, A.
Vossen, V. Vrba,, E. Vznuzdaev, X. R. Wang, D. Watanabe, K. Watanabe, Y. Watanabe,, Y. S. Watanabe,
F. Wei, R. Wei, J. Wessels, A. S. White, S. N. White, D. Winter, S. Wolin, J. P. Wood, C. L. Woody, R.
M. Wright, M. Wysocki,, B. Xia, W. Xie, L. Xue, S. Yalcin, Y. L. Yamaguchi, K. Yamaura, R. Yang, A.
Yanovich, J. Ying, S. Yokkaichi, J. H. Yoo, I. Yoon, Z. You, G. R. Young, I. Younus, H. Yu, I. E.
Yushmanov, W. A. Zajc, A. Zelenski, C. Zhang, S. Zhou, L. Zolin, and L. Zou (PHENIX Collaboration)

共著者リスト③
A. Adare, C. Aidala, N. N. Ajitanand, Y. Akiba, R. Akimoto, J. Alexander, M. Alfred, H. Al-Ta'ani, A.
Angerami, K. Aoki, N. Apadula,, Y. Aramaki,, H. Asano, E. C. Aschenauer, E. T. Atomssa, R. Averbeck,
T. C. Awes, B. Azmoun, V. Babintsev, M. Bai, N. S. Bandara, B. Bannier, K. N. Barish, B. Bassalleck, S.
Bathe,, V. Baublis, S. Baumgart, A. Bazilevsky, M. Beaumier, S. Beckman, R. Belmont, A. Berdnikov, Y.
Berdnikov, D. S. Blau, J. S. Bok, K. Boyle, M. L. Brooks, J. Bryslawskyj, H. Buesching, V. Bumazhnov,
S. Butsyk, S. Campbell, P. Castera, C.-H. Chen,, C. Y. Chi, M. Chiu, I. J. Choi, J. B. Choi, S. Choi, R. K.
Choudhury, P. Christiansen, T. Chujo, O. Chvala, V. Cianciolo, Z. Citron, B. A. Cole, M. Connors, M.
Csanád, T. Csörgő, S. Dairaku,, T. W. Danley, A. Datta, M. S. Daugherity, G. David, K. DeBlasio, K.
Dehmelt, A. Denisov, A. Deshpande, E. J. Desmond, K. V. Dharmawardane, O. Dietzsch, L. Ding, A.
Dion, P. B. Diss, J. H. Do, M. Donadelli, L. D'Orazio, O. Drapier, A. Drees, K. A. Drees, J. M. Durham,
A. Durum, S. Edwards, Y. V. Efremenko, T. Engelmore, A. Enokizono, S. Esumi, K. O. Eyser, B. Fadem,
N. Feege, D. E. Fields, M. Finger, M. Finger, Jr., F. Fleuret, S. L. Fokin, J. E. Frantz, A. Franz, A. D.
Frawley, Y. Fukao, T. Fusayasu, K. Gainey, C. Gal, P. Gallus, P. Garg, A. Garishvili, I. Garishvili, H. Ge,
F. Giordano, A. Glenn, X. Gong, M. Gonin, Y. Goto, R. Granier de Cassagnac, N. Grau, S. V. Greene, M.
Grosse Perdekamp, T. Gunji, L. Guo, H.-Å. Gustafsson, T. Hachiya, J. S. Haggerty, K. I. Hahn, H.
Hamagaki, H. F. Hamilton, S. Y. Han, J. Hanks, S. Hasegawa, T. O. S. Haseler, K. Hashimoto, E. Haslum,
R. Hayano, X. He, T. K. Hemmick, T. Hester, J. C. Hill, R. S. Hollis, K. Homma, B. Hong, T. Horaguchi,
Y. Hori, T. Hoshino, N. Hotvedt, J. Huang, S. Huang, T. Ichihara, H. Iinuma, Y. Ikeda, K. Imai, J. Imrek,
M. Inaba, A. Iordanova, D. Isenhower, M. Issah, D. Ivanishchev, B. V. Jacak, M. Javani, M. Jezghani,
J. Jia,, X. Jiang, B. M. Johnson, K. S. Joo, D. Jouan, D. S. Jumper, J. Kamin, S. Kanda, S. Kaneti, B. H.
Kang, J. H. Kang, J. S. Kang, J. Kapustinsky, K. Karatsu, M. Kasai, D. Kawall, A. V. Kazantsev, T. Kempel,
J. A. Key, V. Khachatryan, A. Khanzadeev, K. M. Kijima, B. I. Kim, C. Kim, D. J. Kim, E.-J. Kim, G. W.
Kim, H. J. Kim, K.-B. Kim, M. Kim, Y.-J. Kim, Y. K. Kim, B. Kimelman, E. Kinney, Á. Kiss, E. Kistenev,

R. Kitamura, J. Klatsky, D. Kleinjan, P. Kline, T. Koblesky, Y. Komatsu, B. Komkov, J. Koster, D.
Kotchetkov, D. Kotov, A. Král, F. Krizek, G. J. Kunde, K. Kurita, M. Kurosawa, Y. Kwon, G. S. Kyle, R.
Lacey, Y. S. Lai, J. G. Lajoie, A. Lebedev, B. Lee, D. M. Lee, J. Lee, K. B. Lee, K. S. Lee, S Lee, S. H.
Lee, S. R. Lee, M. J. Leitch, M. A. L. Leite, M. Leitgab, B. Lewis, X. Li, S. H. Lim, L. A. Linden Levy, M.
X. Liu, B. Love, D. Lynch, C. F. Maguire, Y. I. Makdisi, M. Makek, A. Manion, V. I. Manko, E. Mannel,
S. Masumoto, M. McCumber,, P. L. McGaughey, D. McGlinchey,, C. McKinney, A. Meles, M. Mendoza,
B. Meredith, Y. Miake, T. Mibe, A. C. Mignerey, A. Milov, D. K. Mishra, J. T. Mitchell, Y. Miyachi, S.
Miyasaka,, S. Mizuno, A. K. Mohanty, S. Mohapatra, P. Montuenga, H. J. Moon, T. Moon, D. P. Morrison,
S. Motschwiller, T. V. Moukhanova, T. Murakami, J. Murata, A. Mwai, T. Nagae, S. Nagamiya, K.
Nagashima, J. L. Nagle, M. I. Nagy, I. Nakagawa, H. Nakagomi, Y. Nakamiya, K. R. Nakamura, T.
Nakamura, K. Nakano, C. Nattrass, A. Nederlof, P. K. Netrakanti, M. Nihashi, T. Niida, S. Nishimura,
R. Nouicer, T. Novák, N. Novitzky, A. S. Nyanin, E. O'Brien, C. A. Ogilvie, K. Okada, J. D. Orjuela Koop,
J. D. Osborn, A. Oskarsson, M. Ouchida, K. Ozawa, R. Pak, V. Pantuev, V. Papavassiliou, B. H. Park, I.
H. Park, J. S. Park, S. Park, S. K. Park, S. F. Pate, L. Patel, M. Patel, H. Pei, J.-C. Peng, H. Pereira, D.
V. Perepelitsa,, G. D. N. Perera, D. Yu. Peressounko, J. Perry, R. Petti,, C. Pinkenburg, R. Pinson, R. P.
Pisani, M. Proissl, M. L. Purschke, H. Qu, J. Rak, B. J. Ramson, I. Ravinovich, K. F. Read,, D. Reynolds,
V. Riabov, Y. Riabov, E. Richardson, T. Rinn, D. Roach, G. Roche, S. D. Rolnick, M. Rosati, Z. Rowan,
J. G. Rubin, B. Sahlmueller, N. Saito, T. Sakaguchi, H. Sako, V. Samsonov, M. Sano, M. Sarsour, S. Sato,S. Sawada, B. Schaefer, B. K. Schmoll, K. Sedgwick, R. Seidl, A. Sen, R. Seto, P. Sett, A. Sexton, D.
Sharma, I. Shein, T.-A. Shibata, K. Shigaki, M. Shimomura, K. Shoji, P. Shukla, A. Sickles,, C. L. Silva,
D. Silvermyr, K. S. Sim, B. K. Singh, C. P. Singh, V. Singh, M. Slunečka, M. Snowball, R. A. Soltz, W. E.
Sondheim, S. P. Sorensen, I. V. Sourikova, P. W. Stankus, E. Stenlund, M. Stepanov, A. Ster, S. P. Stoll,
T. Sugitate, A. Sukhanov, T. Sumita, J. Sun, J. Sziklai, E. M. Takagui, A. Takahara, A. Taketani, Y.
Tanaka, S. Taneja, K. Tanida,, M. J. Tannenbaum, S. Tarafdar, A. Taranenko, E. Tennant, H. Themann,
R. Tieulent, A. Timilsina, T. Todoroki, L. Tomášek, M. Tomášek, H. Torii, C. L. Towell, R. Towell, R. S.
Towell, I. Tserruya, Y. Tsuchimoto, T. Tsuji, C. Vale, H. W. van Hecke, M. Vargyas, E. VazquezZambrano, A. Veicht, J. Velkovska, R. Vértesi, M. Virius, A. Vossen, V. Vrba,, E. Vznuzdaev, X. R. Wang,
D. Watanabe, K. Watanabe, Y. Watanabe, Y. S. Watanabe, F. Wei, R. Wei, A. S. White, S. N. White, D.
Winter, S. Wolin, C. L. Woody, M. Wysocki,, B. Xia, L. Xue, S. Yalcin, Y. L. Yamaguchi, R. Yang, A.
Yanovich, J. Ying, S. Yokkaichi, J. H. Yoo, I. Yoon, Z. You, I. Younus, H. Yu, I. E. Yushmanov, W. A.
Zajc, A. Zelenski, S. Zhou, and L. Zou (PHENIX Collaboration)

主論文

Measurement of
low transverse-momentum direct photonspin Cu+Cu collisions at sN N = 200 GeVTomoya Hoshino

March 3, 2021

Abstract
The measurement of direct photons in the experiments of relativistic heavyion collisions is an essential tool for exploring the hot and dense matter created by the collisions. The hot-dense matter, called Quark-Gluon Plasma,
is a new state of matter in which quarks and gluons are deconfined from
nucleons. Direct photons are defined by the photons that they do not arise
from the hadron decays. Photons interact with the electromagnetic force,
while quarks and gluons interact only by the strong force with each other.
Thus, direct photons leave the created medium without interaction with otherparticles once produced, and they can carry the QGP information. Therefore, they are an excellent probe into the characteristics of hot-dense matter.
Thermal photons emitted from the hot-dense matter are supposed to be thedominant contribution at the low transverse-momentum region. They are
expected to reflect the thermodynamic properties. Therefore, measurementsof low transverse-momentum direct-photons are crucial to understanding thecharacteristic of QGP.
The PHENIX experiment at the Relativistic Heavy Ion Collider (RHIC)
has carried out the low transverse-momentum direct photon measurementsin p+p, d+Au, and Au+Au collisions. Furthermore, the ALICE experimentat the Large Hadron Collider (LHC) has measured direct photons in Pb+Pb
collisions with higher collision energy than RHIC. Spectra and yields of thedirect photons are measured in the above experiments, and thermal properties are studied within a wide range of system size and collision energy.
We have measured low transverse-momentum direct photons by the virtual photon method in Cu+Cu collisions with the center-of-mass energy per
nucleon pairs of 200 GeV taken at the PHENIX experiment in the year 2005.
Virtual photons convert to low mass electron pairs through internal conversion; therefore, we measure quasi-real virtual photons that appeared aselectron pairs in low invariant mass. The virtual photons are statisticallyextracted as excess above hadronic sources after subtracting a large amountof background. The most crucial part of this analysis is background subtraction to tackle the virtual photon component extraction. We execute toestimate the uncorrelated background by the elliptic flow adjusted mixedevent method. We carry out the well-tuned Monte Carlo simulations toestimate the correlated backgrounds from Dalitz decays and jets. The direct

2
photon component is successfully extracted as the direct photon fraction byfitting on the foreground distribution by backgrounds and known hadronic
contribution.
The direct photon fractions, which are the direct to inclusive photon ratio, are measured as a function of transverse momentum for three collisioncentralities; minimum bias, 0–40%, and 40–94% centrality events. The direct
photon spectra are calculated by converting from the direct photon fractions.
The spectra are compared to the Ncoll scaled p+p results, and the excess yields
are observed in Cu+Cu collisions. The excess yields are parameterized by
an exponential function, and the inverse slope gives an e↵ective temperatureTe↵ = 285 ± 53(stat) ± 57(syst) MeV/c for minimum bias events. The integrated direct photon yield called the rapidity density is calculated from thesumming spectra as a function of Npart . The rapidity densities for Cu+Cu
collisions are compared to the Au+Au results to discuss the centrality andthe collision system size dependences of the direct photon production. The
Cu+Cu data provide the results in small Npart region. A power-law function
can describe the Npart dependence. The rapidity densities are also comparedto the results from lower to higher collision energies with several collision system as a function of charged-particle multiplicity, dNch /d⌘. The power-law
function can describe the multiplicity dependence. It supposes that the lowtransverse-momentum direct photons are originated in the hadron gas phaseand the vicinity of QGP-hadron gas phase transition.
In conclusion, we measure low transverse-momentum direct photons inp
Cu+Cu collisions at sN N = 200 GeV by the virtual photon method with the
PHENIX detector at RHIC. The Cu+Cu results provide the collision systemsize dependence of the direct photon production, especially in small Npartregion. The Cu+Cu and Au+Au results follow the same scaling, and there
seems to be no qualitative change in the photon sources for di↵erent collisionsystem size. The scaling can be applied to the wide range of the collisionenergies, and it suggests that the source of the low transverse-momentum
direct photons is near the transition from QGP to hadron phase.

Contents
1 Introduction
1.1 Quark Gluon Plasma . . . . . . . . . . . . . . . . . . . . . . .
1.2 Relativistic heavy-ion collisions . . . . . . . . . . . . . . . . .
1.3 Geometry of heavy ion collisions . . . . . . . . . . . . . . . . .
1.4 Space time evolution . . . . . . . . . . . . . . . . . . . . . . .
1.5 Direct photons and thermal photons . . . . . . . . . . . . . .
1.6 Direct virtual photons . . . . . . . . . . . . . . . . . . . . . .
1.7 Related measurements . . . . . . . . . . . . . . . . . . . . . .
1.7.1 Dielectron measurement . . . . . . . . . . . . . . . . .
1.7.2 Direct photon spectra . . . . . . . . . . . . . . . . . .
1.7.3 Centrality dependency of direct photons . . . . . . . .
1.7.4 Collisions energy dependence of direct photons . . . . .
1.7.5 Direct-photon collective flow . . . . . . . . . . . . . . .
1.7.6 Direct photon puzzle . . . . . . . . . . . . . . . . . . .
1.8 The thesis motivation . . . . . . . . . . . . . . . . . . . . . . .

12
13
16
17
18
20
22
23
24
28
33
36
39
40
41

2 Experimental setup
2.1 Relativistic Heavy Ion Collider . . . . . . . . . . . . . . . . . .
2.2 The PHENIX detector . . . . . . . . . . . . . . . . . . . . . .
2.3 Global detectors . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 Beam-Beam Counters . . . . . . . . . . . . . . . . . .
2.3.2 Zero-Degree Counters . . . . . . . . . . . . . . . . . . .
2.4 The central arm detectors . . . . . . . . . . . . . . . . . . . .
2.4.1 The Central Magnet . . . . . . . . . . . . . . . . . . .
2.4.2 Drift Chamber . . . . . . . . . . . . . . . . . . . . . .
2.4.3 Pad Chamber . . . . . . . . . . . . . . . . . . . . . . .
2.4.4 Ring Imaging Cherenkov Counters . . . . . . . . . . .
2.4.5 Electro-Magnetic Calorimeter . . . . . . . . . . . . . .

43
43
45
45
47
48
48
48
50
52
53
54

1

CONTENTS
2.5

2

Data Acquisition System . . . . . . . . . . . . . . . . . . . . . 57

3 Analysis
59
3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.2 Event selection and global variables . . . . . . . . . . . . . . . 60
3.2.1 Collected data and data set . . . . . . . . . . . . . . . 60
3.2.2 Minimum Bias Trigger . . . . . . . . . . . . . . . . . . 60
3.2.3 Centrality determination . . . . . . . . . . . . . . . . . 61
3.2.4 Reaction plane determination . . . . . . . . . . . . . . 62
3.3 Charged particle tracking . . . . . . . . . . . . . . . . . . . . . 62
3.4 Electron and positron identification . . . . . . . . . . . . . . . 64
3.5 Electron pair selection . . . . . . . . . . . . . . . . . . . . . . 67
3.5.1 Detector ghost pair cuts . . . . . . . . . . . . . . . . . 67
3.5.2 Photon conversion cut . . . . . . . . . . . . . . . . . . 67
3.6 Electron pair invariant mass . . . . . . . . . . . . . . . . . . . 69
3.7 Detector response in simulations . . . . . . . . . . . . . . . . . 69
3.8 Overview of background subtraction . . . . . . . . . . . . . . . 73
3.9 Simulation-based approach . . . . . . . . . . . . . . . . . . . . 74
3.9.1 Combinatorial backgroud . . . . . . . . . . . . . . . . . 76
3.9.2 Jet-induced correlated pairs . . . . . . . . . . . . . . . 79
3.9.3 Correlated cross pairs . . . . . . . . . . . . . . . . . . . 82
3.10 Background normalization . . . . . . . . . . . . . . . . . . . . 85
3.11 Data-driven approach . . . . . . . . . . . . . . . . . . . . . . . 86
3.12 Cross-check for background evaluation . . . . . . . . . . . . . 90
3.13 Correlated pairs from hadronic decay . . . . . . . . . . . . . . 91
3.14 Open heavy flavor contribution . . . . . . . . . . . . . . . . . 96
3.15 Determination of direct photon fraction . . . . . . . . . . . . . 98
3.16 Systematic uncertainties . . . . . . . . . . . . . . . . . . . . . 102
3.16.1 Background normalization uncertainties . . . . . . . . 104
3.16.2 Particle composition uncertainties . . . . . . . . . . . . 105
3.16.3 Uncertainty in hadronic cocktail normalization . . . . . 105
3.16.4 Uncertainty in the fitting range for r . . . . . . . . . . 105
3.16.5 Summary of systematic uncertainties . . . . . . . . . . 106
4 Results and Discussion
107
4.1 Direct photon fraction . . . . . . . . . . . . . . . . . . . . . . 107
4.2 Direct photon spectra . . . . . . . . . . . . . . . . . . . . . . . 108
4.3 Rapidity density . . . . . . . . . . . . . . . . . . . . . . . . . 115

CONTENTS

3

5 Summary and Conclusion

118

A Data table

122

List of Figures
1.1

1.2

1.3

1.4
1.5

1.6

1.7

1.8

The schematic view of the hierarchy from atoms to quarks andgluons. Atoms are composed of neutrons, protons, and electrons. Quarks and gluons constitute nucleons, such as protons
and neutrons. . . . . . . . . . . . . . . . . . . . . . . . . . . .
Quark-Gluon Plasma appears in the hot-and-dense condition.
In the Quark-Gluon Plasma, quarks and gluons are liberated
from the quark confinement. . . . . . . . . . . . . . . . . . . .
The energy density as a function of the temperature calculated by the lattice QCD. The energy density rapidly changes
around the temperature T ' 160 MeV. . . . . . . . . . . . . .
Theoretical phase diagram of nuclear matter . . . . . . . . . .
A schematic image of the heavy ion collision. Left: Two nuclei collide with the impact parameter b before the collision.
Right: After the collision, the spectator nucleons pass away inthe longitudinal direction, while particles are produced in theparticipant zone. . . . . . . . . . . . . . . . . . . . . . . . . .
A schematic diagram of the space-time evolution in heavyion collisions. Quark-Gluon Plasma is formed through a preequilibrium state after the heavy-ion collision. Produced particles, including hadrons, photons, and leptons, are detected
after the freeze-out. . . . . . . . . . . . . . . . . . . . . . . . .
Sources of direct photons in heavy-ion collisions. Produced
photons in the heavy-ion collisions are classified into two types:
direct photons and decay photons. . . . . . . . . . . . . . . . .
A theoretical prediction of direct photon yield as a functionpof transverse momentum in Au+Au collisions at sN N = 200
GeV. Each photon source has a di↵erent dominant transversemomentum region. . . . . . . . . . . . . . . . . . . . . . . . .
4

12

13

14
15

17

19

21

22

LIST OF FIGURES

5

Feynman diagram of quark-gluon Compton scattering (qg !
g ⇤ ! e+ e q) . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.10 Expected dielectron source in heavy-ion collisions . . . . . . . 24
1.11 Dielectron spectrum in minimum bias Au+Au collisions at
p
sN N =200GeV measured by the PHENIX experiment . . . . 25
p
1.12 Dielectron spectrum in p+p and Au+Au collisions at sN N =200GeV
measured by the PHENIX experiment . . . . . . . . . . . . . 26
1.13 Centrality dependece of the dielectron enhancement in 0.3 <pmee < 0.76 GeV/c2 in Au+Au collisions at sN N = 200 GeV.
The dielectron yields after subtracting the hadronic cocktail
without ⇢ broadening are compared to the model calculations. 28
1.14 Dielectron spectra in Au+Au collisions with several collisionenergies measured by the STAR experiment . . . . . . . . . . 29
p
1.15 Dielectron spectra in Cu+Cu collisions at sN N = 200 GeV
for 0–10% (left) and 10–20% (right) centrality classes measured by the PHENIX experiment . . . . . . . . . . . . . . . . 30
1.16 The double ratio of measured ( /⇡ 0 )Measured invariant yieldratio to the background decay ( /⇡ 0 )Background ratio as a funcp
tion of transverse momentum in Au+Au collisions at sN N =200 GeV measured by the real photon measuremnet in the
PHENIX experiment . . . . . . . . . . . . . . . . . . . . . . . 31
1.17 Direct photon spectra as a function of transverse momenp
tum in Au+Au collisions at sN N =200GeV measured by
the PHENIX experiment. The spectra are obtained for nine
centrality bins, and the solid curves denote the pQCD predictions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
1.18 Direct photon spectra measured by the internal conversionpmethod and the real photons in Au+Au collisions at sN N =200
GeV reported by the PHENIX experiment . . . . . . . . . . . 34
1.19 Thermal photon spectra by the external conversion methodpin Au+Au collisions at sN N = 200 GeV, together with theexponential fit results. . . . . . . . . . . . . . . . . . . . . . . 35
1.20 Integrated thermal photon yields for di↵erent lower transversep
momentum limit in Au+Au collisions at sN N = 200 GeV . . 36
p
1.21 Direct photon spectra in Pb+Pb collisions at sN N = 2.76TeV
measured by the ALICE experiment. The spectra for three
centrality classes, together with several theoretical models, areshown in the figure. . . . . . . . . . . . . . . . . . . . . . . . . 37
1.9

LIST OF FIGURES

6

1.22 Integrated direct photon yields (pT > 5 GeV/c) in several
collision system together with pQCD calculations . . . . . . . 38
1.23 Direct photon elliptic flow v2 and triangular flow v3 in Au+Au
pcollisions at sN N = 200 GeV measured by the PHENIX experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
1.24 Direct photon spectrum and azimuthal anisotropies of the second and third Fourier components in Au+Au collisions at
p
sN N = 200 GeV, together with several theoretical models. . 41
2.1

Relativistic Heavy Ion Collider (RHIC) complex arrangement,
including the LINAC and the Tandem Van de Graa↵ as a preaccelerator, and the Alternating Gradient Synchrotron (AGS).
2.2 The configuration of the PHENIX detector in 2005. The drawing shows the beam view (Top) and side view (Bottom) of thedetector. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 The BBC detector. (a) shows a BBC element, a photomultiplier. (b) shows a BBC array. . . . . . . . . . . . . . . . . . .
2.4 The cut-away view of the zero degree calorimeters. . . . . . .
2.5 The PHENIX Central Magnet . . . . . . . . . . . . . . . . . .
2.6 The construction of Drift Chamber frame . . . . . . . . . . . .
2.7 The wire position and the stereo wire orientation in Drift
Chamber. Left: the wire position layout within one sector
and inside the anode plane. Right: a schematic diagram ofthe stereo wire orientation. . . . . . . . . . . . . . . . . . . . .
2.8 Left: The pad and pixel geometry. Right: Pad design . . . . .
2.9 A cutaway view of one arm of the PHENIX RICH detector . .
2.10 Interior view of a Pb-scintillator calorimeter module showing
a stack of scintillator and lead plates, wavelength shifting fiber
readout and leaky fiber inserted in the central hole. . . . . . .
2.11 Exploded view of a lead-glass detector supermodule. . . . . . .
2.12 Schematic diagram of the PHENIX on-line system . . . . . . .
3.1
3.2

44

46
47
49
50
51

52
53
54

55
56
57

RHIC delivered Luminosity in Run-5 for Cu+Cu collisions at
p
sN N =200GeV . . . . . . . . . . . . . . . . . . . . . . . . . . 60
The correlation between BBC multiplicity and and ZDC energy deposit to determine centrality in the PHENIC experiment 61

LIST OF FIGURESThe schematic image of reaction plane in heavy-ion collisions.
The reaction plane is defined by the impact parameter and thebeam direction. . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 The schematic view of a track reconstruction by the Drift
Chamber in x-y plane . . . . . . . . . . . . . . . . . . . . . . .
3.5 A schematic image of the production of photon conversion
electron pair at the beam pipe . . . . . . . . . . . . . . . . . .
3.6 Single electron pT compare with the data and the simulation .
3.7 The elD variable comparison between the data and the simulation for electrons. . . . . . . . . . . . . . . . . . . . . . . . .
3.8 The elD variable comparison between the data and the simulation for positrons. . . . . . . . . . . . . . . . . . . . . . . . .
3.9 Hit map for dcphi and zed . . . . . . . . . . . . . . . . . . . .
3.10 Hit map for emcphi and emc-z . . . . . . . . . . . . . . . . . .
3.11 Reaction plane resolution as a function of centrality measuredpwith the BBC detector in Cu+Cu collisions at sN N = 200
GeV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.12 Single-electron elliptic flow v2 as a function of transverse mop
mentum with the best-fit result in Cu+Cu collisions at sN N =200 GeV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.13 Invariant mass distributions for near-side jet and back-to-backjets evaluated by the PYTHIA8 and PISA simulations. . . . .
3.14 The invariant mass shapes for ⇡ 0 and ⌘ cross pairs producedby the EXODUS and PISA simulation with the configuration
pof sN N = 200 GeV Cu+Cu collisions. . . . . . . . . . . . . .
3.15 Like-sign and unlike-sign electron-pair invariant-mass distributions of the data together with evaluated backgrounds for
Cu+Cu minimum bias events. . . . . . . . . . . . . . . . . . .
3.16 Like-sign and unlike-sign electron-pair invariant-mass distributions of the data together with evaluated backgrounds for
Cu+Cu minimum bias events. . . . . . . . . . . . . . . . . . .
3.17 Like-sign and unlike-sign electron-pair invariant-mass distributions of the data together with evaluated backgrounds for
Cu+Cu 0–40% centrality events. . . . . . . . . . . . . . . . . .
3.18 Like-sign and unlike-sign electron-pair invariant-mass distributions of the data together with evaluated backgrounds for
Cu+Cu 40–94% centrality events. . . . . . . . . . . . . . . . .

7

3.3

63
64
68
70
71
72
73
74

77

79
81

84

86

87

87

88

LIST OF FIGURES

8

3.19 Acceptance correction factor ↵ as a function of electron-pairinvariant mass for each transverse momentum and centrality . 89
3.20 The invariant mass distributions for the like-sign foregrounds
and their acceptance-corrected distributions in three centrality
bins: (top) minimum bias, (middle) 0–40%, and (bottom) 40–
94%. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
3.21 The invariant mass distribution of electron pairs for the unlikesign foregrounds, the acceptance-corrected like-sign pairs, andthe data after subtracting background by the data-driven approach with three centrality bins: (top) minimum bias, (middle) 0–40%, and (bottom) 40–94%. . . . . . . . . . . . . . . . 92
3.22 The comparison of invariant mass distributions between theacceptance-corrected foreground like-sign and BGSUM
evalu++,
SUM
ated by the simulation-based approach with the BG++, /FG
pfor Cu+Cu minimum bias events at sN N = 200 GeV. . . . . 93
3.23 The comparison of invariant mass distributions between theacceptance-corrected foreground like-sign and BGSUM
evalu++,
ated by the simulation-based approach with the BGSUM
/FG
++,
p
for Cu+Cu 0–40% centrality events at sN N = 200 GeV. . . . 95
3.24 The comparison of invariant mass distributions between theacceptance-corrected foreground like-sign and BGSUM
evalu++,
SUM
ated by the simulation-based approach with the BG++, /FG
pfor Cu+Cu 40–94% centrality events at sN N = 200 GeV. . . 96
3.25 The invariant mass shape of a hadronic cocktail evaluated byp
the EXODUS and PISA simulation for sN N = 200 GeV
Cu+Cu collisions . . . . . . . . . . . . . . . . . . . . . . . . . 97
3.26 The evaluated cc̄ contribution together with the backgroundsubtracted distribution . . . . . . . . . . . . . . . . . . . . . . 98
3.27 The expected invariant-mass shape for direct virtual photonpin Cu+Cu collisions at sN N = 200 GeV. The expected shapeis calculated using ⌘ 0 in the hadronic cocktail simulation. . . . 100
3.28 The e+ e pair mass distributions in Cu+Cu Minimum Bias
collisions for four transverse momentum regions. The data(closed circles), the fit function (red curve), hadronic contribution (blue curve), and the background BGSUM . . . . . . . . 102

LIST OF FIGURES

9

3.29 The e+ e pair mass distributions in Cu+Cu 0–40% collisions
for four transverse momentum regions. The data (closed circles), the fit function (red curve), hadronic contribution (bluecurve), and the background BGSUM . . . . . . . . . . . . . . . . 103
3.30 The e+ e pair mass distributions in Cu+Cu 40–94% collisions
for three transverse momentum regions. The data (closed circles), the fit function (red curve), hadronic contribution (bluecurve), and the background BGSUM . . . . . . . . . . . . . . . . 104
4.1

4.2

4.3

4.4

4.5
4.6

Direct photon fraction measured with the virtual photon method
as a function of transverse momentum in Cu+Cu collisions at
p
sN N = 200 GeV . . . . . . . . . . . . . . . . . . . . . . . . . 108
Direct photon fraction measured with the virtual photon methodpfor di↵erent collision systems in sN N = 200 GeV: (a) p+p
collisions, (b) d+Au collisions, (c) Cu+Cu collisions by thiswork, and (d) Au+Au collisions. Expectations from NLO
pQCD calculations are also shown by curves. . . . . . . . . . . 109
p
Decay photon spectra in Cu+Cu collisions at sN N = 200
GeV for minimum bias, 0–40%, and 40–94% centrality classes
calculated by the EXODUS simulation. . . . . . . . . . . . . . 111
Direct photon spectra in Cu+Cu collisions for (a) minimum
bias, (b) 0–40%, and (c) 40–94% centrality events. The Cu+Cu
minimum bias result is shown together with the TAA scaled
p+p spectra and its fit results. The central and peripheral results for Cu+Cu collisions are compared to the p+p parameterized function and the Npart scaled Au+Au peripheral results.
Furthermore, the inverse slopes of the exponential function fit
to the data give the e↵ective temperature. . . . . . . . . . . . 113
The e↵ective temperature as a function of Npart for Cu+Cup
and Au+Au collisions at sN N = 200 GeV . . . . . . . . . . . 114
Rapidity densities of the direct photon yield for pT > 1 GeV/c
as functions of Npart and dNch /d⌘ together with the Au+Au
results. The power-law functions are the fit results for the
Au+Au data. . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

LIST OF FIGURES
4.7

10

Rapidity densities of direct photons with pT > 1 GeV/c asa function of dNch /d⌘. The rapidity densities cover the wideprange of collision energies from sN N = 39 to 2760 GeV andthe collision nuclei of Au+Au, Pb+Pb, and Cu+Cu. The
rapidity density data are fitted by a power-law function withthe fixed ↵ = 1.25. . . . . . . . . . . . . . . . . . . . . . . . . 117

List of Tables
3.1
3.2
3.3
3.4

3.5

3.6
3.7

The summary of electron identification cuts used in this study 65
Signal and background contributions in low mass electron pairs. 75
The best-fit parameter values in A/ exp (B/pT ) for single-electronpelliptic flow in Cu+Cu collisions at sN N = 200 GeV . . . . . 78
Considered QCD processes in PYTHA simulation. g denotes
a gluon, fi,j,k are fermions with flavor i, j, and k, and f¯i,j,k are
the corresponding antiparticles. . . . . . . . . . . . . . . . . . 80
The parameters in the modified Hagedorn function for the ⇡ 0meson for 0–40%, 40–94%, and minimum bias centrality binspin Cu+Cu collisions at sN N = 200 GeV . . . . . . . . . . . . 83
Considered decay modes and their branching ratios in the
hadronic cocktail simulation by EXODUS . . . . . . . . . . . 94
Meson to ⇡ 0 ratios and their uncertainties . . . . . . . . . . . 94

4.1

Considered hadrons and their decay modes in the decay photon simulation by EXODUS. Branching ratios are from theParticle Data Group. . . . . . . . . . . . . . . . . . . . . . . . 110

A.1
A.2
A.3
A.4
A.5
A.6
A.7

Direct photon fraction in Cu+Cu minimum bias . . . . . . . . 122
Direct photon fraction in Cu+Cu 0–40% centrality . . . . . . 122
Direct photon fraction in Cu+Cu 40–94% centrality . . . . . . 123
Direct photon yield in Cu+Cu minimum bias . . . . . . . . . 123
Direct photon yield in Cu+Cu 0–40% centrality . . . . . . . . 123
Direct photon yield in Cu+Cu 40–94% centrality . . . . . . . 123
Direct photon rapidity density in Cu+Cu collisions . . . . . . 124

11

Chapter 1
Introduction
Quarks and gluons are the most fundamental particles, and they constitutehadrons. Gluons hold together quarks by the strong force. Quarks and gluons cannot be taken out by themselves, and the phenomenon is called quark
confinement. Relativistic heavy-ion physics aims to explore the nature of thecreated hot-and-dense matter where quarks and gluons are liberated from
confinement. The quark deconfined phase is called Quark-Gluon Plasma.
The early universe, a microsecond after the Big Bang, is considered to be
Quark-Gluon Plasma. Ultra-relativistic heavy-ion collisions are the only experiments reproducing the Quark-Gluon Plasma in the laboratory.

Figure 1.1: The schematic view of the hierarchy from atoms to quarks andgluons. Atoms are composed of neutrons, protons, and electrons. Quarks
and gluons constitute nucleons, such as protons and neutrons. [1]12CHAPTER 1. INTRODUCTION

13

In the first half of this chapter, we introduce relativistic heavy-ion collisions and Quark-Gluon Plasma with current experimental results related
to this thesis. In the last half of this chapter, we focus on explaining direct photons emitted from Quark-Gluon Plasma and describing our thesis
motivation.

1.1

Quark Gluon Plasma

Quark-gluon plasma is a new state of matter that appears in high-temperatureand high-density state [2]. Quarks and gluons are the most fundamental
particles constituting nuclear matters. In the low-temperature state, quarks
themselves are confined by the strong interaction mediated by gluons. Under extreme conditions, however, quarks and gluons are deconfined, and they
constitute a plasma state. Quarks and gluons are liberated from nucleonsin the plasma. In the early stage of the universe, immediately after the
big bang, the state was Quark-Gluon Plasma. The phase transition to thehadronic phase occurred 10 microseconds after the big bang as the temperature dropped.

Figure 1.2: Quark-Gluon Plasma appears in the hot-and-dense condition. In
the Quark-Gluon Plasma, quarks and gluons are liberated from the quark
confinement. [3]The dynamics of quarks and gluons is described by Quantum Chromodynamics (QCD), a theory of strong interactions. QCD exhibits an attribute

CHAPTER 1. INTRODUCTION

14of the asymptotic freedom that the coupling strength between quarks andgluons decreases with increasing energy and momentum scales. The strengthof the force is stronger over the long distance.
According to the asymptotic freedom property [4], under the extraordinarily high-temperature and high-density condition, quarks and gluons do
not constitute hadrons, yet, they are the component of the many-body system, which is called as Quark-Gluon Plasma. The new state is first proposedby Bjorken in 1982 [5].

Figure 11: The energy density normalized by T 4 as a function of the temperature on Nt = 6, 8

Figure
TheTheenergydensity as alimit
functionof the temperature calculated by
and 101.3:
lattices.
Stefan-Boltzmann
SB = 3pSB is indicated by an arrow.
the lattice QCD. The energy density rapidly changes around the temperature
T ' 160 MeV. [6]The phase transition was initially conjectured in the 1970s and studied
as a phenomenological model called the MIT bug model [7]. The model
describes the QCD phase transition using phenomenology, which explains
the di↵erent characteristics between the inside and outside the hadron. Thismodel is an instinctive picture, and then the model itself is not QCD and notaccurate. The phase transition temperature calculated from the boundary
condition by the model is Tc ' 130 MeV. This calculation is considered withthe three kinds of pions, and other hadron’s contribution is ignored.

CHAPTER 1. INTRODUCTION

15

The numerical QCD lattice calculation at finite temperature based on thefirst-principles calculation has confirmed the QCD phase transition. Figure
1.3 shows an energy density as a function of temperature calculated by alattice QCD [6]. This calculation considers u, d, and s quarks. The energy
density rapidly changes around the temperature T ' 160 MeV. This temperature is estimated phase transition temperature, Tc and the energy density
PHENIX/ Nuclear
Physicsstate
A 757and(2005)
184–283
increases about
tenCollaboration
times between
a hadronic
a QGP
state.

191

Fig. 2. Theoreticalof nuclear
matterfor two
as a The
functionof temperature
T andFigurephase
1.4: diagram
Theoretical
phase
diagramofmassless
nuclear quarks
matter.
black
lines
baryon chemical
potentialµ[12].
indicate the phase transition between di↵erent phases. The diagram shows

as a function of temperature T and baryon chemical potential µ. [8]which hadrons could retain their in vacuo properties under these conditions. Lattice calcuFigure 1.4
showstheoretical change
QCD phase
diagram[8], ofwhich
theoccurs overlations also indicate
that
this asignificant
in thebehavior
the showssystemstate of matter with the relationship between temperature and energy dena small range
in temperature (∼ 20 MeV), and suggest that the change of phase includes
sity. Although the lattice QCD calculations indicate the phase transition
the restorationof approximatechiralsymmetry
resultingfrom greatly
reducedtheor vanishing
to QGP
from the hadronicphase
and criticaltemperature
Tc . However,quark constituent
boundarymasses.
between the hadronic matter and the QGP matter is still unknown,
In the andlimittheofcharacteristic
massless noninteracting
eachbosonicexperimentally.
degree of freedom conof QGP is alsoparticles,
not yet fully
understood
π2 4tributes 30 T to the energy density; each fermionic degree of freedom contributes 78 thisvalue. The corresponding “Stefan–Boltzmann” limits of the energy density εSB for the caseof 2(3) active flavor quark–gluon plasma is then⎧$%
⎨ 2f · 2s · 2q · 3c 7 + 2s · 8c π 2 T 4 = 37 π 2 T 4 ,
(1)
8
30
30
εSB = $
⎩ 3 · 2 · 2 · 3 7 + 2 · 8 % π 2 T 4 = 47.5 π 2 T 4
(2)
f
s
q
c8
s
c 30
30
after summing over the appropriate flavor, spin, quark/antiquark and color factors forquarks and spin times color factors for gluons. The large numerical coefficients (37 andCHAPTER 1. INTRODUCTION

1.2

16

Relativistic heavy-ion collisions

Quark-Gluon Plasma appears in high temperature and low baryon density,
such as in the early Universe at the first 10 5 seconds after the Big Bang.
The only possible approach to create the QGP state in the laboratories isthe ultra-relativistic heavy-ion collision experiments. The experiments canreproduce the hot-and-dense condition by colliding the heavy nuclei, such ascoppers and golds.
The heavy-ion collision experiments can achieve the high-temperatureand high-density conditions by accelerating and colliding ions up to near
the speed of light. Many experiments have researched the QGP state andexplored its characteristics with the various collision systems and energies.
Researching the QGP state in Relativistic Heavy Ion Collider (RHIC)
at Brookhaven National Laboratory (BNL) began in the year 2000 with thep
Au+Au collisions at sN N = 130 GeV. In the next year, 2001, the full energypof sN N = 200 GeV in Au+Au collisions was archived. Extensive results ofexperimental observations in RHIC implies the formation of QGP [9, 10, 11,12]. In the Large Hadron Collider (LHC) at CERN, several experiments arealso researching the characteristic of QGP. The LHC has begun operatinginreach to a higher collision energy than RHIC,
p 2008, and the collider canps = 14 TeV for p+p and sN N = 5.5 TeV for Pb+Pb collisions.
Two major results would implicate the production of high-temperatureand high-density matter created in the heavy-ion collisions. High transversemomentum particle suppression is the first measurement that high transversemomentum particle productions are strongly suppressed compared to that of
p+p collisions [13]. The results imply that the particles produced in initial
hard scattering interact with the hot-and-dense matter and lose their energy.
The other significant result is the strong elliptic flow [14]. The produced
particle distribution in momentum space is not uniform but has azimuthal
anisotropy with respect to the reaction plane. The overlapping region of two
nuclei is a short ellipse in the direction of the reaction plane, and the insideof the region is high pressure. The generated particles follow the pressure
gradient and are in motion. Consequently, the geometry of the collisions isconverted into an anisotropy in momentum space. It was found that the viscosity of the produced matter is close to zero, the perfect-fluid, by comparing
to the relativistic hydrodynamic calculations [15].

CHAPTER 1. INTRODUCTION

1.3

17

Geometry of heavy ion collisions

The Glauber model quantifies the geometrical configuration of the collision.
The model is widely used in high-energy heavy-ion physics. It can express thecollisionas theimpact parameter b, the number of binary nucleonElliptic geometry
Flow: A Brief
Review
4
nucleon collisions Ncoll , the number of participating nucleons Npart and the
2. Event
Characterization
nuclearoverlapfunction TAB (b) [16].
Spectatorsb

Participants
before collision

after collision

Figure 2. Left: The two heavy-ions before collision with impact parameter b. Right:

Figure 1.5: ATheschematic
image of the heavy ion collision [17]. Left: Two
spectators continue unaffected, while in the participant zone particle production
nuclei collide with
the impact parameter b before the collision. Right: After
takes place.
the collision, the spectator nucleons pass away in the longitudinal direction,
while particles are produced in the participant zone.

Heavy-ions are extended objects and the system created in a head-on collision
is di↵erent from that in a peripheral collision. To study the properties of the
Two nuclei are accelerated to close to the speed of light by accelerator
created system, collisions are therefore categorized by their centrality. Theoretically
andthecollidein theultra-relativistic
apcentrality
is definedby the impactheavy-ion
parameter experiment.
b (see Fig. 2) These
which, nuclei
however,pear’pancake’
due
to
the
Lorentz
contraction
andcollidewithgeometricalcannot be directly observed. Experimentally, the collision centrality can be inferred
1/Nev dNev/dnch

overlap. The overlap is defined by the impact parameter b shown in Fig. 1.5.
102000(b) in the experiment. Besides,(a)
The parameterb is associated with centrality
Pb-Pb N
1800
Au-Au N
the interacting nucleons in the geometrical
overlap
regionarecalledpartic1600
10
Pb-Pb N
1400
ipants, and the nucleons outside the region
are called spectators, Au-Au
which
are
N
1200
una↵ected by the collisions. Ncoll is the total
numberofnucleon-nucleon
col1000
10
lisions in the participants, whereas Npart 800
is the total number of the nucleons
600
includedintheparticipants.
10400
The distribution of nucleons in a nucleus
can be described with the nuclear
200
0
density 0⇢A (r)
0
2
4
6
8
10
12
14
500 as 1000
1500
2000
2500
3000
Impact Parameter [fm]Multiplicity
Z
TA (s)= distribution
dz⇢A (z,s)Pb-Pb collisions at ps = 2.76 TeV(1.1)
Figure 3. a) Charged
particle
from
-2

bin

bin

-3

part

part

0 - 5%

5% - 10%

10% - 20%

20% - 30%

30% - 40%

40% - 50%-5

50% - 60%

-4NN

measured with ALICE, showing a classification in centrality percentiles (from [20]).
b) Number of participating nucleons Npart and binary collisions Nbin versus impactpparameter for Pb-Pb and Au-Au collisions at sNN = 2.76 and 0.2 TeV, respectively.

from the measured particle multiplicities, given the assumption that the multiplicity
is a monotonic function of b. The centrality is then characterized by the fraction,⇡b2 /⇡(2RA )2 , of the geometrical cross-section with RA the nuclear radius (see Fig. 3a).

CHAPTER 1. INTRODUCTION

18

where s is the coordinates in (x, y), which indicates the center of nucleus.
The nuclear overlap function of nucleus A and B can be expressed using theparameter b, TA and TB asZ
TAB (b) = d2 sTA (s) TB (s b) .
(1.2)
where d2 s = 2⇡sds is the two dimensional overlap area.
The number of binary nucleon-nucleon collisions Ncoll is described using
TAB asZ
inin
Ncoll (b) = d2 s Nb) = N(1.3)
N TA (b) TB (sN · TAB (b)inwhere N
N is the inelastic cross section of the nucleon-nucleon interaction.
The number of participating nucleons Npart isNpart =
+

1.4

Z

Z

d2 sTA (s) (1exp (N N TB (s

b)))
(1.4)

2

d TB (s

b) (1

exp (

N N TA (s))) .

Space time evolution

Figure 1.6 shows the schematic diagram of the space-time evolution in heavyion collisions. Relativistic heavy-ion collisions produce hot and dense matter.
The created matter develops while undergoing several phases from the initial
hard scattering to the final hadron emission. The time evolution of theheavy-ion collisions is as follows.
Pre equilibrium
Two accelerated heavy ions collide head-on and pass through each other,
causing nucleons to release kinetic energy in the overlapping region where
passed nuclei through. The collision occurs at z = 0 and time t = 0 along thelongitudinal axis in the center of mass frame. Initial hard scattering between
partons occurs, and the overlap region becomes high energy density. This
phase is named the pre-equilibrium phase, and perturbative QCD following
parton cascade can describe this phase. This phase becomes a local thermalequilibrium state shortly.

CHAPTER 1. INTRODUCTION

19

Figure 1.6: A schematic diagram of the space-time evolution in heavy-ion
collisions. Quark-Gluon Plasma is formed through a pre-equilibrium state
after the heavy-ion collision. Produced particles, including hadrons, photons,
and leptons, are detected after the freeze-out. [18]Quark-Gluon Plasma
The reaction area expands by the initial pressure in the collision. Quarks
and gluons continue to lead to multiple scattering; eventually, the system
would reach the local thermal equilibrium. The system reaches sufficienttemperature 300⇠600 MeV and energy density to form Quark-Gluon Plasma(QGP). The formation time is expected to be ⇠0.6 fm/c. The hydrodynamics
can describe this QGP phase.

CHAPTER 1. INTRODUCTION

20

Mixed phase and Hadronic gas
After the QGP formation, the system expands rapidly, and thereby the temperature drops down to the critical temperature Tc ⇡ 170 MeV. Once the
QGP matter reaches the Tc , the matter begins to hadronize in which quarks
and gluons are confined into hadrons. This phase is called the hadronic gas.
The hadronic matter expands with the collectivity, and the system temperature goes down.
The mixed phase exists if the transition has occurred in the first-orderphase transition in which thermodynamic variable discontinuously changes.
The perturbative QCD calculations suggest that the transition is cross-overthat the variables change continuously.
Freeze out
The system shifts to the freeze-out phase when the temperature reaches thefreeze-out point TF ⇡ 100 MeV. The type of particles is fixed because theinteracting particles’ mean free path is smaller than the system size. Finally,
the elastic collisions between hadrons cease, and the system reaches a thermal
freeze-out point, whereby the momentum of all particles are frozen.

1.5

Direct photons and thermal photons

Direct photons are the photon that they do not arise from hadron decays[19]. They are an essential probe to understand the characteristics of hot
and dense matter created in the ultra-relativistic nucleus-nucleus collisions.
Electromagnetic probes include direct photons, are rare probes in the heavye2
ion collisions because the coupling constant ↵ = 4⇡h̄c
in QED is smaller thangs2
the constant ↵s = 4⇡h̄c in QCD. Photons only interact with the electromagnetic force, while quarks and gluons interact with the strong force. Therefore,
photons can carry pure information about the phase where they are emitted[20]. Besides, photons are produced in the whole stages of the time evolution
in the heavy-ion collisions. Consequently, direct photons are a clean probe tounderstand the time-evolution of the created system in heavy-ion collisions.
Typical photon sources in heavy-ion collisions are shown in Fig. 1.7 [21].
Photons are generally classified into direct photons and decay photons. Decay photons are originated from electromagnetic decays of hadrons such as⇡0 !
. Direct photons arise from the initial hard scattering, thermal

5hundred MeV – few GeV pT range, and we will put the word in quotation marks whenever experimental
results are discussed.

CHAPTER 1. INTRODUCTION

21

Collisions

Decay

Direct0

Stable hadrons: π 0,η,K ,...

Prompt

ThermalOther
Fragm.
Jet-medium

QGP
Hard scatt.
Pre-equilib.

Hadron gas

Jet
Bremsstr.

HadronBremsstr.

Resonance
decay
FIG. 1.1.7:
Prevalentterminology,
referringto theof realcollisions.
photons in heavy
ion physics
FigureSourcesof direct
photonsinsources
heavy-ion
Producedphotons in the heavy-ion collisions are classified into two types: direct photons
and decay photons. [21]Other sources
includephotons
fragmentationin vacuum,
knownTheand measured
in pp [19, 31–
radiations
from
QGPfromandjethadrongas, andother wellsources.
initial hard34]. They should be distinguished from jet Bremsstrahlung which occurs while the parton is still traversing thescattering
producesandperturbative
QCD
modelsphotons
can [35, 36](QGP) medium
and losing
energyprompt
in it [19].photons,
Jet-mediumor thejet-photon
conversion,
jet-thermal
express
photons
areloss
emittedthefromparton andare a special
case ofit.theThermal
ultimate partonenergywhere aashighpT black-bodyquark collidesradiation
with a thermaltransfers the
all itsa photon photon
flying outmeasurementin the same direction(seeIV B).
hotmomentum
medium.toThermal
is direct
proof
toHadronensureBremsstrahlung
that
happeninginthehadrongas
isyet
anothersourceofphotons[37,
38]).
the created matter is above the phase transition temperature, and it also canthe thermal equilibrium time of the medium. Figure 1.8 shows a theoWordsaccessof caution.
There aremanyprediction
sources of direct
photons
that yield
are hard
impossible
disentangle
experimentally. This
reticalof direct
photonas aorfunctionof totransverse
momentum
p

in to
Au+Au
collisions at whensN N comparing= 200 GeV
Above
the 3 GeV/cregion,in the highoften leads
some misunderstanding
data[22].
to modelcalculations.
For instance,
the
major
sourceispQCD
photonsbyinitialhardscatteringofthecollisions.
pT region (above 4-5 GeV/c), dominated by hard scattering, experiments often publish results on isolated
photons evenin theA+A1 collisions[39], using
These
results arethen compared
Below
GeV/c region,
thewell-defined
dominantisolation
source criteria.
is thermal
photons
emittedto perturbative QCD (pQCD) calculations, but the comparison is only valid if the same isolation criteria arefrom the hadron gas. The QGP thermal radiation is most sensitive between
applied as in the data. In case of pp this is relatively straightforward but in A+A the underlying event has
1 < pTsimulated,< 3 GeV/c.
contributionof decay
is about 10 times
that(from theto be properly
too – Thea verynon-trivial task.
Also, photons
in A+A “jet-conversion”
photonsof ofdirectphotons. In
experiments,
photons
areadditional
measured
as an
integralphotons ininteractiona hard-scattered
fastthepartonwith the medium)
are ansourceof isolated
the experiment,
but seldom
includedincludingin theory calculations.
of all photon
sources,
direct and decay photons. Direct photons
Even thedirect and decay
decay photons
become problematic. Short-lived resonances,aredistinction
measuredbetween
by subtracting
photoncan
contributions.
like , , a1 are sources of decay photons [40], but rarely if ever are actually subtracted by the experimentsfrom the inclusive photon yields (not the least because the parent distributions are usually not or poorly
known. Typically only 0 and decays are considered and the effect of all other hadron decays included in
the systematic uncertainties). While raising this issue may sound somewhat pedantic, we should point out
that at some point for instance the a1 has been predicted to be a major source of photons [41].

B.

The fundamental processes to produce direct photons

In this section we review the fundamental sources that were believed for a long time to be the main sourcesof photons in relativistic heavy ion collisions. More “exotic” mechanisms will be described in the context of
the “direct photon puzzle” (see Sec. VI).

14
at LHC, due the significantly larger system sizes towards thermal freezeout.
All these features are readily implemented [44, 63] into the thermal fireball description employed for SPS energies
above. In addition, the primordial pQCD component changes its xt -scaling behavior [45] which is accounted for byreplacing the parametrization Eq. (16) by Eq. (17). For simplicity we here refrain from introducing a nuclear kT
broadening, which is expected to be much less pronounced (and/or compensatedby shadowing corrections) at colliderpenergies. First data on high-pt hadron production in d-Au collisions at s=200 GeV [64, 65, 66] indeed indicate only
1. INTRODUCTION
a comparativelyCHAPTER
small enhancementof around 20-30% over the spectra measured in p-p collisions.22
Our photon predictions for full RHIC energy are summarized in Fig. 12. The thermal component has been evaluated
10

1

10

0

10

−1

10

−2

10

−3

10

−4

10

−5

10

−6

<Nch>=800−2

q0 dNγ/d q [GeV ]1/2

Central Au+Au (s =200AGeV)3|y|<0.35

Hadron Gas
QGP (Ti=370MeV)
initial pQCD (pp)
sum

0

1

2

3

4

qt [GeV]FigureIntegrated
1.8: A photon
theoreticaldirectAu+Au
photonyield as a function
FIG. 12: (Color online)
emissionprediction
spectra fromofcentral
p collisions at RHIC. Short-dashed line: pQCD
photons from primordial
N-N
collisions;
dashed-dottedline:
thermal
QGP
radiation;
thermal hadron gasof transverse momentum in Au+Au collisions at sN N =long-dashed
200 GeV.line:
Eachemission; solid line: total direct photon yield.
photon source has a di↵erent dominant transverse-momentum region. [22]with a typical formation time, 0 = 1/3 fm/c, as used before in dilepton [63] and charmonium [58] applications (itis also consistent with hydrodynamic approaches that correctly reproduce the elliptic flow measurements which areparticularly sensitive to the early phases, see Ref. [67] for a recent review). One notes that the spectrum decomposes
into essentially 3Any
regimes:
at oflowhigh-energy
energies, q0 1
GeV, thestill thermal
hadrons,sources
photons
alsomajor
emit source
virtualarephotons
that thepho- whereas at highenergies, q0
3GeV, prompt pQCD photons dominate. The intermediate+region, 1q0 3 GeV, appears to be a
tons
intoforlow
invariant-masselectronpairs).
If virtual
promising window
to convert
be sensitive
thermalQGP radiation.
Thepairs
latter(ehase been
calculated
assuming chemicallyphotoninvariant-massthroughout.
m ⇤ is more
twice ofhowever,electronthat
mass
vir-phases are gluone , theequilibrated quarkand gluon-densities
It isthanconceivable,
them
early
QGP
convertsmuch
to anelectronThistheproduction
attributes
thereduced). In thisdominated, i.e. tualwith photon
quark fugacities
smallerthan pair.
one (evengluon fugacities
could becase, on the onehigher-order
hand, the photon
emissivities
atgiven
temperatureareseverely
suppressed.
On
the other hand, if
process of direct photon production.
most of the total entropyisproducedsufficiently
early,
smallerfugacities
imply
largertemperatures,
Figure 1.9 shows an example of the virtual photon production in gluon thus increasing
the photon yield. The interplay of these effects has been studied for dilepton production in Ref. [63], where it
Compton scattering. The Compton scattering occurs at the initial collision
has been found that the net effect consists of a slight hardening of the QGP emission spectrum with a pivot pointin heavy-ion
The bescattering
associateswithproducingof gluons in theirat M '3 GeV. For
photons thecollisions.
situation mighteven moreprocess
favorable
due to theparticipation
lowinvariant-masselectronpairsthroughtheinternal
conversion.
Another
production (e.g. g + q ! g , as opposed to leading-order q q̄ ! ee for dileptons).
0⇤
We finally turnto the of
LHC,
Fig. 13.photon
Accordingto our estimates,sourcethecf.virtualis Dalitz
decays (⇡assuming! +a formation! +timee+ eof)0.11 fm/c (translating into Ti '850
MeV forbydNthe
the formula
QGP window
ch /dy'3000),
described
Kroll-Wada[23]. extends significantly further in transverse momentum
than under RHIC conditions, cf. left panel of Fig. 13, although this feature is sensitive to: (i) the formation time (ii) a
The associated electron pair production can relate to photon production
possible chemical undersaturation of the QGP, (iii) nuclear effects on the initial pQCD yield. The transition from HG
to QGP dominated emission occurs again close to qt =1 GeV. In the right panel of Fig. 13 we illustrate the sensitivityof the thermal spectra with respect to the produced charged particle muliplicity within our schematic fireball evolution
model. For simplicity, we assumed the same formation time and expansion parameters for both Nch =3000 and 2000.
We then find that the total integrated photon yield (i.e., for transverse momenta above 50 MeV) scales as Nch with
'1.4 if the same thermal freezeout temperature Tf o '90 MeV is imposed. This value for is somewhat larger than
the 1.2 found in hydrodynamic caclulations of Ref. [68], but confirms the deviation from the naive quadratic behavior( =2). However, the latter is approached (and even exceeded) for the yield at higher transverse momenta; e.g., when
integrating over qt with a lower bound of 1 GeV (2 GeV), increases to ⇠1.9 (2.3).

1.6

Direct virtual photons

CHAPTER 1. INTRODUCTION

23

Figure 1.9: Feynman diagram of quark-gluon Compton scattering (qg !
g ⇤ ! e+ e q)with the formula written as
dN 2
2↵ 1
=
dmee
3⇡ mee

s

1

4m2e
m2ee

✓

2m2
1 + 2e
mee

◆

SdN

(1.5)

where ↵, me , mee are the fine-structure constant, the electron and the electronpair mass, respectively. S is a process dependent factor, including a form
factor and a phase-space. For virtual photons, the factor goes to 1 as mee !
0 or mee ⌧ pT . Equation 1.5 describes the relationship not only decays fromvirtual photons but also electron pairs from Dalitz decays. Therefore, theshape of invariant mass distributions is di↵erent between virtual photons andelectron pairs from Dalitz decays.

1.7

Related measurements

This section introduces dielectron and direct photon results measured in several collision systems and energies in RHIC at BNL and the LHC at CERN.
We primarily focus on the low transverse-momentum region in heavy-ion
collisions, which are directly related to the thesis. Dielectrons are produced
throughout the entire stages of the collision system time-evolution, as well
as direct photons. These electromagnetic probes have no color charge, andtherefore they can provide clean information to understand the time evolution of the created matter.

CHAPTER 1. INTRODUCTION

Dielectron measurement
dNee / dydm

1.7.1

24

πo,η Dalitz-decays
ρ,ω
Φ

DD

J/Ψ
Ψl
Drell-Yan

Low-

Intermediate-> 10 fm

0High-Mass Region> 1 fm1

2< 0.1 fm

3

4

5
2

mass [GeV/c ]Figure 1.10: Expected dielectron source in heavy-ion collisions [24]pairs or dielectrons
are anprobeofforinvariant
underigure 1.2: ExpectedElectron-positronsources for dilepton
production
as excellent
a function
mass in ultrar
standing the created matter’s time-evolution due to escaping from the matvistic heavy-ion collisions[16].
ter without final state interactions. Therefore, the dielectron spectra containthe whole time evolution and dynamics. The properties of low-mass vector mesons are a candidate for searching chiral symmetry restoration in thehigh-temperaturestate. Moreover,the so-called
direct photon
contribution
fromthe realized in a str
ansition is associatedwith deconfinement(the’Wilsonline’),
again
internal
conversionisalso
includedinthespectraatthelowinvariantmass
rst-order transition. Thus, for heavy quarks one might hope to become sensitive to feature
region.
econfinement. This seems
indeedthe case:
the confining
potential
heavy quarkon
Figure 1.10
showstoanbeexpecteddielectron
spectrum inheavy-ion within
colliates (J/ , ) willbe[24].
Debye-screened
to freelycolorthecharges
in a QGP leadingsions
The spectra can due
be classified
into moving
three regions:high-mass,intermediate-mass,and low-mass
regions. The high-mass
is located of, e.g., J/ mes
issolution of the boundstates [17].
As a consequence
the finalregion
abundance
above the J/ invariant mass. The dominant contribution in this region isand thus their contribution to the dilepton spectrum – is suppressed, signaling (the onset
the hard scattering on partons. Dielectrons are produced through the Drell-

he deconfinement transition. This very important topic will not be covered in the present rev
ee Refs. [18] for the recent exciting developments. Finally, the intermediate-mass region (IMmight allow insights into aspects of quark-hadron ’duality’. As is evident from the saturatio
he vacuum annihilation cross section e+ e ! hadrons by perturbative QCD above ⇠ 1.5 G
he essentially structureless thermal ’continuum’ up to the J/ can be equally well described
ther hadronic or quark-gluon degrees of freedom. However, as a QGP can only be formed
igher temperatures than a hadronic gas, the intermediate mass region might be suitable toJ/ ψ → ee
ψ ’ → ee
cc → ee (PYTHIA)
bb → ee (PYTHIA)

π0ee

DY → ee (PYTHIA)

ηee

sum

5

10-1

π0 → γ ee
η → γ ee|y| < 0.35

-2

30

25

min. bias Au+Au sNN = 200 GeV
DATA

10

peT > 0.2 GeV/c

J/ ψ → ee
ψ ’ → ee
cc → ee (PYTHIA)
sum
cc → ee (random correlation)
bb → ee (PYTHIA)
DY → ee (PYTHIA)

η’ → γ ee
ρ → eeω → ee & π0ee
φ → ee & ηee

10-3

10-4

10-5

10-6

10-7

3

3

3.5

4

3.5
4
mee (GeV/c2)

Data/Cocktail

5dN/dmee (c2/GeV) IN PHENIX ACCEPTANCE

CHAPTER 1. INTRODUCTION

10

0

0.5

1

1.5

2

2.5

3

3.5

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

1
10-1
4
4.5
mee (GeV/c2)+
FigureFIG.
1.11:26:Dielectron
spectrumin minimum
Au+Au
at(Color online)
Inclusive
mass bias
spectrumof ecollisions
e
p
+
pairs
in
the
PHENIX
acceptanceinminimum-bias
Au
+
Au
s
=200GeVmeasuredbythePHENIX
experiment[25]
NN
ass spectrum of e ecompared to expectations from the decays of light hadrons+ p collisions comparedand correlated+ decays of charm, bottom and Drell-Yan. The
light hadrons and cor-Yan process(qq̄ ! l l ) andcorrelatedsemi-leptonic
decays of heavy
contribution
expected
if thedynamic correlationof c quark
Drell-Yan. The contri-pairs, charm0
as wellJ/ andparticles.
The invariant
mass
range
c̄ is asremovedis shown
separately.
Statistical(bars)
andbetween
ently normalized based andand
J/
is
the
intermediate
region.
Thermalradiationdielectronssystematic (boxes) uncertainties are shown separately. The arisen
he bottom panel showsfrom thehot medium
arehadron
expected
to contributeto the region
by the theocontribution
fromdecaysis independently
normalized
own sources. The sysreticalbasedmodels.
The electron
pairs originatedfrom theon mesonmeasurementsin PHENIX.
Thesemi-leptonic
bottom paneldecay ofshown as boxes, whilecc̄ is ashows
dominant
backgroundintheintermediate-mass
region.
The
low-mass
the ratio of data to the cocktail of known sources.
The
n as band around 1.
regionsystematic
places underthe meson
invariantmass.
Dalitzdecaysof ⇡ 0 and
uncertainties
of thedata areshown
as boxes,
while⌘ mesons
contributes as⇢ andaround! also1.appear in
the uncertainty
on thethe dominant
cocktail issource,
shown andas bandthe region. In-medium decay of ⇢ meson arising from the hadronic phase issions. In this case weexpected to be another dominant source. The lifetime of the ⇢ meson, 1.3

n scaled to match thescale it by the mean
(as given in Table I).
n is washed out by
ion of c and c̄ quarks
m the heavy flavor
the angle randomly
fixed to the experi-tron distributions from charm show substantial medium
modifications [6]. Thus, it is hard to understand how the
dynamical correlation at production of the cc̄ remains unaffected by the medium. Case (ii) leads to a much softer
mass spectrum, as shown by the dotted curve in Fig. 26).
This would leave significant room for other contributions,e.g. thermal radiation.
We have integrated the yield in the mass region 1.2 toCHAPTER 1. INTRODUCTION

26

104
10

0<pT <5 GeV/c

3

102
10
1

p+p & Au+Au at sNN = 200 GeV
5
Au+Au min. bias × 10
3
Au+Au 0-10% × 10
Au+Au 10-20% × 10
Au+Au 20-40%
Au+Au 40-60% × 10-1
Au+Au 60-92% × 10-2
p+p × 10-3

Yield/Ncoll (10-8)

dN/dmee (c2/GeV) IN PHENIX ACCEPTANCE

fm/c, is much shorter than the expected lifetime of the hadronic phase, and⇢ couples to the ⇡⇡ channel strongly. Therefore, the shape and the yield canreflect on the medium modifications due to chiral symmetry restoration [26].
In addition, the quasi-real virtual photon contribution appears in the region
where the low transverse-momentum is much greater than its invariant mass.
Any source of real photons also emits virtual photons, which convert to low
mass dielectrons. The contribution arises from the initial hard scatteringsuch as Compton scattering and thermal radiation from the hot medium.

20
18
16

Au+Au

sNN =

Yield (1.2<mee<2.8

14
12
10

10-1
Au+Au MB

10-2

8

10-3

6

10-4

4

0-10%

2

10-5

0
0

10-6

50

100

10-20%

10-7
20-40%

10-8
10
10

-9

40-60%-10

10-11

60-92%

10-12

p+p

0

0.5

1

1.5

2

2.5

3

3.5 4 4.5mee (GeV/c2)

FIG. 28: (Color onlinin the mass range 1.2
Statistical and systema
Also shown are two banof the contribution fromthe bands reflects the
only.

Au+Au
/2) (10-6)

at

part

FigureFIG.
1.12:27: Dielectron
spectrumin p+pand
Au+Auof e e(Color online)
Invariantmass
spectrumpsN N pairs=200GeVmeasuredby the PHENIX
experiment[25]the model
inclusivein pT compared
to expectations
fromof hadron decays for p + p and for different Au + Au centrality classes. The charmed meson decay contribution based onpythia [77] is included in the sum of sources (solid blackline). The uncorrelated charm is shown with the dottedline. Statistical (bars) and systematic (boxes) uncertainties
are shown separately. The systematic uncertainty on the expected hadronic sources is not shown: it ranges from 10%
in the 0 region to 30% in the region of the vector mesons.
The uncertainty on the charm cross section, which dominates

Yield / (N+collisions

30

(a)
25

Yield (150<m
p+p
Au+Au

20

15

10

COCKT

CHAPTER 1. INTRODUCTION

27

Dielectron spectra have been measured in p+p and Au+Au collisionsp
at sN N = 200 GeV reported by the PHENIX experiment [25]. Figure
1.11 shows the inclusive dielectron invariant-mass spectrum in minimumbias Au+Au collisions. The inclusive spectrum is compared to expectations
from hadronic decays, heavy flavor, and Drell-Yan contributions, which areevaluated by the well-tuned simulations. The data and expectations arecompared as a ratio. An enhancement appears at the low invariant-mass
region. The enhancement factor, defined as the ratio between the measured
and the expected yields, is studied for di↵erent centralities. The enhancement
increases with centrality, and it is qualitatively consistent with the conjecturethat an in-medium enhancement arises from the scattering process of ⇡⇡ or q q̄annihilation. Figure 1.13 shows the measured spectra for six centrality bins
in Au+Au collisions, together with p+p results. The expectations from thehadron decay models represented by the solid and dashed lines are comparedto the measurements. The detailed study of the enhancement is reportedby the PHENIX experiment [27]. The excess yields calculated by the datasubtracted hadronic cocktail excluding vacuum ⇢ are consistent with the
expectations from the thermal radiation from the hadronic (⇢ broadening)
and QGP phases.
The STAR experiment measures the dielectron production in several colplision energies from sN N = 19.6 to 200 GeV [28, 29, 30]. The RHIC collider
provided several beam energies to study the phase diagram of the QCD matter, and the program is called the Beam Energy Scan. Figure 1.14 shows thepresults of the dielectron spectra with several collision energies from sN N =19.6 to 200 GeV [30]. The enhancement in the invariant mass region of the! and mesons are studied in several collision energies. The invariant mass
and width of vector mesons could be modified because of interactions withthe hot and dense matter. The STAR experiment studies the mass shapepand width of ! and in Au+Au collisions at sN N = 200 GeV [29]. The
mass shift from the measurement agrees with the PDG values within theuncertainties.
pDielectron invariant-mass spectra in Cu+Cu collisions at sN N = 200
GeV are reported as a preliminary result by the PHENIX experiment [31].
The spectra for 0–10% and 10–20% are shown in Fig. 1.15. The inclusive
spectra are compared to the expectations from hadronic cocktail, heavy flavor, and Drell-Yan contributions. The large enhancement in the mass above
the pion mass and below the omega mass is reported in the minimum bias
events.

CHAPTER 1. INTRODUCTION

28

Yield/Npart in PHENIX acceptancecays that domina
1 GeV/c2 , are defor pions and mT
Au+Au sNN=200 GeV
0.3<mee<0.76 GeV/c2
2butions from sem
dielectron excess
and bottom) me
mc@nlo genera
ρ broadening + QGP (Rapp)tions. Both gen
1
IMR. However, tdiffer from each
Precise measurem
entire phase spac0
A small enha
PHENIXLMR with respe
0
100
200
300
is distributed ov
Npart
5 GeV/c). It in
2.3±0.4(stat)±0.
FIG. Centrality
36. (Colordependece
online) Centrality
dependenceof the dielecFigure 1.13:of the dielectron
enhancementin 0.3 <p
2 defined as (datatronGeV/c
excess,) comparedmee < 0.76
in Au+Au collisionscocktail
at sN Nexcluding= 200 GeV.
The dielec- pythia is used t
to thethermalradiationfrom thecocktail
hadronic( broadening)andare bution. If insteadtron yields
after
subtracting
the hadronic
without⇢ broadening
tors are ⇠40% sm
QGPphasesfrommodel calculations(dashed line) [74].
comparedto themodel
calculations.
[27]
be 1.7±0.3(stat)±+pDielectron azimuthal anisotropy is measured in Au+Au collisions at sN N =ment of e e pa
PHENIX, in Au+
1.45[73],STAR
veryexperiment
similar to[32].
the Thescaling
thermalpho200 GeV
by theresultofofthe
dielectron
azimuthal2
is not confirmed
tonatyield[64,invariant69]. Within
uncertainties,
present
data
anisotropy
the lowmass region,mee < 1.1 theGeV/c, is consistentanalysis. In parti
consistent
with forthis⇡ 0scaling
as illustrated
in Fig.
36,
with theare
simulatedanisotropy, ⌘, !, and. The dielectron
anisotropy
2
at high mass
region,< mthe2.9 GeV/c ,dependence
is consistent withthe excess,estimated low pT (pT < 1 G
whichalso 1.1
showsof theee < centrality
anisotropycc̄ subtracting
contribution. the cocktail without theresults are consis
i.e. magnitude
the datafrom
afterSTAR Collabora
vacuum , together with the expected power-law scaling
two experiments.
1.7.2 (dashedDirectline).
photon spectra
In the IMR, t
Direct photons are also a clean probe in heavy-ion collisions because they
are color blind particles originating from the whole stage. Direct photons tions of the expe
VI. SUMMARYAND
CONCLUSIONS
carry pure information
about the propertyof createdmatter. Supposing the of heavy flavor m
hot-and-dense matter is created in the heavy-ion collisions, the matter would first scenario, theradiate thermal
photons.
photons
are assumed
that theypappear
PHENIX
hasThermal
measuredinvariantmass spectra,
T dis- in assuming that th+
the low tributionstransverse-momentum
regionbytheoreticalmodels.
Meanwhile,and the centrality dependence of the e e pairthe same in Au+Au
ption effects produ
production in Au+Au collisions at sN N = 200 GeV.
quarks with the
The use of the HBD provided additional electron identifiserved with respe
cation to the central arm detectors, additional hadron reamounts to 1.5 ±jection and increased rejection of the combinatorial backcollisions. In th
ground.
approach is adop
A new analysis procedure based on neural networks
tally decorrelated
has been developed that combines in an efficient way the
becomes 2.5 ± 0.
information from the HBD and the central arm detec×10−6

STAR

106

Au+Au 0-80%
pe >0.2 GeV/c
T|ηe|<1, |yee|<1

29

e+e-

Cocktail Sum

π0→γ ee

η→γ ee0

ω→ee & ω→π ee

Data/Cocktail

dN/dMee/Nevt (GeV/c2)-1

CHAPTER 1. INTRODUCTION

20
15

η’→γ ee

φ→ee & φ→ηee

J/ ψ→ee

cc→ee

DY→ee

10

200 GeV2

10

27 GeV× 2.5E5

19.6 GeV

5
0

39 GeV

10× 3E4

27 GeV

10−25
× 2.5E2

039 GeV×1

10

× 6E-3

5

62.4 GeV

62.4 GeV

10−6

0

1

2

3

0

2

Mee (GeV/c )00.

FigureFIG.
1.14:1. Dielectron
spectrain Au+Au
collisionsinvariant
with several
Backgroundsubtracted
dielectron
masscollision
FIG. 2.
The ratio oenergies
measured
by
the
STAR
experiment[30]
spectra within the STAR acceptance from sNN = 19.6, 27,
cocktail with the and39, 62.4, and 200 GeV 0 80% most-central Au+Au collisions.
and cocktail. The gray
Errorsbars produced
and openinboxes
represent
statistical
Model calculations by R
promptphotons
the initial
hardthescattering
areandthesysdominant
tematic
uncertainties
inthemeasurements.
The
black
solid
PHSD [14, 15] were sepa
contribution at the high transverse momentum region.
curves represent the hadronic cocktail with the gray bands
and compared to the rerepresenting the cocktail uncertainties. The curves underwith the curves.
Directphotonsathigh-transverse
momentumregionneath the sNN = 62.4 GeV hadronic cocktail curve and grayband
represent
components atregion
62.4 GeV.
For betDirect photons
at the thehighcocktailtransverse-momentum
are mainly
produced
presentation,
the measurements
cocktail measures
predictions
by theter
initialhard scattering.
The PHENIXandexperimentcentrality
we integrated the acce
are notoflisted
inphotonorder production
by energy but
have beenscaledatbypfacdependence
directin Au+Au
collisions
sN N = 200
5423spectra in the mass reg
10photons, 3 10are, 2.5
10 , 1,
6 10 thefor decay
resultsphotons
GeV tors[33]. 2.5
Directmeasured
byand
subtracting
ure 4 shows the integ
sNN = 200,
19.6, Accordingly,
27, 39, and 62.4
GeV, respectively.
from atthe inclusive
photons.
experiments
measure the inclusive

certainties from the measurements and the cocktail are
shown in the figure as the open and filled boxes, respectively. The 6% uncertainty from STAR’s acceptance correction and the uncertainty of dNch /dy are not shown in
the figure. Model calculations [13–15] in Fig. 3 include
contributions from broadening of the spectral function

dNch /dy from the 0 8p
at sN N = 27, 39, an
viously published resup
Au+Au collisions atdition, we compare topsN N = 17.3 GeV fopmeasurements at sN
systematic uncertaint

10-1

10-2

Total cocktail
Hadrons → ee (EXODUS)
cc → ee (PYTHIA)
bb → ee (PYTHIA)
Drell-Yan
Data

Cu+Cu 0-10%
sNN = 200 GeV|y| < 0.35
pe > 0.2 GeV
T

-3

10

10-2

Total cocktail
Hadrons → ee (EXODUS)
cc → ee (PYTHIA)
bb → ee (PYTHIA)
Drell-Yan
Data

Cu+Cu 10-20%
sNN = 200 GeV|y| < 0.35
pe > 0.2 GeV
T

-3

10

-5

10

10-5

-6

10

10-6

10-7

10-7
PHENIX Preliminary
-8

10-1

10-4

10-4

10 0

1/Nevt dN/dmee (C 2/GeV) in PHENIX ACCEPTANCE

1/Nevt dN/dmee (C 2/GeV) in PHENIX ACCEPTANCE

result are shown. The MB, 0 10% and 10 20% Au+Au spectra have an excess above the
cocktail in the region above the and below the masses. In the case of the MB, this excess
is remarkably large, a factor of 4.7 ± 0.4(stat) ± 1.5(sys) ± 0.9(model) above the expected
cocktail yield. The Au+Au excess is largest in the most central collisions and recedes as thecentrality decreases. The integrated yield increases faster than the square of the average number
2 ). This is seen in Figure 4 where the yield in theof participating nucleons in the collision (Npart
CHAPTER 1. INTRODUCTION
30
N
increases faster than linear in Npart .
mass region 0.15 to 0.75 GeV/c2 over part
2

0.5

1

1.5

2

2.5

3

3.5
4
mee (GeV/c2)

PHENIX Preliminary
-8

10 0

0.5

1

1.5

2

2.5

3

3.5
4
mee (GeV/c2)

p
FigureFigure5. The
6. Thedielectronspectra
mass spectra
spectraFigure 1.15:
Dielectronin Cu+Cu
collisions
atdielectronsN N = mass
200 GeVforin
in 0 10% Cu+Cu collisions overlaid with 10 20% Cu+Cu collisions overlaid with
0–10% (left) and 10–20% (right) centrality classes measured by the PHENIX
the cocktail. The yellow bars represent the the cocktail. The yellow bars represent theexperiment[31]
systematic
errors.
systematic errors.
photonspectra,whereastheMonte here,Carlosimulations
evaluate
decayof the
The
Cu+Cu
centrality
data, firstpublishedallowsus to gain insight
intothethe onset
0photonspectra
based
on
the
measured⇡and⌘spectra.
Thefollowing
excess. The Cu+Cu 0 10% data contains an excess in the low mass region, as shown in Figure
doubledefined:5. Theexcessratio
is notispresent
in the 10 20% data, in Figure 6, or in the more peripheral centrality
bins. This is consistent with the centrality trend seen in Figures 3 and 4. The Cu+Cu results( /⇡ 0about)Measured
provide valuable additional information
the emergenceof the enhancement. With these
MeasuredR=⇡. a function of centrality.
(1.6)
0
new results, theories should attempttodescribe
theenhancementas( /⇡ )
Background
Background0

denominatoris the ratio of background photon to ⇡ , while the numer3.1. The
Virtualphotonstheratioof themeasured⇡ 0 .pTSignificant
deviationsof theTheatorp+p is
and
MB
Au+Au
mass
spectra inphoton
differenttopair
slices are shownin Figures
7 and 8respectively.
In theabove
p+p case
theindicate
data matches
the photon
cocktail fairly
well,particularly
at low pT ;double ratio
unity
a direct
excess.
Figure1.16 showspthere exists an excess in all p slices with
there
is adouble
small excess
pT . In the
Au+AuatcaseTtheratioatinhigh
Au+Au
collisions
sN N = 200 GeV. A significant
the excess
largest portion
in
the
low
p
ranges.
This
leads
us
to
consider
that
the
Au+Au
excess has
T
is observed at high transverse-momentum.
two sources, one that dominates at high pT and another that dominates at low pT .
Direct photon spectra are calculated from the double ratio and measured
One such source is direct virtual photons that convert to dielectron pairs. Virtual photons
inclusiveby
spectraandit expressesasare produced
the same
processesthat generatereal photons. A direct photon component, or
thermal photon component, is described according to Equation 1 when the mass is much smaller
than the pT (m < 0.3 GeV/c2 andpT >= 1 1GeV/c)
R 1 measured .
(1.7)
direct
The calculated direct photon
spectra2for various
1 dN centralities are shown in Fig.
d2 N
ee
'
[34].
(1)
1.17. The vertical error bars
dmeewith
dpT the3 arrowmee dpTindicate the measurement consistent with zero yields. The solid curves in the figures express perturbative
The photonic component is modeled in EXODUS, filtered by the acceptance and smeared by
QCD predictions. The theoretical calculations can describe the measured
the detector resolution. This shape is shown in Figure 9. By looking at the ratio of the excess
dataespeciallyin thethemodeledhigh transverse-momentum
Meanwhile,above
the well,cocktail
divided bydirect photon shape, R, region.
we can compare
the massin the low transverse-momentum region, the total errors are too large to5compare with the pQCD predictions adequately.

tral)

PbSc (Central)

5 GeV/c

3 GeV/c

7.0%

9.8%

8.5 GeV/c
7.2%

12.0%

10.3%

12.5%

14.1%

10.5%

11.4%

0
0

minant sources of systematic eryields extracted independently
tromagnetic calorimeters. The
two pT values in central events
he combined 0 and inclusive
pproximate statistical and systhe most peripheral and most(γ / π )Measured / (γ / π )Background

CHAPTER 1. INTRODUCTION

6
5 0-10%4
32
1
0
6
5 20-30%
4
3
2
1
0
6
5 60-92%
4
3
2
1
0

4

31

10-20%

30-40%MinBias

19.8%

17.7%

18.4%

32.5%

2.1%

10.5%

2.4%

3.2%

3.2%

12.0%

9.1%

12.5%

13.7%

12.4%

10.8%
Figure 1.16: The double ratio of measured ( /⇡ 0 )Measured
invariant yield ratio
FIG. 1: Double ratio0 of measured ( / 0 )Measured invariant
16.8%
to the background/⇡ )Backgroundratio as0 a function of transverse
yield ratiodecay
to the( backgroundp decay ( / )Background ratio as
4.1%
momentumain
Au+Au
collisionsats=200for
GeV
Nfunction of pT for minimumNbias
andfivemeasured
centralitiesbyofthe real
13.4%
photon measuremnet
in the PHENIX
experiment[33]=
200 GeV (0-10%
is the most
Au+Au collisions
at s

0

18.4%

15.7%

14.1%

0.6%

12.6%

14.0%

35.4%

2.2%

13.1%

9.7%

11.2%

45.6 %

1.9%

10.3%

2

4

6

8 10 12 14 0
pT (GeV/c)

2

4

6

8 10 12 14
pT (GeV/c)

NN

11.3%

central). Statistical and total errors are indicated separately
and PbSc combinedon each data point by the vertical bar and shaded region, reThe direct
photonThe
yieldsin curvesthe high
region can bealCentralspectively.
solid
aretransverse
the ratio ofmomentum
pQCD predictions
described
bytheN
scalingfromp+pcollisions,whereasthehadrondescribedcoll
in the text to the background photon invariant yield yields
5 GeV/c
3 GeV/c
8.5 GeV/c0basedinonthe
theheavy-ion
measured collisions
yield for[34,eachcentrality
class. The can be
are suppressed
35].
The suppression
17.0%
13.9%
16.1%
shadedaroundthecurvesindicatethevariationof the
35.3%
1.8%
9.6%
measured by
the Rregion
variable
given
by
AA
pQCD calculation for scale changes from pT /2 to 2pT , plus
15.6%
11.5%
15.9%
3
3
the Ncoll uncertainty.
28.8%
0.6%
3.8%
E d NAAE d NAA

RAA =

dp3
dp3
=
.
3
d3 NppNcoll E dp3
TAA d dpN3pp
0

(1.8)

are based on the measured
and spectra [16] assumHere, the denominator and numerator denote the TAA scaled invariantyield
ing m -scaling for all other radiative decays ( ,Ks0 , ).
in p+p collisions Tand invariant yield in heavy-ion collisions, respectively.
The comparison is made as the ratio of measured (inclusive) / 0 and calculated background / 0 since thisnvariant mass peak, by
the photons
Directlow transverse
momentumhas theatadvantagethat many
uncertainties, such as them ionizing charged particles
energyscale,
canceltovaryingin theratio. from
Sincethe hot
At bethe low transverse-momentum
region,extent
thermalphotons), and by the correlation0
thespectra of the background calculations are taken
medium are expected the dominant source. Direct photon spectrum in relatum of electron and positron
to be the same as the measured spectra we haveimaging Cherenkov detector
eposit in the EMCal. From
/ 0 Measured
MeasuredR =⇡(1)
ed that the accuracy of the0( / )Background
Backgroundtter than 1.5%.
matic errors in the PbSc andand any significant deviation of the double ratio above
uncertainties in: (i) the yield
unity indicates a direct photon excess. In Fig. 1 an excess
rection, and (iii) the energy
is observed at high pT with a magnitude that increases
utions of these effects to thewith increasing centrality of the collision.
4%

102

200 GeV Au+Au Direct Photon<Ncoll> scaled NLO pQCD

-1

10
1
d2Nγ
2
2 π pT Nevt dpTdy (c/GeV)

32

10-4
10-7

MinBias x 10

3

0 -10% x 10

0

2

1.5

1

10-20% x 10-2

10-10

0.5
20-30% x 10-4

10-13

-6

30-40% x 1010-1640-50% x 10-1950-60% x 10

-8

0
0

50

-10

10

60-70% x 10-12

-22

10

70-80% x 10-14

10-25
0

RAA (pT > 6.0 GeV/c)

CHAPTER 1. INTRODUCTION

80-92% x 10-16

2

4

6

8 10 12 14 16 18

pT (GeV/c)
Figure 1.17: Direct photon spectra as a function of transverse momentum inp
FIG.
2: Direct
invariantyields byasthe
a PHENIX
functionexperiment.
of transAu+Au
collisions
at sN N =200GeV
measuredverse momentum
9 centrality
andminimumbias
The spectra
are obtained forfor nine
centrality selections
bins, and thesolid
curves denote
Au+Au
collisions
at
=
200
GeV.
The
verticalerrorsthe pQCD predictions. [33]NNbar on each point indicates the total error. Arrows indicate
measurements consistent with zero yield with the tail of thetivistic heavy-ion collisions was first measured in the WA98 collaboration atarrow
indicating
confidence
levelyield
upper
limit. The
the SPS
colliderin CERNthe[36,90%37]. The
direct photon
measurementin
solid
curvesare
pQCD
predictions
described
in
the
text.
the central Pb+Pb collisions was interpreted either as thermal photons fromextracted as Direct = (1 R 1 ) · Measured are shown in
Fig. 2 for all nine centrality selections as well as minimum bias, and compared to the same NLO calculations.
The binary collision scaled predictions are seen to provide
a good description of the measured direct photon spec-

FIG. 3: Ratio
number of bingiven by Nparcles) yields int
yield is taken
text. The err
error on Ncolcertainty of th
at the right.

each integrat
yields are tak
above. As no
is observed to
diction for all
the centrality
shown by op
yield [13] is u
The observ
yields and N
observations
17.3 GeV [14the hNcoll i-sc

CHAPTER 1. INTRODUCTION33

QGP or multiple soft scatterings without QGP formation [38]. The PHENIX
experiment at RHIC has successfully measured low transverse-momentumpdirect-photons in p+p, d+Au, and Au+Au collisions at sN N = 200 GeV[25, 39, 40]. Thermal photons are observed in Au+Au collisions, whereas the
p+p and d+Au results are consistent with the pQCD calculations. As mentioned above, the signal-to-background ratio in real photon measurements
worsens at the low transverse-momentum region due to the vast number ofbackgrounds and detector resolution degradation. Therefore, the measurements have done by the virtual photon method. The method uses the internalconversion that the virtual photons convert to electron pairs. The method
improves the signal-to-background ratio by a factor of about 5 to avoid ⇡ 0meson contribution.
The first measurement of thermal photons is reported in Au+Au collisionsp
at sN N = 200 GeV by the PHENIX experiment [39]. The direct photon
spectra for three centrality bins are shown in Fig. 1.18. The Au+Au resultswith three centralities are presented together with the p+p results. The
theoretical prediction from pQCD calculations describes the p+p results well,while an excess over the prediction is observed in Au+Au collisions. The
direct photo excess yields in Au+Au collisions are implied by the thermalradiation from the QGP matter. The e↵ective temperature is obtained fromthe fit by an exponential function to the yields, and T = 233 MeV/c for theminimum bias collisions. The STAR experiment also measure direct photonsp
via the virtual photon in Au+Au collisions at sN N = 200 GeV with thetransverse momentum ranges 1 < pT < 3 GeV/c and 5 < pT < 10 GeV/c[41].
p
It is remarkable that the direct photons at sN N = 200 GeV are only
measured in p+p, d+Au and Au+Au, yet to be measured in Cu+Cu collisions. Consequently, it is worth measuring the direct photons in Cu+Cu
collisions to compare the other collision system at the same collision energy
to study the collision system-size dependence.

1.7.3

Centrality dependency of direct photons

Low transverse-momentum direct photons are also measured by the external conversion method. The method improves the real photon measurement,
and it uses the conversion electron pairs originated in the interaction between real photons and detector materials. The direct photon measurement
via the external conversion extends to the lower side of the transverse mo-

5

2

2.5

3

3.5

4

4.5
p (GeV/c)

AuAu Min. Bias x104
3

10of the direct photon comor bars and the error band
atic uncertainties, respecO pQCD calculation (seeAuAu 0-20% x102

102

AuAu 20-40% x10p+p10

Turbide et al. PRC69

1
10-1

10-2

3

T

34

104

3

3

+Au (Min. Bias)

Ed3N/dp (GeV-2c3) or Ed σ/dp (mb GeV-2c3)

CHAPTER 1. INTRODUCTION

-3

10

10-4
10-5
-6

10

10-7 1

2

3

4

5

6

7

p (GeV/c)
uncertainties, and theTe distorted spectrum totainties in r. The sysFigure 1.18:
photonspectrameasuredby the (pinternalconversion
FIG. Direct
4: (color
online)Invariantcross section
p + p) and inmethod andthe yield
real photons
in Au+Au
at a functionsN N =200
revariation of mlow is alsovariant(Au + Au)of directcollisions
photons asof pGeVT.
portedby
the
PHENIX
experiment[39]
inty is the particle comThe filled points are from this analysis and open points are0, namely the / ratio
from [19, 20]. The three curves on the p + p data represent
calculations,
thethedashedcurvesshow awith
modipT for p + p (Au + Au)
mentum NLO
range.pQCD
It is also
successfulandthat
methodmeasuresa widefied
power-law
fit
to
the
p+p
data,
scaledbyT.
ThedashedAAs [17]. This corresponds
range of centrality compared to the virtual photon method. Therefore, thecurvesare exponentialplus
the TAAp + p fit.
in the p + p (Au + Au)
detailed (black)production
mechanismsof direct
photons
canscaled
be provided
by theThe
dotted
(red)
curve
near
the
0–20%
centrality
data
is a
2
measurements.
GeV/c . Other sources
theory calculation [7].
The external conversion method is performed in Au+Au collisions at
inty in the data to cockpsN N = 200 GeV, and the results of the thermal photon spectra are shown in
Fig. 1.19. The thermal photon spectra are calculated from the direct photon
f the direct photon comthissubtracting
mass range
process
unity
spectra bythethescaledp+p dependent
results. Thefactor
slopesS ofis the
spectraomponent fit in (a) pindicate+pwithinafew
percentforanyphotonsource.
the estimated e↵ective temperature of the created matter. The. The curves represent
Figure 4 comparesthe direct
photonwith pree↵ective temperatures
are calculated
from thefit by spectra
an exponentialfunction

leading-order perturbaation [18]. For p + p,
O(pT )/d incl (pT ), wherecross section from theincl(pT ) is the inclusive
Au, the curves represent
ere TAA is the Glauberincl

viously measured direct photon data from [19, 20] andNLO pQCD calculations [18]. The systematic uncertainty of the inclusive photon (14% from the uncertainty
in the e+ e pair acceptance correction[12]) is added inquadrature with the systematic uncertainties of these
data. The p + p data are shown as an invariant crossinel
section using d = ppdN .
In this analysis we have converted the yield of excess

n pT spectra in cen–60% and 60%–92%.
dths in this analysis.
dified power-law fit toation below 1 GeV/c,upper limits, other

1
d2 N
2
2p pT dpT dy [(GeV/c) ]smaller inverse slope than the Ncoll scaled p+p contribution.
Figure 8 shows that we observe similar behavior wheninvestigating the centrality dependence in more detail.
The solid curves are again the p+p fit scaled by the respective number of binary collisions, and they deviate
CHAPTER 1. INTRODUCTION
significantly from the measured yields below 3 GeV/c.

101
100

(a)
±25(stat)239±7(syst) MeV/c35(b)±33(stat)261±8(syst) MeV/c

10 1
10 2
10 3
10 4
10 5 0-20%
101
100
10

(c)
±28(stat)226±6(syst) MeV/c

1

20-40%(d)±50(stat)242±6(syst) MeV/c
Au+Au
psNN = 200 GeV

10 2
10 3
10 4
10 5 40-60%

60-92%

0 1 2 3 4
1 2 3 4 5
ully corrected mea7] via the relation
pT [GeV/c]much larger systemsion probability, theFigureFIG.
1.19:9.Thermal
photonthe externalconversion(Colorp
online)spectra
DirectbyphotonpT spectra
after method
sub- indo not cancel.
Au+Au
collisions
at NcollsN Nscaled
= 200
GeV,
together withthe exponential
tractionof thep+pcontribution
in centrality
bins fit
results.
[42]
0%–20%, 20%–40%, 40%–60% and 60%–92%. Uncertainties
pT spectra for minare plotted as in Fig. 8. Dashed lines are fits to an exponential
ished Au+Au data
functionin the0.62.0GeV/c< pandT < 2.0 GeV/c.
are the p+p photonwith the
fit range
0.6 range< pT <
GeV/c,
they are approximately 240
points (open circles)MeV/c independents of centrality. Figure 1.20 shows the integrated thermal
Finally
directof photon
contribution
frompromptas athefunction
the numberof participants
Npartfor di↵erent
ement [2], while thephoton yields
processes (as estimated by the Ncoll scaled p+p directe from the analysis
photon yield, shown by the curve in Fig. 8) is subtracted
a sets, respectively.
to isolate the radiation unique to heavy ion collisions.
the p+p data with
The results are depicted in Fig. 9. While the origin ofs shape was used inthis additional radiation cannot be directly establishedfit [36], we find pa(it could be for instance thermal and/or initial state ra= 2.26 ± 0.78 anddiation, or the dominant source could even be pT depenematic uncertainties
dent), it is customary to fit this region with an exponen-

with the number ofwell for charged pa
60%–92%
12.1 ± 3.1
12.5 ± 2.6
25.8 ± 4.0
238 ± 50 ± 6
calculated with a G
0%–92% 251.1 ± 26.7 106.3 ± 5.0
268.8 ± 8.2
242 ± 28 ± 7
lar to Npart by pickquarks within the nscribed by scaling w
of centrality, see Table II. In contrast, the yield clearlyconsistent with a po
CHAPTER
1. INTRODUCTION
increases
with centrality. We have quantified this by in- 36
the number of quar
tegrating the photon yield above a threshold pmin
T . Wean exponent of =thethresholdfrom 0.4integration.
to 1.4 GeV/cshow
that oflimitsvariedof lowertransverse
momentum
The toNpartdependence
In most theoretic↵
the centrality
dependence
does notresultfrom functiona change
the integrated
yields havethe same powerin thepower-law
ANpart,involves binary coland theaverageat
power↵=
1.3810).
± 0.03(stat) ± 0.07(syst).
of shape
low resultspT (seeFig.
hadrons, in hot andrate from a unit vosquare of the numb101
ticle production sho
stituents [23, 40]. B
0imately proportiona
10
photon emission to
the increasing react1
creasing volume will
10
pT > 0.4 GeV/cthat one expects 1 <pT > 0.6 GeV/cjust as observed.
pT > 0.8 GeV/c
2
Recent theoretica
10
pT > 1.0 GeV/c
confirm our finding t
pT > 1.2 GeV/csion increases appropT > 1.4 GeV/c3
of Npart . In the P
10
1
2
10
10
is approximately
Npart
the shape of the spe
our data. A hydroFigure1.20:10.
Integrated
thermal Integrated
photon yields
for di↵erent lower transverse-law increase of the
FIG.
(Color online)
p thermal photon yields as
momentumlimit ofin N
Au+Au
collisions
at lowersN N p=T 200
GeV [42] limits.
from 1.67 to 1.9, ina function
different
integration
part forThe dashed lines are independent fits to a power-law.
integration threshol
Photon production
1.7.4 Collisions energy dependence of direct photons to scale with Npart w
duction mechanisms
DirectTABLE
photonsIII.
haveFitted
also beenmeasuredfrom
in lower
collisionenergies
parameters
fitting
power-lawfitsin thehave distinctly differ
ee
RHICdN
colliderandhigher collision energies in the LHC. RHIC provides
the= ANpart for integrated yields with different lower pT
dyfrom enhanced ther
exploration
limits. of the QCD phase diagram with Beam Energy Scan (BES) in
2010 and 2011 as BES phase-1 [43]. The PHENIX experiment collectedmagnetic field is expppmin
T collision data at
the Au+Au
sN N = 39 and 62.4 GeV and reported directthe strength of the fi
photon (GeV/c)
production [44]. Besides, the LHC collider canAprovide higher collisionparameter [19]. Thenergies thanbecauseit ±hasa larger
circumference,about1030 3km. Theincrease more slowl
0.4 RHIC
1.36± 0.080.08(7.85± 2.96 ± 4.52)
ALICE experiment at the LHC reported the direct photon measurement
incesses, but a quantip ± 0.14 ± 0.12 (2.20 ± 1.54 ± 1.64) 10 3
0.6
1.41
82.6 ± 9.3

56.0 ± 5.3

126.6 ± 6.1

225 ± 28 ± 6

dN
dy

40%–60%Pb+Pb collisions at sN N = 2.76 TeV [45].
0.81.42 ± 0.07 ± 0.11 (1.07 ± 0.39 ± 0.75)
1.0
1.35 ± 0.06 ± 0.07 (7.70 ± 2.32 ± 4.37)
1.2
1.36 ± 0.09 ± 0.07 (3.90 ± 1.79 ± 2.81)
1.4
1.40 ± 0.06 ± 0.10 (1.63 ± 0.47 ± 1.11)

10 3
10 4
10 4
10 4

The yield increases with a power-law function Npart ;

V.

SUMMA

We have isolated
yield emitted in Au
spectra does not deALICE Collaboration
37

Pb-Pb sNN = 2.76 TeV A exp(-p / T eff)
T
0-20% ALICE
0-20%
20-40% ALICE
20-40%
40-80% ALICE

T

102

T

d2N γ

dir
1
(GeV-2c 2)
2π N ev. p dp dy

Direct photon production in Pb-Pb
CHAPTER 1. INTRODUCTION

10

1
x 102

10−1
x 101
10−2

10−3

10−4

10−5
0.5

Paquet et al.
arXiv:1509.06738
Linnyk et al.
arXiv:1504.05699
v. Hees et al.
NPA 933(2015) 256
1

1.5

2

x 100
Chatterjee et al.
PRC 85(2012) 064910+ JHEP 1305(2013) 030
2.5

3

3.5

4

p (GeV/c )T

Fig. 6: (Color online) Comparison of model calculations from Refs. [59–62] withp the direct photon spectra inp
Figureat1.21:
photonspectraPb+Pb
at thes20–40%
N N = 2.76TeVsNN Direct= 2.76 TeV
for the
0–20%in(scaledby acollisions
factor 100),(scaled by a factor
Pb–Pb collisions
measured
by
the
ALICE
experiment
[45].
The
spectraforthreecentrality
10) and 40–80% centrality classes. All models include a contribution from pQCD photons. For the 0–20% andclasses,
togetherwith several
theoreticalare shown in the figure.
20–40% classes
the fitwith an exponentialfunctionis shownmodels,in addition.

p
QCD. All models
includecontribution
from
pQCD
photons,
different parameterizationsareFigure1.21theshows
the direct
photonspectrain however,
Pb+Pb collisions
at sN N =used. The2.76
model
of vanHees
et al. [60]based on in
idealhydrodynamics
with initial
flow (prior
TeV.
The
spectraare ismeasuredthreecentrality bins,
and they
are to thermalization)[65]. Theto
photonproduction
ratesmodels
in the hadronic
phasecalculations
are based on witha massive
Yang-Mills
compared
severaltheoreticalfrom pQCD
di↵eramesons,along
withadditional
production
channels
descriptionentof parameterizations.
gas of π , K, ρ , K , andThe1 inverse slope of the exponential function gives(including
anti-/baryons)evaluated temperature,with the in-mediumρ spectral[19].
fromandπ –π and K–
the e↵ective
and theresultsfunction
are T =
297Bremsstrahlung
MeV for 0–20%
K̄ is also included [66], in the calculation shown here together with π –ρ –ω channels recently describedin Ref. [67]. The space-time evolution starts at τ0 = 0.2 fm/c with temperatures T0 = 682, 641, 461 MeV
for the 0–20%, 20–40%, and 40–80% classes, respectively, at the center of the fireball. The calculation
by Chatterjee et al. [61, 68] is based on an event-by-event (2+1D) longitudinally boost invariant idealhydrodynamic model with fluctuating initial conditions. An earlier prediction with smooth initial conditions was presented in Ref. [69]. Hadron gas rates are taken from the massive Yang-Mills approachof Ref. [19]. Bremsstrahlung from hadron scattering is not included. The hydrodynamic evolution in
the model of Chatterjee et al. starts at τ0 = 0.14 fm/c with an average temperature at the center of thefireball of T0 ⇡ 740 MeV for the 0–20% class and T0 ⇡ 680 MeV for the 20–40% class. The calculation

ntegrated yields
ollow the sameby the pQCD
consistent withher yield than at

10− 1
10− 2

A+A/p+p → γ dir + X
Pb+Pb, sNN = 2760 GeV
Au+Au, sNN = 200 GeV
p+p, s = 200 GeV
p+p, s = 62.4 GeV

PHENIXpsN N = 200 GeV.
α = 1.25

10− 3
10− 4

T

yields for the
cale as ð7.140%
nd the same
1.680Þ × 10−4 ×
compared to thebtained from thehe corresponding
point. The width
tainties on the fit
A trend but lower
wn arepthe
ﬃﬃﬃ scaled
for s ¼ 62.4,
d independent of

LHC reaches higher than the RHIC collision energy ofdNγ /dy (5.0 < p < 14.0 GeV/c)

ntegrating the inT ¼ 5.0 GeV=c.
be dominated bylisions, while themore sensitive tos. The results are=dη. Also plotted
h fixed α ¼ 1.25

significant considering the 25% systematic uncertainty on
the calculation.
While the functional form AðdN ch =dηÞα describes theintegrated direct photon yields well, it is not unique. For
instance, the data can be equally well fitted byAðdN ch =dηÞþ BðdN ch =dηÞ4=3 [58]. For the data in 38
CHAPTER
1. INTRODUCTION
Fig. 3, this fit results in parameters A ¼ ð8.68 % 3.06Þ ×−4
B ¼ ð3.09% 0.45Þ
10−4 . temperature
The important
pointinisthe
41010
MeVandfor 20–40%
centrality.
The×e↵ectivemeasured10− 5Ncoll scaled prompt photons−6

p+p fit, s = 200 GeV
pQCD, s = 2760 GeV
pQCD, s = 200 GeV
pQCD, s = 62.4 GeV

10

10− 7
10

dNch/dη

102

103

η≈0

Figureyields(pT (p> T5 >
GeV/c)
in severalvscolFIG.1.22:
4. Integrated
Integrateddirect
directphoton
photonyield
5.0 GeV=c)lisionsystemtogetherwith
pQCD
calculations[44]
dN =dη, for different data sets. The dashed lines show powerchlawfits to the data with fixed slope of α ¼ 1.25. Integrated yields
The integrated yields of direct photons are measured in several collisionfrom [44].
pQCDscaledby N coll by
arethealso
shown.
systems
Thecalculations
integrated yieldis calculated
integralof the direct

photon spectrum. Figure 1.22 shows the integrated yield as a function ofdNch /d⌘ in p+p, Au+Au, and Pb+Pb collisions. The yield dN /dy has a022301-7
scaling described as proportional to (dNch /d⌘)↵ with ↵ ⇡ 1.25. The integrated yields for several collision systems are compared to the expectationfrom pQCD calculations. The same scaling can describe the integrated yields
for given collision energy, but an additional multiplicative factor is needed
to explain the collision energy dependence.

CHAPTER 1. INTRODUCTION

1.7.5

39

Direct-photon collective flow

The elliptic flow of charged hadrons was first observed in Au+Au collisionsp
at sN N =130 GeV at the STAR experiment [14]. The elliptic flow is anasymmetry of the azimuthal distribution with respect to the reaction plane.
The azimuthal anisotropy is supposed to be zero in the simple nucleus-nucleus
collisions. However, the strong azimuthal anisotropy has been measured byexperiments [15, 46, 47, 48]. Therefore, strong anisotropy is meant to be
produced by particle interaction and space-time evolution. In the non-central
collisions, the participant’s shape is elliptical, and thus the shape leads toa pressure gradient. The particles inside the created matter move following
the pressure gradient, and the matter expand over time. Relativistic viscoushydrodynamic calculations can describe the elliptic flow well [49, 50, 51].
The hydrodynamical calculations can describe the experimental results well.
Comparing the experimental and theoretical results that the created medium
behaves like a nearly perfect liquid [52]. The theoretical calculations suggest
13
that the medium has early local thermalization [53].

v2

0.3

0.2

(a) 0-20%
Direct photon vn
Conversion method
Calorimeter method23(c) 40-60%
0.3

0.2

0.2

0.1

0.1

0.1

1
0.15 0(d) 0-20%(b) 20-40%
PHENIX 2007 and 2010
Au+Au 200 GeV

0.3

4 0.15 0
1(e) 20-40%

2

3

4 0.15 0
1(f) 40-60%

0.1

0.1

0.05

0.05

0.05

3

4

2

3

4

v3

0.1

2

0

0

0

1

2

3

4

0

0

1

2

3

4

0

1

p (GeV/c)T

FIG. 6. Direct photon v2 and v3 at midrapidity (| | < 0.35), for different centralities, measured with the conversion method(solid circles, green) and calorimeter method (solid squares, black).
2 The event plane was determined3with the reaction plane
detector (1 < | | < 2.8). The error bars (boxes) around the data points are statistical (systematic) uncertainties.

E d N3 (GeV -2)
dp

E d N3 (GeV -2)
dp

Figure 1.23: Direct photon elliptic flow v and triangular flow v in Au+Au
pcollisions at sN N = 200 GeV measured by the PHENIX experiment [54]yield(a) Invariant yield(b) v(b) v for diThe(a) Invariant
PHENIX
experimentreports the large
azimuthal anisotropy
10
0.2
0.2
p
rect1 photons in Au+Au
collisions at sN N =200 GeV [54, 55].
The mag0.15
0.15
1
2

Primordial 1
Primordial 2

0.1

10-1

0

10-3

Data
Solid line

10-5
4
3
2
1

Au+Au 20-40%
sNN=200GeVYield is from PRC 91, 064904

0

0.15
0.1
0.05

QGP w/o viscous
QGP w/ viscoussemi-QGP
w/o viscous(All three include HG)1(c) v3

2

Calorimeter
Conversion

3
4
PHENIX

0.1
0.05

10-2

0.2

10-4

10-1

0.05

10-2

2

PRL114, 072301
and priv. comm.

3

NPA933, 256
and priv. comm.

0

10-3

0

0.2

10-4
10-5
Data
Solid line

3

10

4
3
2
1

Au+Au 20-40%
sNN=200GeVYield is from PRC 91, 064904

0.15
0.1
0.05

1
(c) v3

2

Calorimeter
Conversion

3
4
PHENIXCHAPTER 1. INTRODUCTION

40

nitude of the elliptic flow for direct photons is comparable to one observedfor hadrons [56]. Figure 1.23 represents the results for the second and thirdorder Fourier components for several centralities in Au+Au collisions. Bothmeasured Fourier components of direct photons are found to be of a large
magnitude. The second-order Fourier coefficient has a centrality dependence,
while the third-order Fourier coefficient has no centrality dependence. The
ALICE experiment also reports the elliptic flow of inclusive and direct photonpin Pb+Pb collisions at sN N = 2760 GeV [57]. The experiment measures the
direct photon flow via the external conversion method, and the magnitude ofthe direct photon elliptic flow shows a similar to the PHENIX measurement.

1.7.6

Direct photon puzzle

Low transverse-momentum direct photons are expected to contain the thermal photons as a dominant contribution. The spectrum and yield of thedirect photons are sensitive to the temperature. The slope of the spectrum
is proportional to Te↵ , and the yield is proportional to T 3 . The azimuthal
anisotropy has a sensitivity to the space-time evolution with collective motion. Therefore, direct photon measurements help us to understand the characteristics of the created matter and its evolution.
Figure 1.24 shows the results on the direct photon measurement of thepyield and azimuthal anisotropy in Au+Au collisions at sN N = 200 GeV[54]. The direct photon spectrum measures the large yield of direct photons
in the low transverse-momentum region. The result suggests that low momentum direct photons are emitted from the early stage, where the systemtemperature is high. The direst photon azimuthal anisotropy measures alarge magnitude of v2 comparable to hadron v2 . The v2 result implies that
low momentum direct photons are produced in the late stage, where thesystem collectivity is sufficiently built up.
Both experimental results are compared to several theoretical models simultaneously. The comparison shows a large deviation between the data andmodels in either the yield or anisotropies. Low momentum direct photons
are thought to be dominantly contributed from thermal photons radiated by
Quark-Gluon Plasma. However, theoretical models struggle to explain the
direct photon production at the same time. This problem is called the direct
photon puzzle.

p (GeV/c)T

E d N3 (GeV -2)
dp

rapidity (| | < 0.35), for different centralities, measured with the conversion methodhod (solid squares, black). The event plane was determined with the reaction planeboxes) around the data points are statistical (systematic) uncertainties.
CHAPTER 1. INTRODUCTION
41

) v2

3

10

(a) Invariant yield
PRL114, 072301
and priv. comm.

1

QGP w/o viscous
QGP w/ viscoussemi-QGP
w/o viscous(All three include HG)

10-1

2

3
4
PHENIX

0.1

0

10-3

0

0.2
-4

alorimeter
onversion

10

-5

Data
Solid line

10

1

0.15

0.05

10-2

1
) v3

(b) v2

0.2

2

3

4

p (GeV/c)

4
3
2
1
0

Au+Au 20-40%
sNN=200GeV

3
4
PHENIX

0.1
0.05

0

1

2

3

4

0

p (GeV/c)T

2

Calorimeter
Conversion

0.15

Yield is from PRC 91, 064904

1(c) v3

T

0

1

2

3

4

p (GeV/c)T

1.24:
photon spectrum
and azimuthal
anisotropiesof the secields [3] and v2 with Figure
FIG.
8. Direct
Comparisonof the direct
photon yields
p and v2 , v3
and third
Fourier components
in Au+Au
at undersN N =three
200 GeV,or v2 correspond to ond witha hydrodynamical
model[46, 47]collisions
calculated
togetherwithseveraltheoreticalmodels.
[54]
mpt photon compodifferent assumptions including the “semi-QGP” scenario [14].

1.8

The thesis motivation

photonpuzzle” remains unresolved. High quality data
thesis motivation is to study the production of low transverse-momentum
e the anisotropies The ofyields andv2 and v3 fordifferent
collision
systems,
direct-photons
in ultra-relativistic
heavy-ioncollisions.
Directphotonsindo not
ynamics [14].
cludingvery
asymmetric
ones,
and
energies
would
help
to
participate in the strong interaction; therefore, they are an excellent probe to
improve
understandingof matter.
direct photonpro- areerential and more studyfurther
the properties
andourdynamicsof the createdDirect photons
ductionrobustmust
be abledescribe
prove, the “direct emitted
in the because
entire stagesof themodels
collisions,and they
carrytopure
informationof the stage in which they were produced.
Direct photon production has been measured in various collision systems
and energies in RHIC and the LHC experiments. The yields and anisotropy
are measured, and the experimental results are compared to the theoreticalmodels. However, any theoretical approaches do not exist to simultaneously

CHAPTER 1. INTRODUCTION

42

explain the observed data for both yields and anisotropies. The large thermal
photon yield is expected to be produced at the early stage, whereas the large
azimuthal anisotropy is supposed that the photons are originated in the laterstage. The contradiction of the thermal photon production is known as “thedirect photon puzzle”.
The thesis presents the measurement of low transverse-momentum directp
photons in Cu+Cu collisions at sN N = 200 GeV. Direct photons are measured by the virtual photon method. The data was taken by the PHENIX
experiment at the RHIC collider in Brookhaven National Laboratory. The
PHENIX detector has an excellent ability to measure electrons and positrons
with a wide range of transverse momentum.
Direct photon measurement in Cu+Cu collisions provides additional information on the collision system-size dependence of low transverse-momentum
direct photon production. This thesis focuses on three centrality classes; minimum bias, 0–40% as central collisions, and 40–94% as peripheral collisions.
These collisions are compatible with the Au+Au peripheral collisions.
We extract the virtual photon contribution as an excess over the known
hadron decay contributions in the invariant mass distribution. The extracted
contribution, the direct photon fraction, is converted into the direct photon
spectra. The measured spectra for three centrality classes are compared to
the Au+Au results, and the e↵ective temperature is calculated from theinverse slope of the spectra. The direct photon rapidity density is also investigated as a function of the number of participants, Npart . The Cu+Cu
results provide the system-size dependence of the production, and we discuss
the collision system dependence of the direct photon production.
The structure of this thesis is as follows. Chapter 2 describes the introduction of the experimental setup. Chapter 3 expresses the analysis method for
direct photon measurement via virtual photons, including subtracting a large
amount of background and signal extraction. The next chapter, Chapter 4,shows the measurement results, including the discussion about the direct
photon spectra and rapidity density compared to results in other collisionsystems. Finally, Chapter 5 gives the conclusion of the thesis.

Chapter 2
Experimental setup
We measured nucleus-nucleus collisions by the Pioneering High Energy Nuclear Interactions eXperiment (PHENIX) at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory (BNL). In this chapter, we
introduce an overview of the RHIC complex and the PHENIX detector.

2.1

Relativistic Heavy Ion Collider

The Relativistic Heavy Ion Collider (RHIC) locates at Brookhaven National
Laboratory (BNL) in Long Island, New York, the United States. The purposeof the collider experiment is to discover a new high-temperature and highdensity matter and research the characteristics of the QGP state in ultrarelativistic nucleus-nucleus collisions.
RHIC can accelerate and collide various nuclei from light ions, protons toheavy ions, uranium. The maximum energy at RHIC is up to 100 GeV per
nucleon for copper and gold, and that of a proton is 250 GeV. The collisionenergy of RHIC is one order of magnitude higher than that of the Alternating
Gradient Synchrotron (AGS) at BNL and the Super Proton Synchrotron(SPS) at CERN.
Figure 2.1 shows the RHIC complex arrangement, including four experiments and pre-accelerators. The RHIC collider comprises two individual
superconducting rings of 3.8 km in circumference, one for the clockwise ring,the Blue ring, the other for counter-clockwise, the Yellow ring. These tworings intersect at six points, and the four experimental facilities, PHENIX,
STAR, BRAHMS, and PHOBOS, are initially located at each one of the in43

240

CHAPTER 2. EXPERIMENTAL SETUP

44

M. Harrison et al. / Nuclear Instruments and Methods in Physics Research A 499 (2003) 235–244

Fig. 4. Arrangement of detectors along the RHIC ring.

Figure 2.1: Relativistic Heavy Ion Collider (RHIC) complex arrangement,
including the LINAC and the Tandem Van de Graa↵ as a pre-accelerator,
and the Alternating Gradient Synchrotron (AGS). [58]and provide a close to 4p solid angle coverage. The
Magnets with radial magnetic field geometry,exclusiveuse ofMuon Trackers,tersection
several points.
layers of
steel
slabs
as
Clock positions enumerate
the points;
the high-resolution
PHENIX facilityand high-speed
siliconmicro-strip devices for the detection eleMuon Filters, locatesand Muon-Identifying
Detectors.
at 8 o’clock and theSTAR facility
at 6 o’clock.
willaremakethe spectrometer
The combination ofthesedetectors
willTandem
facilitateVan dement
The
LINAC
and theGraa↵
the sourceof the ions Table Top size
andalso
provideitwitha verygood tracking andtheidentificationof
leptons,
and pre-accelerator for protons and heavy ions such as copper andgold, high data ratecapability
for ofdetection
ofand
chargedhadrons, and respectively.
photons. AThe
Multiplicity/Vertex
injected atoms are partiallystrippedelectrons,
the hadrons andleptons in The
selectedsolid angles.
The Time-of-Flight
Detector that surrounds
pipe,
acceleratedthe
ionsbeam
send tothe Beam–
Booster Synchrotron.
ion beamis stripped
screens
improvetheparticle
identification capBeam Counters,
andZero-degree
Calorimetersagain and reaches 37 % of the speed of light. After the booster, the ion beams
ability of the detector.
(ZDCs), identifies the collisions and their location
The BRAHMS detector consists of a two-arm
along the beam direction. This concept will let
magnetic spectrometer, one in the forward direcPHENIX detect the phase transition in a number
tion for measurement of high momentum particles
of observable signatures simultaneously. Only the
but with a small solid angle and the other on theCentral Spectrometer was available for the 2000
side of the collision point for the mid-rapidity
physics runs.
region. Both arms are movable to variable
The PHOBOS detector consists of a two-arm
settings to cover wide ranges of kinematicalmagnetic spectrometer (one arm for 2000 physics
regions. The technology used in this detector isruns) as its central detector and a series of ring

CHAPTER 2. EXPERIMENTAL SETUP

45

are injected into Alternating Gradient Synchrotron. The AGS accelerates thebeams up to 28 GeV for proton and 10.8 GeV per nucleon for heavy ions.
After that, the ion beams are delivered to RHIC through the AGS-to-RHIC
Beam Transfer Line with stripping of electrons at the AGS exit. Finally, thebeams are accelerated and stored in RHIC.

2.2

The PHENIX detector

The Pioneering High Energy Nuclear Interactions eXperiment (PHENIX) is
designed to measure several fundamental probes in heavy-ion collisions, especially electromagnetic probes [59]. The PHENIX detector comprises threedetector systems: the global detectors, the central arm spectrometers, andthe muon arm spectrometers. Figure 2.2 shows the detector configuration on
both the beam and side views in 2005. The PHENIX detector has an excellent particle identification capability in a broad transverse momentum range
to measure photons, leptons, and hadrons simultaneously. The central arms
placed on the east and west sides dedicate themselves to measure photons,
electrons, and hadrons, whereas the muon arms located on both the north andsouth sides give muon measurements. Besides, the global detectors measure
the start timing, collision vertex, centrality, and reaction plane. The central
arms are employed in this study to measure low transverse-momentum direct
photons, and it covers pseudo-rapidity, ⌘, with ±0.35 and azimuth with 90
degrees. In the following sections, we describe the details of the PHENIX
detectors focusing on related to the thesis.

2.3

Global detectors

The global detectors characterize the collision events by measuring the collision vertex, particle multiplicity related to the centrality, and reaction plane.
Once the collision occurs, the global detectors determine the start timing
for time-of-flight measurement and give the start signal to spectrometers.
The PHENIX experiment has two global detectors, the Beam-Beam Counters inside the central arm and the Zero-Degree-Counter located far from thedetector center.

CHAPTER 2. EXPERIMENTAL SETUP

46

Figure 2.2: The configuration of the PHENIX detector in 2005. The drawing
shows the beam view (Top) and side view (Bottom) of the detector. [60]

CHAPTER 2. EXPERIMENTAL SETUP

2.3.1

47

Beam-Beam Counters

The Beam-Beam Counters (BBCs) are a pair of Cherenkov detectors locatedon the north and south sides around the beam pipe at a distance of ± 144.35
cm from the nominal interaction point [61, 62]. Each of the BBC comprises 64
elements of a mesh-dynode type photomultiplier tube (PMT) with a quartz
Cherenkov radiator. The BBC detector covers the range of 3.1< |⌘| <3.9 inpseudo-rapidity and full azimuthal angle (= 2⇡).

(a)(b)

Figure 2.2: Components of the BBC. (a) shows a photomultiplier tube (PMT)

FigureThe BBCshows
a BBC
a photomultiplier.
with a2.3:
diameterof 25.4detector.
mm and a (a)
30 mm
thick
Quartzelement,
window mounted
in front of(b)it.showsa BBC
array.assembled[63](b) shows
64 PMTsto one unit.
BBC has four essential roles: to trigger the PHENIX Minimum-Bias

Their task is to measure the energy of spectator neutrons, which did not parevents,
to determine collision vertex, centrality, and reaction plane. Beticipate in the collision and therefore carry still a large fraction of the beamsides, BBC measures the collision timing for the time-of-flight measurement
momentum. While charged particles like spectator protons are deflected bytogetherwith the Time-of-Flight detector.
the “DX” dipole magnet in front, neutrons hit the ZDC and create a hadronicThe
BBCs
determine
thecreatedcollisionvertextimingthe di↵erence
shower. Neutral
particles
withintheandheavy
ionby
collision
moving andinaverage
hit timehave
betweenthe anorthsouthside counters.
vertexforwardofdirection
typicallymuchandsmallerenergy.
The ZDC The
consistofzvtx
and the sampling
start timing
t0 arecalorimeter
calculatedmadeby theequations;
Cherenkov
hadronicof afollowing
tungsten alloy
with a conical coverage of 21 mrad aroundthe beam direction. The energy resolution ofp
TSouth TNorth
the ZDC is E /E = 85%/zvtxE= 9.1%.
⇥c
(2.1)
2
The total energy deposited by spectator
neutrons can be used in anticorrelation with the total charge
TSouth deposited+ TNorth in(2the⇥ BBCL/c) to determine the centrality of the collisiont0as=shown in Fig. 2.4. The centrality is a measure (2.2)
for2
how much the two colliding ions overlap. In addition to the centrality deterwhere
L is thethe ZDCknown
fromcenterof the bias
PHENIX
mination
alsodistanceserves as
parttheof theminimum
triggerdetector
in heavyto
thedetector
144.35information,
cm, and c isbutthewithspeedof light. of ⇡ 200
ionBBC
collisions
and position,
provides timing
a resolution
ps it is less accurate than the BBC.

CHAPTER 2. EXPERIMENTAL SETUP

48

The collision centrality is measured by the BBC multiplicity along with
the ZDC deposit energy, and the reaction plane is determined by the azimuthal distribution of the measured particles in the BBC described in detailin Sections 3.2.3 and 3.2.4, respectively.

2.3.2

Zero-Degree Counters

The Zero-Degree Counters (ZDCs) are a pair of hadron calorimeters locatedat a distance of 18 m downstream of the PHENIX north and south sides[64]. The ZDCs measure the energy of spectator neutrons, which does notparticipate in the collision interactions. Besides, the detectors are standard
equipment in all experiments in the RHIC collider. Figure 2.4 shows the cutaway view related to the ZDC detectors. The Dipole Magnets are installed
between the interaction point and the ZDC. Therefore, the charged particles
in the spectators are deflected by the magnet, and the neutral particles,
neutrons, only hit the ZDC and deposit the energies. The ZDC detectors
provide the centrality determination.

2.4

The central arm detectors

The PHENIX Central Arms locates on the west and east sides. Each arm
covers the pseudo-rapidity and azimuthal angle ranges of |⌘| < 0.35 and| | < ⇡/2, respectively. Several detectors are installed in the central arms tomeasure electrons, photons, and hadrons. The Drift Chambers (DCs) and
Pad Chambers (PCs) determine the charged particle trajectories and measure their momenta. The electric charge signs of the particles are identified
by the trajectory curvatures. The Ring Imaging Cherenkov counter (RICH)
provides electron identification by energy-momentum matching. Electromagnetic calorimeters (EMCals) consists of eight separate sectors: two sectors
located in the bottom of the east arm are lead-glass (PbGl), the other six
sectors are lead-scintillator (PbSc). In the following subsections, we describe
the detectors used in this study.

2.4.1

The Central Magnet

The PHENIX Central Magnet is comprised of the Central Magnet and theMuon Magnets [66]. The Central Magnet provides the magnetic field aroundCHAPTER 2. EXPERIMENTAL SETUP

49

Figure 2.4: The cut-away view of the zero degree calorimeters. [64]Fig. 1.
Plan view of the collision region and (section A-A) ”beam’s eye” viewof collision
the zdc location
indicating
deflectionof protons
andprovide
chargedthe
fragments( withthevertex point,
while
the Muon
Magnets
magnetic
Z/A⇠
1
downstream
of
the
”DX”
Dipolemagnet.
field for the forward and backward region of the PHENIX detector. The

Central Magnet is used for charged particle measurement by the central arm
magnetic energy emission into this region is predicted to be negligible so thisdetectors. The Central Magnet consists of two pairs of concentric Helmholtz
measurement is not emphasized in our design. Since the spatial distribution of
coils; the inner and outer pair. The inner coils provide a magnetic field aroundneutrons emitted in the fragmentation region carries only limited information
the interaction point parallel to the beam direction with axial symmetry. In
about the collision, the calorimeters are built without transverse segmentation.
this thesis, electrons and positrons are measured by the central arm detectors,
and they follow a curved path in the magnetic field. The Muon Magnets are
The Forward Energy resolution goal was determined by the need to cleanly
utilized for muon measurement by the muon spectrometers.
resolve the single neutron peak in peripheral nuclear collisions. The natural
Figure 2.5 shows a cut-away view for the PHENIX Central and Muon
energy spread of emitted single neutrons[1] being approximately 10% a resoMagnets andE their magnetic field lines in (++) configuration. The Helmholz
lution of  20% at E = 100 GeVappeared reasonable.
coil can be Eoperated withn the same (++) or opposite (+ ) polarity. The
data we use in this study is collected with the same polarity configuration.
The limited available space between the RHIC beams at the ZDC location
The coverage of the magnetic field is 70 < ✓ < 110 and |⌘| < 0.35.
imposes the most stringent constraint on the calorimeter design. As can be
The provided magnetic field allows charged particle tracking and momentum
seen from Figure 1, the total width of the calorimeters is only cannot exceed
10 cm (equal to 1 nuclear interaction length ( I ) in tungsten). We designed
the ZDC’s to minimize the loss in energy resolution due to shower leakage,
which can cause fluctuation in measured shower energy through dependence
on position of impact and random fluctuations in shower development.

Finally, the ZDC’s are required to withstand a dose of ⇠ 105 rad., which isthe expected exposure during several years of RHIC operation[3].

CHAPTER
2. EXPERIMENTAL
CHAPTER
2. EXPERIMENTAL SETUP
SETUP

50

38

PH ENIX

-4.0

-2.0

0.0

2.0

4.0

Z (m)

Magnetic field lines for the two Central Magnet coils in combined (++) mode

Figure 2.5: The PHENIX Central Magnet [65]Figure 2.6: PHENIX central magnet field lines.
analysis. The magnitude of the magnetic field at R =0 cm is 0.5T, and it
gradually decreases with approximately the Gaussian profile to zero at R >determinepT Then,of eachparticle
andpass
ultimately,
the invariant
massof particle
250 cm.
chargedparticles
straight throughin the RICH
detector
the magnetic
field’s no e↵ect.
pairs. due
Theto DCalso participatesin the pattern recognition at high particle

track densities by providing position information that is used to link tracks
2.4.2
Drift PHENIX
Chamberdetector sub-systems.
throughthe various
The Drift Chambers (DCs) is the primary tracking detector in the PHENIX
experiment
for measuring
charged particle trajectories [67]. The DCs are
The Time
Expansion
Chamber
located between 2.02 and 2.48 meters in radius from the beam axis. The
The Time[76]theis coveragecomposed
24 large
Drift Expansion
Chamber is aChambercylindrical (TEC)
shape withof |z|of<a90set
cmofand⇡/2 azimuthal
multi-wiretrackingangle.
chambers and it resides in the East arm. The TEC mea-sures all charged particles passing through its active area, providing direction
vectors that are matched to additional track information from the DC’s andPC’s. It also enhances the momentum resolution at pT 4 GeV/c by combining with the DC to provide a long lever arm for improved track-angle
resolution.

CHAPTER 2. EXPERIMENTAL SETUP

51

R
.02
=2
m

o
90
6m

2.5 m

R

.4
=2

Ti frame
mylar window
Figure 2.6: The construction of Drift chamber frame [67]Figure 2.6: The PHENIX Drift Chamber Frame [89].
The inside of the DCs has filled a mixture gas of 50% Algon, 50% Ethane,
and a small fraction of alcohol. The mixture gas randomly ionizes whenin the !thee+charged
e decay
channelwith aTheresolution
betterthan
its natural width
particles
pass through.
ionized electronsfromthe primary2
ionization
are driftedwith
towards
an necessity
anode wire into
an perform
electrical field.
of 4.4 MeV/c. Inprocess
conjunction
thein aThehigh particle
chargedparticle trajectories
are reconstructedby hitstracks
in subsequentmultiplicity
environment(as many
as two hundredin theanodes.
central Au+Au
Figure 2.7 shows a schematic view of a Drift Chamber. Mylar windows

collisions) this imposes the following requirements on the DC:• Single wire resolution better than 150 µm in r.

• Single wire two track separation better than 1.5 mm.
• Single wire efficiency better than 99%.

CHAPTER 2. EXPERIMENTAL SETUP

52

4.5 degr.

Wire orientations, top view
V2 − planes

U2 − planes

Termination wires

Back wire

V1 − planes~ 1800 mm

X2 − planes

Gate wires
U1 − planes
Potential wire
sense (anode)
X1 − planes

wire

anode planecathode plane

U

X

V

Sector, side view

Figure 2.7: Left: Cut-away view of the wire layout within one keystone of the

Figure2.7: The wireandthe stereo
stereowire
wireorientation
orientation
Drift Chamber.
Right:position
Plan viewof the[89].in Drift Chamber. Left: the wire position layout within one sector and inside the anodeplane. Right: a schematic diagram of the stereo wire orientation. [67]and titanium support frames enclose the drift zone of the gas-filled region.
The DC is consists of 20 sectors covering 4.5 degrees in azimuth.
The Drift Chamber with the help of the Pad Chamber measures the
trajectories for charged particles, and it determines transverse momentum
down to 200 MeV/c. The curvature of the track determines the momentum
since the curvature is in inverse proportion to the momentum.

2.4.3

Pad Chamber

49

The Pad Chambers (PCs) are multi-wire proportional chambers consistingof three individual layers, PC1, PC2, and PC3 [67]. Each PC has a single
wire plane inside a gas volume bounded by two cathode planes. The PCs areoperated with a mixed gas of 50% argon and 50% ethane. The PC1 is theCHAPTER 2. EXPERIMENTAL SETUP

53

innermost layer between the DC and the RICH in both the East and the Westarms. The PC2 is the middle layer installed behind the RICH only in theWest arm. The PC3 is the outermost layer in front of the Electro-Magnetic
Calorimeter (EMCal) in both arms.

Anode wire
Field wire

8.4mm
Center pixel

1.5mm
2.7mm

Side pixel

8.2mm

Figure 2.9: Left: the pad and pixel geometry. Right: Interleaved pad design. [89].

Figure 2.8: Left: The pad and pixel geometry. Right: Pad design [67]Theof PCsprovidesthree-dimensional
space-points of charged
2.2.4system
Ring
Imaging
Cherenkov
Counterparticles outside the magnetic field. The PC1 also provide z-coordinate at
A charged particle travelling in a medium with a velocity c that is greater
the exit of the DCs that is essential for determining three-dimensional vecthan the speed of light in this medium, cn = c/n for a medium with refractive
tor index
momentumcharged radiation
particles.under
Theangle
PC2cosandare).used to rejectn, emitsofCherenkov✓C PC3= 1/(nmany backgroundproduced
andCounterparticle-detector
In each of the tracks
two central
arms a by
Ringparticle
Imagingdecays
Cherenkov(RICH)
interactions
outsidetheapertureoftheDC.
is installed between the inner and outer tracking detectors following the firstlayer of Pad Chambers [90]. Its main purpose is the separation of electrons
from the large background of charged pions produced in heavy-ion collisions. In
2.4.4 Ring Imaging Cherenkov Counters
combination with the Electromagnetic Calorimeter it also provides information
for anelectronCherenkov
trigger in pCounters+ p collisions.
Behindwindowwith asA RingImaging(RICH)
is a thegasentrance
Cherenkov
detector
2
3
an
area
of
8.9
m
a
volumeof40misfilledwithCOasradiatorgas,which
a primary device to identify electrons and6 positrons2 among a large amount
has a refractiveindex
n 1 = 410
⇥ 10 [29], [68].
corresponding
to a thresholdof charged
pions in
theofPHENIX
experiment
ThepRICH
is installed2
velocity t = 1/n = 0.99590168 and a -factor of t = 1/ 1
t = 34.932.
betweenthe PC1 and PC2 in both the east and west arms.
This leads to a Cherenkov threshold of p = m⇡ t t = 4.87 GeV/c for charged
The principle of Cherenkov2 detectors tis thata charged particle traveling inpions (m⇡ = 139.570 MeV/c ), while electrons (me = 0.511 MeV/c2 ) exceed
a mediumwith a thresholdvelocity alreadyc emitswith
the aCherenkov
with GeV/c.
the angle
the Cherenkov
momentumradiationof pt = 0.018
4cos ✓Below
=
1/
(n
)
becausethevelocityisgreater
than
the
speed
of
c
the pion threshold the RICH has a hadron rejection of 10 to 1. light inthat medium.
The
thresholdof Cherenkov
radiation
pions
at about
A cut-away
viewof the RICH
detector is shownin Fig.for
2.10.
The areCherenkov
4.9 light
GeV/c,
whileelectrons
are
at
about
0.02
GeV/c.
Therefore
theis focused by two intersecting spherical mirrors with a total area of 20RICH
m2
onto twoof 1280 photo-multipliertubes(PMT) eachare locatedprovidese/⇡arrays
discrimination
below the pion
thresholdand whicha hadronrejection
4 side of the entrance window. An average number of 10 photons peroneitherratio of 10 to 1 below the threshold.
⇡ 1 particle are emitted under the angle of ✓C ⇡ 9 mrad. They are focused
to a ring on the PMT array with an asymptotic radius of ⇡ 11.8 cm. The
glass in front of the photo tube absorbs light with wave lengths below 200 nm.
The mirror reflectivity is 83% at this wave length and rises to 90% at 250 nm.
In p + p collisions the RICH also serves as Level-1 trigger on rare events
51

CHAPTER 2. EXPERIMENTAL SETUP

54

Figure 2.10: A cut-away view of one arm of the PHENIX RICH detector [90].

Figure 2.9: A cutaway view of one arm of the PHENIX RICH detector [68]with electrons. The trigger is comprised of 64 non overlapping trigger tiles in
The PMTschematic
view triggerof thetile
RICH
is shown
in Fig.
2.9.anTheeacharray. Eachconsistsof 4( ) ⇥5(z)PMTs,
area RICH
which isconsistsofthreeparts:
agas
vessel,reflective
mirrors,andphotomultiplierapproximately corresponds to the size of a Cherenkov ring of a ⇡ 1 particle.

tubes. The CO2 gas as radiator gas is filled in 40 m3 vessel between theentrance
exit windows. TheCalorimeter48 composite mirrors forming two inter2.2.5 andElectromagnetic
secting spherical surfaces focus the Cherenkov ring onto the photomultiplier
High-energy
electrons
and photons
losematter predominantly
via
tubes
with a totalreflecting
area of 20
m2energy. One inthousandtwo hundred eighty
Bremsstrahlung and e+ e pair production, respectively. The amount of energy
photomultiplier tubes are installed in two arrays located behind the central
they lose is defined by the radiation length X0 , which is both (a) the meanmagnet;therefore, the particles originated from the collisions do not directlylength of traversed matter after which an electron has lost all but 1/e of its
hit energy
the tubes.
and (b) 7/9 of the mean free path for e+ e pair production by a photon.
The Electromagnetic Calorimeter (EMCal) measures the energy and positionand electrons. Furthermore,
it serves as trigger on rare events
2.4.5 photons
Electro-Magnetic
Calorimeterwith high momentum photons. It comprises of eight sectors covering each 22.5
azimuth and ⌘ = Calorimeter±0.35 in pseudo-rapidity.
All four sectorsof the position
West
Thein Electro-Magnetic(EMCal) measures
the spatial
and thetwo top sectors
the East[69].
Arm Electrons
are shashlikand
typephotons
lead-scintillator
andArmenergyof electrons
and inphotons
lose their(PbSc)
calorimeter. The
bottom sectors areenergyin sampling
matter predominantly
viatwoBremsstrahlung
andlead-glass
electron (PbGl)
pair proCherenkov
calorimeters,
which
had
been
used
previously
in
the
CERN
experduction, respectively. The radiation length X0 is defined as the lengthof theiment WA98 at the SPS.
electron’s energy reduced to 1/e.
The PbSc calorimeter contains a total of 15,552 individual towers which
The PHENIX EMCal is located at the most outside of the central arms
are made of 66 sampling cells with alternating layers of 1.5 mm Pb and 4 mmcovering
the rangeof 70  ✓ 110 [98].
subtending
azimuthangle
scintillator(1.5%PT/0.01%POPOP)
A module90as inshown
in Fig.
2.11 for52

CHAPTER 2. EXPERIMENTAL SETUP

55

Figure 2.11: View of a PbSc module showing the layers of Pb and scintillator, theFigure2.10: shifting
Interiorfibers
view
a phototubes
Pb-scintillator
calorimeter
wavelength
andoftheattached
to the back.module showing
a stack of scintillator and lead plates, wavelength shifting fiber readout andleaky fiber inserted in the central hole. [69]comprises of four optically isolated towers which are read out individually.

each arm. The PHENIX EMCal is installed2 in both east and west arms, andEach tower has measures 5.535 ⇥ 5.535 cm across and has a length of 37.5
eachcomprises
fourtosectors.
Inmodules
the eastarearm,
top sectors
cm,armwhich
corresponds
18 X0 . 36
heldtheby atwocommonsupportare
installed
lead-scintillator
calorimeter(PbSc),
while
two bottom
sectors
structure
called super module.
18 supermodules
formthea sector.
The energy
areresolution
a lead-glass(PbGl).
of thecalorimeter
PbSc Calorimeter
is In the west arm, all four sectors arelead-scintillator calorimeter.
8.1%
E
The lead-scintillator calorimeter(PbSc)2.1%.
is a shashlik type sampling(2.2)
calorime= p
EE
ter. The PbSc calorimeter contains 15,552
individual towers, and each tower
is made of 66 sampling cells with 18X0 and about 30 mm of Moliere radius.
A module
is shown
in Fig.
2.10.
Thesefour(SM)
towersEach containing
sector of thefour
PbGltowers
calorimetercomprisesof 192
super
modules
arewhich
optically
isolatedandconnected
tothewavelength
shifting
fiber.
The
contain each 24 modules as shown in Fig. 2.12. Each module measures
photomultipliers
locatedon(14.3
the X
backsideof the tower. The energy and4 ⇥ 4 cm2 across,areis 40
cm long0 ), and read out with a photomultiplier53

CHAPTER 2. EXPERIMENTAL SETUP

56

position resolutions of the PbSc calorimeters are as follows, respectively.
E

E
PbSc
(E, ✓) =
x

=p

8.1%
E (GeV)

1.55(mm)

2.1%

5.7(mm)p
E (GeV)

where ✓ is an impact angle of particle, and

(2.3)

!

⇥ sin(✓)(2.4)

is given by radiation length.

photomultiplierwith housing

steel plates

mirror foil

lead glass matrix withcarbon fibre/epoxy

LED boardreflective coverphotodiode withpreamplifier

Figure 2.12: View of a PbGl super module.

Figure 2.11: Exploded view of a lead-glass detector supermodule. [69]Thecalorimeter(PbGl)
a Cherenkov
calorimeter
which hadatitslead-glass
end. The energy
resolutionof theis PbGl
Calorimeterisbeen previously used in the WA98 experiment at the SPS collider at the
5.9% 192 supermodules, and each superCERN. The PbGl calorimeterEcontains
0.76%.
(2.3)= p
E Figure
E 2.11 is shown the PbGl supermodule
module consists of 24 modules.
made of 6⇥4 modules. The module has 14.4X0 and 36 mm of Moliere raWith
thickness of 18
X0 in thePbSc
and 14.3 mylar
X0 in thedius andareaindividuallywrappedwithaluminizedfoil PbGl,
to be respecopticallytively, electrons and photons will deposit their energy within the calorimeter aselectromagnetic shower of subsequent Bremsstrahlung and e+ e pair creation.
In the PbSc the electrons within the electromagnetic shower created in the
Pb-layer produces scintillation light in the scintillator layers. The scintillation
light is guided by wavelength shifting fibers to the phototubes located at theback of each tower. In the PbGl, which has a refractive index of n = 1.648, theelectromagnetic showers is detected by Cherenkov light radiated by electrons
in the shower. The Cherenkov light is read out at the end of the Calorimeterby photomultiplier tubes.

CHAPTER 2. EXPERIMENTAL SETUP

57

isolated. The energy and position resolutions of the PbGl calorimeters are
obtained by the followings, respectively.
5.9%
=p
E
E (GeV)E

PbGl(E) = 0.2(mm)
x

2.5

0.8%.

(2.5)

8.4(mm)p
E (GeV)(2.6)

Data Acquisition System

The overview of the Data Acquisition System (DAQ) in the PHENIX experiment is described in this section [70, 71]. The expected interaction rate
provided by the RHIC collider varies from a few kHz for central Au+Au collisions to a few hundred kHz for p+p collisions. Furthermore, several hundred
particles are passed through the detector in central Au+Au collisions, while
aCHAPTER
few particles2. inEXPERIMENTAL
p+p collisions. TheSETUP
measured particles include various ob-47
servables: hadrons, leptons, and photons. Therefore, the PHENIX DAQ isdesigned to handle various event sizes and rate seamlessly.

GL1
Busy

GTM

ut
So
C
ZD

Data packets
over fiber~350000 ch
Shield Wall

Missing:• ARCNET Serial Interface to FEMs
• High and Low Voltage Control andassociated control systems• Alarm system

MTM

RHIC clocks

DCM

Data Packets
over Parallel
FIFO InterfaceD
ov atapa er Pa
ss NE ck
in V etg
Bu IS ss To
kenPartitioner
DCB

FEM

Clock

RHIC
Computing
Facility
End
User

Busy

Clock, Trigger,
Mode bits
over fiberhA(e S u.g b s.E y
as ste
tD m
C
)

ZD

C

N

L1

or
th

TriggerCountingrooma few miles later'trigger' is a placeholder
for a much more complex'Local Level 1' trigger system

Interaction region

GL1 Global Level 1 Trigger
GTM Granual Timing Module
MTM Master Timing Module
DCB Data Collection Board
DCM Data Collection Module
FEM Front End Module
SEB Sub Event Buffer
ATP Assembly Trigger Processor

OnlineMonitoring

SEB
SEB
SEB
SEB
ATM Switch
ATP

Linux Farm
~600 CPU's

tapestorage
1.2PB

20MB/s
250TB/yr

Figure 2.12: Schematic diagram of the PHENIX on-line system [71]Figure 2.12: Schematic diagram of the PHENIX On-Line system.
decision. The LVL1 trigger and lower levels of the readout are clock-driven
by bunch-crossing signals from the RHIC clock. The higher levels of readout
and the LVL2 trigger are data-driven where the results of triggering and dataprocessing propagate to the next higher level only after processing of a given
event is completed.

CHAPTER 2. EXPERIMENTAL SETUP

58

Figure 2.12 shows a schematic diagram of the PHENIX DAQ. The RHIC
derivers the beam with the 9.4 MHz fundamental clocks corresponding to
106 ns of the time interval between beam crossing. All PHENIX FrontEnd Electronics Modules (FEMs) are synchronized to the RHIC clock. The
RICH clocks are received by the Master Timing Module (MTM), and themaster timings are transmitted to the FEMs via the Granual Timing Module (GTM). The FEMs are placed in the PHENIX Intersection Region (IR),and they convert the analog signals from the detectors into digital data. The
Level-1 Trigger (LVL1) selects interesting events and rejects events due tolimited DAQ rates. The LVL1 is triggered based on the logical combination of the Local Level-1 decisions generated by the trigger detector, suchas the BBC and ZDC detectors. Once the LVL1 decision is generated, theFEMs transfer the bu↵ered data to the Data Collection Module (DCM) located at the PHENIX Counting House. The data packets are sent to the
Sub Event Bu↵ers (SEB). Then they are transferred to the PHENIX Online
Control System (ONCS) for online monitoring and logging and to the HighPerformance Storage System (HPSS) at RHIC Computing Facility (RCF) for
physics analysis.

Chapter 3
Analysis
This chapter describes the analysis for low transverse-momentum directp
photon measurement in Cu+Cu collisions at sN N = 200 GeV with the
PHENIX experiment. We explain the analysis, including background reproductions, signal extraction, and estimation of the systematic uncertainties.

3.1

Overview

The PHENIX experiment collects the Cu+Cu collision data with a minimum
bias trigger in 2005, the Run-5 of the RHIC operation. Low transversemomentum direct photons are measured by the virtual photon method because the signal-to-background ratio can be improved compared to the real
photon measurement. A virtual photon decay into an electron-positron pair.
Accordingly, the virtual photon method measures e+ e pairs. The direct
virtual photon contribution is statistically extracted as the remainder of thee+ e invariant mass distribution after subtracting extensive backgrounds andknown hadronic contributions. The background contributions are evaluatedfrom both well-tuned Monte Carlo simulations and the experimental data.
Once the direct photon contribution is extracted, the direct photon spectra
and the rapidity density are calculated.
Section 3.2 describes the data set used in this analysis. The event trigger and global variables for characterizing the collision events are explained.
Sections 3.3 and 3.4 express the charged particle tracking and electron identification by the PHENIX central arm detectors, respectively. Section 3.5
explains the extraction of electron pairs. Section 3.7 shows the tuning for59dings of 2005 Particle Accelerator Conference, Knoxville, Tennessee
CHAPTER 3. ANALYSIS

60

the Monte Carlo simulations used for the background estimation. Sections
3.8 to 3.14 describe the background estimations and their subtraction. Section 3.15 describes the extraction of the direct photon fraction. At last, we
ND PERFORMANCE
OF RHIC AS A CU-CU COLLIDER*
describe the evaluation of systematic uncertainties in Section 3.16.

ai, D.S.Barton, J.Beebe-Wang, M.Blaskiewicz, J. M. Brennan, D.Bruno, P.Cameron, R.
ttavio, A.Drees, W.Fischer,
C.Gardner,
J.Glenn, P.Harvey,
T.Hayes,variables
H-C.Hseuh,
3.2G.Ganetis,
Eventselectionand global
U.Iriso, R.Lee, V.N.Litvinenko, Y.Luo, W.W.MacKay, G.Marr, A.Marusic, R.Michnoff,
Nicoletti, B.Oerter, V.Ptitsyn,
T.Russo,data
J.Sandberg,
3.2.1 T.Roser,
Collected
and T.Satogata,data set C.Schultheiss,.Trbojevic, N.Tsoupas, J.Tuozzolo, K.Vetter, A.Zaltsman, K.Zeno, S.Y.Zhang, W.Zhang
The data of Cu+Cu collisions at the center-of-mass energy per nucleon pairp Upton, NY, USA
Brookhaven National Laboratory,of 200 GeV, sN N = 200 GeV, is taken in the PHENIX experiment at thep
RHIC collider in the year 2005. The collision system of Cu+Cu at sN N =In the next sections we will address the machine
200 GeV is only taken in 2005 at RHIC. This analysis is based on a minimum
performance as8a Cu-Cu collider, reliability and uptime,
rations, started in November
bias sample
4.95operations⇥ 10 collision
events withthe z-vertex within 25 cm ofandofnewand diagnostics
developments.
till June 2005, consistsofathe nominal interaction point equivalent to 0.44 nb 1 .
lisions at 100 GeV/u followedons (pp) at 100 GeV [1]. We
all performance of the RHIC
time as a Cu-Cu collider, andperational experience with Au,
ollisions. We will also discusssuch as a β* squeeze to 85cm
action regions from the design
ements, machine performancereliability and uptime issues.

DUCTION

nning, RHIC has been for the
Cu-Cu collider: 8 weeks of(HE) of 100 GeV/u, followed
Figure delivered
1: Luminosity
for the Cu-Cu
run atfor100GeV/c
Luminosity
in Run-5
Cu+Cu collisions at(LE) of 31.2 GeV/u andFigure
1 day 3.1: RHICp
gy of 11 GeV/u.
sN N =200GeV [72]PERFORMANCE AND LIMITATIONS(Tandem, Booster and AGS)y in only 1 week, produced Figure 1 summarizes RHIC performance in the Cu-Cu
ons/bunch with 10 π-mm-mrad high energy run. Measured integrated luminosity at the 4
3.2.2 Minimum Bias Trigger
ed for luminosity production. experiments (beams collided at Star and Phenix withdelivered for beam studies.
The minimum
bias attrigger
is withdefinedby amsignalof both the
β*=0.90,
Brahmsβ*=2.6and atcoincidence
Phobos withue ring were establishedvery
BBCand ZDCdetectorsignals. The
BBC
has a sensitivity
to both particles
β*=3m)
is comparedto theminimum
and maximum
nly 54 minutes from the first luminosity projections [3] used for run planning.
circulating beam. A short-to- Minimum projections were based on RHIC performanceort that developed in the 80 to in Run-4 with Au and assuming the same charge perup, repairs, and re-cooling in 3 bunch with Cu ions. RHIC as a Cu-Cu collider exceeded
er the discovery, diagnosis and the maximum projection by integrating 15 nb-1 at the lowtion, set-up with both beams β* experiments, more than a factor 2 over the initial goal
gressed rapidly. Overnight for the run of 7 nb-1. The cross section for n-pairwere set-up in 5 days and production of Cu-Cu ions was measured to be 2.6 barn [4]CHAPTER 3. ANALYSIS

61

from inelastic collisions and backgrounds from beam-gas and upstream interactions. At the same time, the ZDC is sensitive to inclusive interactions,
including inelastic collisions and Coulomb dissociations. Therefore, requiring
the coincidence can reduce the backgrounds.

3.2.3

Centrality determination

Centrality is an experimental variable in heavy ion collisions related to the impact parameter. Two heavy-ions collide with the impact parameter b shownin Fig. 1.5. The impact parameter describes the geometry of the collisions.
However, the parameter can not be measured in experiments. Consequently,
to characterize the collision geometry, the centrality is defined by corresponding the BBC multiplicity and the ZDC energy deposit.

BBC versus
ZDC analog
The andlines andrepre2: Mass squared versus mom
Figure 3.2: FIG.
The 1:correlation
between
BBCresponse.
multiplicity
ZDC FIG.
energysent the centrality cut boundaries.
distribution in Au+Au collisions
deposit to determine centrality in the PHENIC experiment [73]lines indicate the PID cut bounprotons (anti-protons) from left

Figure 3.2 shows the correlation between the BBC multiplicity and ZDC
energy deposit
representing
centrality
boundaries.
The multiplicity
TABLE
I: The averagenuclearoverlap function( TAuAu ), measured
theincreases
number ofproportionally
nucleon-nucleon tobinary), andby the BBC
the collisions
number (ofNcoll
participants,
Npart ,
thenumberofparticipantnucleons(N)
obtainedfrompartwhile the deposit energy in ZDC decreases. Therefore, the anti-correlationa Glauber Monte Carlo [8, 14] correlated with the BBC and
ZDC response for Au+Au at sNN = 200 GeV as a functionof centrality. Centrality is expressed as percentiles of AuAu
= 6.9 barn with 0% representing the most central collisions.
The last line refers to minimum bias collisions.
Centrality
0- 5%
0-10%
5-10%
10-15%

TAuAu (mb 1 )25.37 ± 1.77
22.75 ± 1.56
20.13 ± 1.36
16.01 ± 1.15

Ncoll
1065.4 ± 105.3
955.4 ± 93.6
845.4 ± 82.1
672.4 ± 66.8

Npart
351.4 ± 2.9
325.2 ± 3.3
299.0 ± 3.8
253.9 ± 4.3

B.

Track S

Charged particle tracks are
based on a combinatorial Hougives the angle of the track inmain bend plane is perpendicu

CHAPTER 3. ANALYSIS

62

appears between the BBC and ZDC measurements. The boundary of thecentrality is determined by the clock method expressed as✓◆(QBBC Q0 /Qmax
BBC )
1
,
(3.1)
centrality = tan
max
EZDC /EZDC

max
where Qmax
BBC and EZDC is the maximum values of the BBC measured multiplicity and ZDC deposit energy, respectively. The available range of thecentrality in the PHENIX experiment is from 0 to 94% due to the trigger
efficiency. Moreover, the measured centrality can be related to the impact
parameters using the Monte Carlo simulation with the Glauber model, including the detector response. In this analysis, we measure the direct photons
with the three centrality classes; minimum bias, 0–40%, and 40–94%.

3.2.4

Reaction plane determination

A reaction plane is a geometrical plane defined by the impact parameterand the beam direction shown in Fig. 3.3. The reaction plane is used for
azimuthal anisotropy measurements of produced particles. The angle of thereaction plane is measured from the azimuthal angles of produced particles
described asP◆✓
Yn = i !i sin (n i )
1
1
P
= tan
(3.2)
n
Xn = i !i cos (n i )where Xn and Yn are the n-th harmonic event flow vectors, and i is theparticle azimuthal angle.
In the PHENIX experiment, the reaction plane is measured by the BBC
detector located in the mid-rapidity 3.1 < ⌘ < 3.9. The reaction plane resop
lution is around 15% in Cu+Cu collisions at sN N =200 GeV and depends
on the centrality. In this analysis, we use the reaction plane information
to measure single electron azimuthal anisotropy to correct the combinatorial
background shape described in Sec. 3.7.

3.3

Charged particle tracking

We explain the method for the reconstruction of charged-particle tracks andtheir momentum measurement in this section. Tracks and momenta forcharged particles, including electrons and positrons, are reconstructed byPb by about 50% because the nucleon-nucleon inelastic cross section increases by aboutthat amount at the respective center of mass energies of 0.2 and 2.76 TeV.
3. Anisotropic Flow

63

ct
io
n

z

R
ea

y

Pl

an
e

Flow signals the presence of multiple interactions between the constituents of themedium created in the collision. More interactions usually leads to a larger magnitudeof the flow andbrings the system closer to thermalization. The magnitude of the
CHAPTER
3. ANALYSIS
flow is therefore a detailed probe of the level of thermalization. The theoretical tools

x,bFigure 4. Almond shaped interaction volume after a non-central collision of two

Figure 3.3: The
image withof reaction
in(reaction
heavy-ioncollisions.
nuclei.schematic
The spatial anisotropy
respect to theplanex-z plane
plane) translates
intoa
momentumanisotropyoftheproducedparticles(anisotropicflow).
The reaction plane is defined by the impact parameter and the beam direction. [17]to describe flow are hydrodynamics or microscopic transport (cascade) models. In thetransport models flow depends on the opacity of the medium, be it partonic or hadronic.
the Drift Chambers and Pad Chambers. Once nucleus-nucleus collision ocHydrodynamics becomes applicable when the mean free path of the particles is muchcurs,
charged particles are emitted and passed through the magnetic fieldsmaller than the system size, and allows for a description of the system in terms offorcedby thequantities.
PHENIXThis
centralThey
are bentof totheofperpendicularmacroscopic
gives magnet.
a handle on
the equationstate
the flowing
direction
withrespect toonthe
beamofpipes
untilthey carriveattheDC. Whenmatter and,in particular,
the value
the soundvelocity.
s
chargedparticles
reach
the
DC,
they
travelstraight
outduetoalmostExperimentally, the most direct evidence of flow comes from the observationof noanisotropic
flowoutsidewhich is thethe anisotropy
in particle momentum distributions correlated
magnetic
field
DC.

Charged particle tracks are reconstructed in a two-dimensional space coordinated by and ↵. is the azimuthal angle of a track, and ↵ is an inclination angle of a track with respect to the straight line connecting to the vertex
point. Figure 3.4 shows the schematic view of the two-dimensional space forthe track reconstruction. The angle depends on a particle’s momentum,
and the angle is inverse proportional to the momentum. The curvature signdepends on the particle’s charge. The ↵ angle allows the determination of
the transverse momentum pT , and the relation between ↵ and pT is approximately expressed as:
↵'

K
pT

(3.3)

where K is the e↵ective magnetic field integral from the vertex point to theDC.

with infinitely high momentum would be reconstructed with an angle ↵ = 0
CHAPTERANALYSISanda low pT 3.
particleis reconstructed with a large angle ↵.

64

Figure 3.4: The schematic view of a track reconstruction by the Drift ChamFigure
angle
ber in2.6
x-yTheplane[63] is measured in the Drift Chamber. This angle is proportional
to charge/pT .

3.4

Electron and positron identification

We describe the electron identification that is called eID in this section.
Several variables from RICH and EMCal measurements are employed forthe eID.The
The eID
is applied
to the charged particle tracks. We consider the
2.2.3
Pad
Chambers
following variables for the eID summarized in Table 3.1.
The electron identification variables in the RICH are n0, chi2/npe0, and
disp,
while
the variables
theis EMCal
are subsystem
emcsdphi e,which
emcsdze, and particle
dep.
The
Pad
Chambersystem in[18]
the second
providestracking
information. It determines space points along straight line particlen0
The n0 variable
the magnetic
number offield.
hit RICH photomultipliers. The variable
trajectories
outsideis thecounts the hits within an annular region with a radius between 3.4 and 8.4
cm around the track projection. In comparison, a Cherenkov ring emitted
The innermost Pad Chamber called PC1 is located between the Driftby an electron is expected 5.9 cm radius in the RICH detector. We require
the cut with n0 1.
Chamber and the RICH. In the west arm the PC2 is mounted behind the18CHAPTER 3. ANALYSIS

65

Table 3.1: The summary of electron identification cuts used in this studyeID cutsn0
chi2/npe0
q disp2+2condition
1
 15
 7.5
z

dep
pT

3

 -2
0.3 GeV/c

disp
The disp variable is displacement which is the distance between the ring
P center and the track projection. We define the npe0 variable as npe0 = i npei .
The npe0 means the number of photo-electrons within the association radius.
The ring center is reconstructed using npe0 as
PiRi ⇥ Npercenter ⌘
(3.4)
npe0
The disp variable is calculated asqdisp ⌘ (zcross zcenter )2(Rcross

Rcenter )2(3.5)

where Rcenter = (rcenter , zcenter ) and (rcross , zcross ) is the coordinate which is
the track projection onto the PMT plane.
chi2/npe0
The chi2 variable is a 2 -like variable of the Cherenkov ring shape between
the expected and measured rings. The npe0 variable is the number of photoelectrons measured in a given RICH ring. The chi2/npe0 is defined asP
i(Ri R0 )2 ⇥ Npe
chi2/npe0 ⌘ rasso
(3.6)
npe0
where ri is the hit PMT position, r0 is the projection point of an associatedi
track, and Npeis the number of photo-electrons.

CHAPTER 3. ANALYSIS

66

emcsdphi e and emcsdz e
The emcsdphi e and emcsdz e are the distance between the track projection
position and hit position in the EMCal divided by the standard deviation.
The hit position is the center of the energy cluster at the surface of the
EMCal in azimuthal emcdphi and z-direction emcdz, while the coordinate of
the track projection in pemcdphi and pemcdz. The emcsdphi e and emcsdz e
are expressed as follows:
emcsdphi ⌘emcsdz ⌘emcdphipemcdphi
emcdphi (p)emcdz

pemcdz.
emcdz (p)

(3.7)
(3.8)

dep
The dep variable is a quantification of an energy-momentum matching. For
electrons with momentum above 200 MeV, their mass (me = 511keV/c2 ) canbe negligible. Consequently, the energy deposited in the EMCal must matchthe momentum. The variable is calculated as
dep ⌘

(E/p

1)

(3.9)

E/p

where E and p is a measured energy in the EMCal and track momentum,
respectively. E/p denotes the standard deviation of the E/p distribution.
Summary of electron identification
The RICH related variables n0 and npe0 express the association quality between the track and the hits. In contrast, the disp and chi2/npe0 represent thering shape reconstruction quality in the RICH. The combination of emcsdphi
and emcsdz in the EMCal variables indicate the normalized distance between
track projection position and hit position. The variable dep represents thematching with energy and momentum.

CHAPTER 3. ANALYSIS

3.5

67

Electron pair selection

Reconstructed electron pairs are applied to several pair cuts to reject thebackground electron pairs: fake electron pairs from detector ghosts and photon conversion pairs.
The source of any electrons or positrons is unknown; therefore, all electrons and positrons are combined for composing foreground electron pairs.
Before employing the foreground pairs in this analysis, the pair cuts areapplied to the composed electron pairs.

3.5.1

Detector ghost pair cuts

The first pair cut removes the detector ghost pairs arising if two-electron
candidates share the detector information. These electron pairs correlate
and can be the background. There are two kinds of origins for ghost pairs:
one ghost pairs arise if two electrons have an overlapped RHIC ring, while
another produces if two electrons have an overlapping cluster in the EMCal.
The ghost pairs do not appear in the mixed events used to estimate the
combinatorial background described below section, while only appear in thereal events. Therefore, we need to remove the ghost pairs, and then we apply
the following two pair cuts for the foreground electron pairs.
RICH ring-share rejection| dc | < 0.02 ^ | dczed | < 0.5(3.10)

DC ghost-tracks rejection| cross | < 0.01 ^ | crossz | < 25

3.5.2

(3.11)

Photon conversion cut

Photon conversions are created by the interaction between photons and thedetector material. Real photons from the collisions interact within the beam
pipe made of Beryllium (0.3 X0 ) with a radius of 4 cm. These photons convert to electron pairs with a probability of about 0.2%. These o↵-vertex
electron pairs are passed through a less magnetic field than the PHENIX
tracking algorithm assumes; therefore, it leads to an incorrect reconstruction of the particle momentum and the pair’s opening angle. These miss

CHAPTER 3. ANALYSIS

68

reconstructed pairs have an invariant mass up to mee ⇠ 0.3 GeV/c2 . Hence,
photon conversion must be removed from the analysis.

Bee+beam pipe
Figure 3.5: A schematic image of the production of photon conversion electron pair at the beam pipe [63]Figure Figure
3.11: 3.5
Misreconstructionof theopeningof a conversion
Shown areshows the schematic
imageof a photon
conversion. pair.
A photon
the photon
andfromthetheconversion
pair whichis thecreatedthe andbeam
pipe. The real
originatedcollision interacts
withbeaminpipe,
it converts
opening
betweenoriginal
trajectories(dashedis muchtracks
smaller thaninto angle
an electron
pair.theBlue
and redlines represent
the lines)
reconstructedassuming the PHENIX
while dashedare real tracks.
The back
the reconstructed
opening algorithms,
angle, artificiallycreatedlines
by tracking
the particles
real
openingvertex
angle ofthe pairis much smaller than the reconstructed angle.
to thecollision(dottedlines).
This incorrect reconstruction causes having an apparent mass that increases✓◆
with the distance from the collisions vertex.
Therefore,
photon conversion
wthe· uainvariant mass distribution.
electron pairs occur in the specificregionsin.
(3.14)
V = arccos|w||ua|at mee ⇡ 20 MeV/c2 , while
Corresponding the beam pipe origin pairs appear
the detector material origin appears at mee ⇡ 80 MeV/c2 and mee ⇡ 125
HereMeV/c
p1 is 2 .the3-momentum
vectorof the electron
and p2 peakthe 3-momentum
Moreover,the Heliumbag contributes
the conversion
mee 
2
300ofMeV/c.
vectorthe positron.
The following cuts are applied:
To reject the conversion electron pairs, we apply the v cut on the pairs’•orientationm < 0.60in&&
rad The v is defined as
the magnetic
V > 0.1field.

• m < 0.03 &&V

p1 + p2> 0.25 radu=|p1 + p2 |(3.12)To remove beam pipe conversions a harder cut has to be applied, because
v = p1 ⇥ psmears(3.13)respect2
the multiple scattering within Beryllium
the orientation withto the magnetic field more than in air. In addition the resolution of the V
measurement improves with increasing conversion radius. This cut removes> 98% of all conversion pairs.

3.4.3

Event Mixing

As mentioned in the introduction to this Section, most of the e+ e pairs are of

CHAPTER 3. ANALYSIS

69! =u⇥vu ⇥ ẑ
|u ⇥ ẑ|✓◆! · uav = arccos|!||ua |ua =(3.14)(3.15)(3.16)

where p is a momentum vector of electrons, and z is a unit vector of zdirection.

3.6

Electron pair invariant mass

Identified electrons and positrons reconstruct their pair invariant-mass. The
invariant mass of electron pairs are calculated as follows:qmee = (Ee+ + Ee )2 (pe+ + pe )2(3.17)

where E is an energy, and p is a momentum vector of electron and positron.
The square of the energies are calculated from the electron mass andmomentum as:
✓q
◆2
q
2
(Ee+ + Ee ) =m2e+ + p2e+ + m2e + p2e(3.18)
where me is the electron mass = 511 keV/c2 .
The transverse momentum of the pair is calculated as:qpT = (px,+ + py,+ )2 + (px, + py, )2 .

3.7

(3.19)

Detector response in simulations

This section describes the tuning of electron identification variables and detector response, including the acceptance in the simulation. The PHENIX
detectors include a mix of good and bad areas. To stabilize the acceptance,
we remove the lousy acceptance areas from the analysis and discrepancy between the data and the simulations. To evaluate background contributions

CHAPTER 3. ANALYSIS

70

and known hadronic components, we use Monte Carlo simulations; one simulation is for particle decays. Another is for reproducing detector response,
including geometrical acceptance and electron identification efficiencies. The
detector response in simulations must match with the experimental data due
to reproducing background distributions precisely. Therefore, we tune thedetector response in the simulations to replicate the experimental data andconfirm their agreement.

104

104

Single-electron pT

Single-positron pT

Data
Simulation

103

Data
Simulation

103

102

102

10

10

1

1

0

1

2

3

4
5
6
pT [GeV/c]

7

8

9

10

0

1

2

3

4
5
6
pT [GeV/c]

7

8

9

10

Figure 3.6: Single electron pT compare with the data and the simulation
At first, we describe the distribution tuning of single-electron transverse
momentum. EXODUS is a fast Monte Carlo simulation of hadron decays,
and it simulates the particle generations and decays. It can reproduce given
decay modes for a given particle. The input shape of transverse momentum
in the EXODUS simulation is the modified Hagedorn function described inSec. 3.9.3. Generated particles in EXODUS are passed through the PISA
simulation. PHENIX Integrated Simulation Application, named PISA, isa GEANT3-based Monte Carlo simulation [74], and it simulates a detector
response, including reconstruction efficiencies, detector smearing, materiale↵ects, and detector oriented backgrounds [75].
Figure 3.6 shows the transverse-momentum distribution comparison between the data and the simulation for electrons and positrons. In order tocompare the distribution, electron pairs in the experimental data are selectedwith the invariant mass mee < 0.03 GeV/c2 where ⇡ 0 Dalitz decay electrons

CHAPTER 3. ANALYSIS

71

are dominant region. In the simulation, ⇡ 0 Dalitz decays are simulated, andthe generated electrons and positrons are passed through the PISA to simulate the PHENIX detector response. The black and red markers in the figure
denote the experimental data and simulation results, respectively. The reproduced distributions by the simulation are compatible with the experimental
data.
dep
Data
Simulation

1400
1200

10000

n0
Data
Simulation

9000
8000
7000

disp
Data
Simulation

8000

1000
6000
6000
800

5000

600

4000

4000

3000
400
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1000

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-10

-8

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dep

0

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20

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5

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20
disp

n0

1400
8000

chi2/npe0
Data
Simulation

7000
6000

sdphi
Data
Simulation

1400
1200

sdz
Data
Simulation

1200
1000

1000
5000

800

800
4000

600

600
3000

200

200

1000
0

400

400

2000

0

5

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15

0
-10

20
chi2/npe0

-8

-6

-4

-2

0

2

4

6

8

10
sdphi

0
-10

-8

-6

-4

-2

0

2

4

6

8

10
sdz

Figure 3.7: The elD variable comparison between the data and the simulationfor electrons.
Next, we explain the tuning of electron identification (eID) variables inthe simulation. Generated particles by the simulation are applied eID cuts,
which are the same as the experimental data analysis. We check the responseof eID variables in the simulation and compare the variable distributions.
Figures 3.7 and 3.8 show the tuning results of eID variable for both electrons and positrons. The invariant mass of electron pairs in the data is selected below 0.03 GeV/c2 similar to the transverse momentum comparison.
In the simulation, ⇡ 0 Dalitz decay electrons are employed for this comparison. The black and red markers denote the eID variable distributions of thereal data and simulation results, respectively. The tuned eID variables in thesimulation are agreeable with the data.
Lastly, we apply the fiducial cuts to reject the unstable or dead areas in
the detectors. The PHENIX detector contains unstable and dead areas, andthese regions are rejected in the experimental data analysis. In the simula-

CHAPTER 3. ANALYSIS

1400

72

10000

dep
Data
Simulation

1200
1000

10000

n0
Data
Simulation

8000

6000

800
600

disp
Data
Simulation

8000

6000

4000

4000

2000

2000

400
200
0
-10

-8

-6

-4

-2

0

2

4

6

8

10
dep

0

0

5

10

15

0

20

0

5

10

15

20
disp

n0

1600
8000

chi2/npe0
Data
Simulation

7000
6000

1200

1000
800

800

4000

600

600

3000
2000

400

1000

200

0

5

10

15

0
-10

20
chi2/npe0

sdz
Data
Simulation

1200

1000

5000

0

1400

sdphi
Data
Simulation

1400

400
200

-8

-6

-4

-2

0

2

4

6

8

10
sdphi

0
-10

-8

-6

-4

-2

0

2

4

6

8

10
sdz

Figure 3.8: The elD variable comparison between the data and the simulation
for positrons.
tion, we apply the same fiducial cuts in the experimental data to reproduce
the insufficient areas. We consider the two main detectors, the Drift Chambers and the EMCal, for this tuning.
Figure 3.9 represents the Drift Chamber’s hit maps of single electronsand positrons in the data and the simulation. The map is broadly divided
into four segments; In a clockwise direction, North-West, North-East, SouthWest, and South-East are located. The horizontal axis represents zed, whilethe vertical axis is dcphi. The zed parameter is the z coordinate at which
the particle track crosses the PC1. The dcphi is the coordinate of azimuth
angle at which the particle track crosses the DC reference radius. The lowefficiency areas are rejected, and the hit map on the simulation is compatible
with the data.
Figure 3.10 shows the EMCal’s hit maps for both the data and the simulation. The hit maps consist of four segments as well as the DC’s. The
horizontal axis represents emc-z. Meanwhile, the vertical axis denotes theemc phi. These variables represent z and coordinate, respectively. The
low-efficiency areas indicated the box-shape are removed from both the data
and the simulation.

CHAPTER 3. ANALYSIS

73

16

3.5

14

3
12

dcphi

2.5
10

2

Data

1.5

8

1

6

0.5
4

0
2

-0.5

dcphi

-1
-100

-80

-60

-40

-20

0
zed

20

40

60

80

0

3.5

9

3

8

2.5

7

2

6

Simulation

1.5

5

1

4

0.5

3

0

2

-0.5

1

-1
-100

-80

-60

-40

-20

0
zed

20

40

60

80

0

Figure 3.9: Hit map for dcphi and zed

3.8

Overview of background subtraction

Direct virtual photon contribution is extracted as an excess over the known
significant component from hadron decays after subtracting extensive backgrounds. The signal-to-background ratio (S/B) is only a few percent in p+p
and d+Au collisions, whereas the S/B reaches 15% in Au+Au collisions.
Therefore, precise background estimation plays an essential role in this analysis.
We employ a simulation-based approach to background estimation andsubtraction in this analysis. This approach employs well-tuned Monte Carlosimulations to estimate correlated backgrounds, together with the data for
the uncorrelated background estimation. The advantage of the approach isthat it realizes a smaller statistical error than a data-driven approach. The
data-driven approach is a background estimation method using the foreground like-sign electron pairs. The reproduced total background by theCHAPTER 3. ANALYSIS

74

emc phi

10

3.5

9

3

8

2.5

7

2

6

Data

1.5

5

1

4

0.5

3

0

2

-0.5

1

-1
-200

-150

-100

-50

0
emc z

50

100

150

0

3.5
5

3

emc phi

2.5

4

2

Simulation

1.5

3

1
2

0.5
0

1

-0.5
-1
-200

-150

-100

-50

0
emc z

50

100

150

0

Figure 3.10: Hit map for emcphi and emc-z
simulation-based approach is compared to the data-driven approach as across-check.
We explain the simulation-based approach first and then describe thedata-driven approach and a cross-check for the background estimation in thefollowing sections.

3.9

Simulation-based approach

In the simulation-based approach, background contributions are estimatedby both the experimental data and the well-tuned Monte Carlo simulations.
After removing detector-oriented fake pairs and conversion pairs, the foreground distributions for unlike-sign (FG+ ) and like-sign (FG++ and FG )pairs can be expressed as

CHAPTER 3. ANALYSIS

75= BGCM + BGXC + BGJP = BGSUM(3.20)XC
JP
SUM
FG++ = BGCM++ + BG++ + BG++ = BG++

(3.21)

FG

FG+= S + BGSUM+ HD+ .
+

(3.22)

The foregrounds (FG) for like-sign pairs are consisted of three kindsof backgrounds; combinatorial background (CM), jet-induced electron pairs(JT), and correlated cross pairs from Dalitz and double Dalitz decays (XC),
while the foreground for unlike-sign structured the backgrounds, correlated
electron pairs from hadron decays, and the signal arising from the virtualphotons. It is notable that the like-sign foregrounds are composed of only
backgrounds, while the unlike-sign foreground includes hadronic and virtualphoton contributions.
The signal component is extracted by subtracting backgrounds from theforeground in unlike-sign pairs. The foreground shapes are reproduced by
the data, while the background shapes are calculated by both the data andthe well-tuned Monte Carlo simulations. The total background distribution is
obtained from the foreground simultaneous fit by all background components
in the like-sign pairs. The scaling factors calculated by the fit can be diverted
into the background scaling for unlike-sign pairs.
Table 3.2 is the summary of the components in foregrounds. Each background estimation are described in the below sections.
Table 3.2: Signal and background contributions in low mass electron pairs.
Component
SignalCombinatorial backgroundJet-induced pair
Correlated cross pair
Hadron cocktail

SourceSymbolDirect virtual photons
S
Uncorrelated origin
BGCM
Near and away sides jets
BGJP
Dalitz and double Dalitz decays BGXC
Hadron decaysHDCHAPTER 3. ANALYSIS

3.9.1

76

Combinatorial backgroud

The combinatorial background is arising from a random combination of uncorrelated electron and positron pairs. Electron pairs are reconstructed withall combinations because we can not identify the correct pairs which are originated from the same parent particle. Therefore, we estimate the distributionof the uncorrelated pairs and subtract them.
The event mixing technique is widely used to reproduce the combinatorial background. This technique uses di↵erent collision events with similar
event topology, and electron pairs are created from two di↵erent events. Similar topology events are selected by using z-vertex position, centrality, andreaction plane. The electron pairs created by the technique can reproduce
uncorrelated pairs because two di↵erent collisions are completely uncorrelated. The event mixing technique has a benefit to reduce the statisticalerror due to increasing the statistics by deepening accumulating in a bu↵er.
As reported in the previous study [27], the traditional event-mixing technique does not fully replicate the foreground combinatorial background. The
elliptic flow leads to the modulation of the foreground combinatorial background distribution. Elliptic flow is an azimuthal anisotropy of particle emission. In non-central heavy-ion collisions, the participant region’s shape iselliptical; in other words, created particles distribute are not uniformly distributed to the reaction plane. The pressure gradient of the hot-and-dense
matter depends on the direction, and particles in the matter expand according to the pressure gradient. This fluid flow leads to elliptic flow, and particles
are observed with non-uniform distribution on momentum space. The electron pairs reproduced by the event-mixing method are randomly picked-up
pairs from the di↵erent events; therefore, they do not have any flow e↵ect on
average. However, in the foreground combinatorial pairs, they are inherentlya↵ected by the flow.
The modulation between the foreground combinatorial background andthe event-mixing background is to be solved if the reaction plane is measured
with perfect resolution. The standard event-mixing technique reproduces the
combinatorial background shape using the same topology events with selecting reaction plane, centrality, and z-vertex. The resolution of the reaction
plane measured by the PHENIX detector has a limitation. Consequently, theevent mixing can not adequately reproduce the uncorrelated combinatorial
background shape. To consider the elliptic flow e↵ect on the event-mixing
method, we employ a weighting method that the flow e↵ect weights the re-CHAPTER 3. ANALYSIS

77

produced shapes.

0.2
0.18

RP resolution

0.16

Beam-Beam Counter

RP resolution

0.14

Cu+Cu collisions at sNN = 200 GeV

0.12
0.1
0.08
0.06
0.04
0.02
0
0

10

20

30

40

50

60

70

80

Centrality [%]Figure 3.11: Reaction plane resolution as a function of centrality measuredpwith the BBC detector in Cu+Cu collisions at sN N = 200 GeV
The elliptic flow can be expressed as the following equation:dN ( )/ 1 + 2v2 cos 2 .
d(3.23)

where v2 is the second-order Fourier coefficient, and the is the azimuthal
angle [27]. Hence, the random combination of the anisotropy a↵ected particles distributes asw( ab ) = 1 + 2v2,a v2,b cos 2 ( ab)(3.24)

where a(b) and v2,a(b) are the pair opening angle and azimuthal anisotropyof each electron in a pair, respectively. The combinatorial background pairs
reproduced by the event-mixing method, the mixed background pairs, areweighted by the w. To evaluate the w, we measure single electron elliptic
flow, v2 as a function of transverse momentum for each centrality class.

CHAPTER 3. ANALYSIS

78

Single electron v2 is measured by the event plane method [76]. The event
plane method is a widely used technique to measure the anisotropy in heavy
ion collisions. Single electron v2 is measured with the equation
v2 = phcos (2 [hcos (2 [2,BBCNorth2 ])i
2,BBCSouth ])i(3.25)

where is the azimuthal angle of an electron, 2 is the reaction plane angle
measured by both BBC North and South, and the denominator represents
the reaction plane resolution caused by the finite multiplicity. The reaction
plane angle is determined byP✓◆wi sin (2 i )
1
1
i
tan P
.
(3.26)
2 =2
i wi cos (2 i )Figure 3.11 shows the reaction plane resolution as a function of centrality measured by the BBC detector. The evaluated results are used as thedenominator in Equation 3.25.
Figure 3.12 shows the results of the single-electron elliptic flow, v2 , as afunction of transverse momentum. We measure the elliptic flow with four
centrality bins: 0–10, 10–20, 20–40, and 40–94%. We apply a simple exponential function fit to the measured v2 . The fit function is expressed by
A/ exp (B/pT ), where A and B are the free parameters, and they are calculated by the least-squares method. The best-fit results are listed in Table
3.3, and they are used for the weight calculation in Eq. 3.24.
Table 3.3: The best-fit parameter values in A/ exp (B/pT ) for single-electronpelliptic flow in Cu+Cu collisions at sN N = 200 GeV
Centrality
0–10%
10–20%
20–30%
30–40%
40–94%

A
0.123
0.163
0.165
0.256
0.154

B
0.243
0.326
0.251
0.593
0.291

CHAPTER 3. ANALYSIS

79

0.5

0.5

Inclusive single electron v
2
Cu+Cu at sNN = 200 GeV
0-10%
Data
fit func = 0.158/exp(0.424/pT)

0.4

Cu+Cu at sNN = 200 GeV
10-20%
Data
fit func = 0.176/exp(0.352/pT)

0.4

flow v 2

0.3

flow v 2

0.3

0.2

0.2

0.1

0.1

0
0

0.5

1

1.5

2

2.5

3

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4

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single electron pT (GeV/c)

1.5

2

2.5

3

3.5

4

4.5

5

4

4.5

5

single electron pT (GeV/c)

0.5

0.5

Cu+Cu at sNN = 200 GeV
20-40%
Data
fit func = 0.214/exp(0.408/pT)

0.4

Cu+Cu at sNN = 200 GeV
40-94%
Data
fit func = 0.132/exp(0.211/pT)

0.4

flow v 2

0.3

flow v 2

0.3

0.2

0.2

0.1

0.1

0
0

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1

1.5

2

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5

0
0

0.5

single electron pT (GeV/c)

1

1.5

2

2.5

3

3.5

single electron pT (GeV/c)

Figure 3.12: Single-electron elliptic flow v2 as a function of transverse mop
mentum with the best-fit result in Cu+Cu collisions at sN N = 200 GeV

3.9.2

Jet-induced correlated pairs

Jet-induced correlated pairs are a background that is produced by two electrons originated from the same jet or back-to-back jets. A jet is a phenomenon that particles are generated concentratedly at a narrow angle. The
initial hard scattering of partons generates the jets. The scattered partonstraversing the medium lose their energy through bremsstrahlung and collisional energy loss and then fragment into collimated particles called jets. The
event mixing technique can not remove the jet-induced electron pairs due totheir correlation. Thus, the invariant mass shape of the jet-induced pairs isevaluated by Monte Carlo simulations.
PYTHIA8 with CTEQ5L parton distribution function simulates jet events
to produce the correlated electron pairs [77, 78, 79]. PYTHIA is a Monte
Carlo simulation widely used in high-energy particle physics for the particle

CHAPTER 3. ANALYSIS

80

Table 3.4: Considered QCD processes in PYTHA simulation. g denotes a
gluon, fi,j,k are fermions with flavor i, j, and k, and f¯i,j,k are the corresponding antiparticles.
MSUB 11 fi fj ! fi fj
MSUB 12 fi f̄i ! fk f¯kMSUB 13fi g ! gg
MSUB 28 fi g ! fi g
MSUB 53 gg ! fk f¯kMSUB 68
gg ! gg

generation from a hard process to a multihadronic final state. We consider
hard quantum-chromodynamics (QCD) processes tabulated in Table 3.9.2.
The evaluation procedure is the same as Reference [27], but PYTHIA8 is usedin this work. Generated particles in the final state in the PYTHIA8 simulation are passed through a GEANT3-based simulation PISA of the PHENIX
detector to consider the detector acceptance and efficiencies.
The foreground electron pairs from the PYTHIA events consist of jetinduced pairs that we are interested in, physical pairs, cross pairs, and combinatorial pairs expressed as
CM
XC
JT
FGsim = BGPP
sim + BGsim + BGsim + BGsim(3.27)

where BGPP
sim denotes the physical pair. Therefore, the jet-induced pairs are
extracted from the foreground pairs from the simulation.
The event-mixing technique evaluates uncorrelated combinatorial backgrounds in the simulated events. It is found that the shape of the like-signinvariant mass distribution for mixed pairs is consistent with that for theforeground pairs in 0.6 < mee < 1.1 GeV/c2 . The specific invariant mass
region is employed for the normalization of the mixed pairs. The physicalpairs and cross pairs are excluded from the foreground by requiring that thepair’s two electrons do not share the same particle in their history. After
subtraction and rejection of combinatorial pairs, physical pairs, and crosspairs, the remaining pairs expresses the jet-induced correlated electron pairs.
The invariant mass shapes for jet-induced electron pairs evaluated by thesimulation are shown in Fig. 3.13. It is known that jets passing througha medium lose energy, and the phenomenon is called jet-quenching. Ac-

CHAPTER 3. ANALYSIS
10

81

10

10

10

- -

e e pairs
11

1.0 < p < 1.5 GeV/c
T

near-side
away-side

10− 1

1

1.5 < p < 2.0 GeV/c
T

near-side
away-side

10− 1

1

2.0 < p < 3.0 GeV/c
T

near-side
away-side

10− 1

T

10− 2

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10− 3

10− 3

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−4

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10

10

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0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5mee (GeV/c2)
10

10

10− 5
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5mee (GeV/c2)

10− 5
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5mee (GeV/c2)

10

10

1

1

3.0 < p < 5.0 GeV/cnear-side
away-side

10− 1

10− 5
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5mee (GeV/c2)
10e+e+ pairs
1

1.0 < p < 1.5 GeV/c
T

near-side
away-side

10− 1

1.5 < p < 2.0 GeV/c
T

near-side
away-side

10− 1

1

2.0 < p < 3.0 GeV/c
T

near-side
away-side

10− 1

T

10− 2

10− 2

10− 2

10− 2

10− 3

10− 3

10− 3

10− 3

−4

−4

−4

10− 4

10

10

10− 5
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5mee (GeV/c2)
10

10

10− 5
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5mee (GeV/c2)

10− 5
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5mee (GeV/c2)

10

10

1

1

3.0 < p < 5.0 GeV/cnear-side
away-side

10− 1

10− 5
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5mee (GeV/c2)
10-e+e pairs
1

1.0 < p < 1.5 GeV/c
T

10

−1

near-side
away-side

1.5 < p < 2.0 GeV/c
T

10

−1

near-side
away-side1

2.0 < p < 3.0 GeV/c
T

10

−1

near-side
away-side

10− 2

10− 2

10− 2

10− 2

10− 3

10− 3

10− 3

10− 3

−4

−4

−4

10− 4

10

10− 5
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5mee (GeV/c2)

10

10− 5
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5mee (GeV/c2)

10

10− 5
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5mee (GeV/c2)

3.0 < p < 5.0 GeV/c
T

10

−1

near-side
away-side

10− 5
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5mee (GeV/c2)

Figure 3.13: Invariant mass distributions for near-side jet and back-to-backjets evaluated by the PYTHIA8 and PISA simulations.
cordingly, the scaling factors of near- and away-side jets are supposed tobe di↵erent in heavy ion collisions. Therefore, the electron pairs from thesame jet and the back-to-back jet are separately plotted. The opening anprim
gleof the two electrons defines the origin of the correlated pair: if
0
prim
prim
<
⇡/2,
the pairs are originated by the same jet. if> ⇡/2, the00pairs are produced by the back-to-back jet.

CHAPTER 3. ANALYSIS

3.9.3

82

Correlated cross pairs

Another non-negligible background arises from double Dalitz decays of the⇡ 0 and ⌘ mesons:⇡ 0 ! e+
1 e1

⇤

+
! e+
1 e1 + e2 e2⌘ ! e+
1 e1

⇤

+
! e+
1 e1 + e2 e2 .

(3.28)

Dalitz decay is a meson decay, and it creates two leptons and a photon in
the final state. Double Dalitz decay is also a meson decay that involved avirtual photon, and it produces four particles in the final state. The crosscombination of electrons from double Dalitz decays give rise to two unlike++ +sign pairs (e+1 e2 and e2 e1 ) and two like-sign pairs (e1 e2 and e1 e2 ). Theseelectron pairs are not a thoroughly combinatorial background, but they areassociated with the ⇡ 0 or ⌘ invariant mass and momentum. Therefore, thecontribution can not be reproduced by the event-mixing method, and it isneeded to evaluate independently.
The Dalitz decay of the ⇡ 0 and ⌘ mesons also lead to the correlated crosspairs if a photon converts into electron pairs via external conversion. A real
photon interacts with detector matters, and it probabilistically decays into
an electron pair. The decays express as:⇡ 0 ! e+
1 e1

+
! e+
1 e1 + e2 e2⌘ ! e+
1 e1+! e+
1 e1 + e2 e2 .

(3.29)The Dalitz decays with the external conversion have four-electrons in the
final state, and then these are taken into account in reproducing the crosspair invariant-mass shape. The contribution from Dalitz decays with theexternal conversion is considered in Reference [27].
The correlated cross pairs themselves can not be reconstructed individually by the data. We employ the Monte Carlo simulations of EXODUS andPISA to calculate the shape of cross pair invariant-mass. The key input to
EXODUS is the momentum distributions. The ⇡ 0 momentum distribution inp
Cu+Cu collisions at sN N = 200 GeV measured by the PHENIX experiment

CHAPTER 3. ANALYSIS

83

is successfully parameterized by a modified Hagedorn function [80, 81]:
E

⇣
⌘ n
d3
(apT +bp2T ) + p /p
=
A
e
.
T
0
dp3

(3.30)The parameters in the function for three centrality bins are summarized inTable 3.9.3. The momentum distribution of the ⌘ meson is obtained from thetransverse invariant-mass scaling, called mT scaling [82]. The parameterized
spectra by the mT scaling are calculated with replacement pT byq
p2T m2⇡0 + m2h(3.31)
where m⇡0 is invariant mass of the ⇡ 0 meson, and mh denotes the invariant
mass of hadrons.

Table 3.5: The parameters in the modified Hagedorn function for the ⇡ 0meson for 0–40%, 40–94%, and minimum bias centrality bins in Cu+Cup
collisions at sN N = 200 GeV

Fit parameter
A [mbGeV 2 c3 ]a [(GeV/c) 1 ]b [(GeV/c) 2 ]p0 [GeV/c]n0–40%(3.5 ± 2.8) ⇥ 102
0.41 ± 0.22
0.22 ± 0.16
0.70 ± 0.09
8.02 ± 0.15

40–94%(3.5 ± 3.7) ⇥ 10
0.49 ± 0.54
6.4 ⇥ 10 3 ± 0.46
0.80 ± 0.76
8.28 ± 2.58

Minibum Bias
(1.8 ± 0.6) ⇥ 102
0.42 ± 0.09
0.20 ± 0.07
0.69 ± 0.04
8.01 ± 0.07

The EXODUS and PISA simulation procedure is as follows: First, Dalitz
and double Dalitz decays of the ⇡ 0 and ⌘ mesons are produced by EXODUS.
The particle generations follow with the flat vertex distribution with |z| <30 cm, flat pseudorapidity distribution within |⌘| < 0.6, and the uniform
azimuthal distribution within 0 < < 2⇡. The modified Hagedorn function
weights the transverse momentum distributions. Second, generated electronsand positrons are passed through the PISA simulation to consider detector
reconstruction efficiencies, smearing, and material e↵ects. Third, we apply
the electron identification and the pair cuts procedures, which are the sameas the experimental data analysis. After the selections, we reproduce theCHAPTER 3. ANALYSIS
10
1

Cross pairs, Cu+Cu MB

10− 1

e e pairs
1.0 < p < 1.5 GeV/c

84

10

10

1

1

10
1

- -

10− 1

10− 1

1.5 < p < 2.0 GeV/c

T

10− 1

2.0 < p < 3.0 GeV/c

T

T

10− 2

10− 2

10− 2

10− 3

10− 3

10− 3

10− 3

10− 4

10− 4

10− 4

10− 4

10− 5

10− 5

10− 5

10− 5

−6

−6

−6

10

0

0.2

0.4
0.6
0.8
mee (GeV/c2)

1

10

0

0.2

0.4
0.6
0.8
mee (GeV/c2)

1

10

0

10

10

10

1

1

1

e+e+ pairs
1.0 < p < 1.5 GeV/c

10− 1

10− 1

0.2

0.4
0.6
0.8
mee (GeV/c2)

1

10− 6
0

T

T

10− 2

10− 2

10− 3

10− 3

10− 3

10− 3

10− 4

10− 4

10− 4

10− 4

10− 5

10− 5

10− 5

10− 5

10− 6
0

10− 6
0

10− 6
0

1

0.2

0.4
0.6
0.8
mee (GeV/c2)

1

10

10

10

1

1

1

1

3.0 < p < 5.0 GeV/c

T

10− 2

0.4
0.6
0.8
mee (GeV/c2)

0.4
0.6
0.8
mee (GeV/c2)

1
10− 1

2.0 < p < 3.0 GeV/c

10− 2

0.2

0.2

10

10− 1

1.5 < p < 2.0 GeV/c

T

3.0 < p < 5.0 GeV/c

T

10− 2

0.2

0.4
0.6
0.8
mee (GeV/c2)

1

10− 6
0

0.2

0.4
0.6
0.8
mee (GeV/c2)

1

10
1

-

e+e pairs
10− 1

10− 1

1.0 < p < 1.5 GeV/c

10− 1

1.5 < p < 2.0 GeV/c

T

10− 1

2.0 < p < 3.0 GeV/c

T

T

10− 2

10− 2

10− 2

10− 3

10− 3

10− 3

10− 3

10− 4

10− 4

10− 4

10− 4

10− 5

10− 5

10− 5

10− 5

10− 6
0

10− 6
0

10− 6
0

0.2

0.4
0.6
0.8
mee (GeV/c2)

1

0.2

0.4
0.6
0.8
mee (GeV/c2)

3.0 < p < 5.0 GeV/c

T

10− 2

1

0.2

0.4
0.6
0.8
mee (GeV/c2)

1

10− 6
0

0.2

0.4
0.6
0.8
mee (GeV/c2)

Figure 3.14: The invariant mass shapes for ⇡ 0 and ⌘ cross pairs produced byp
the EXODUS and PISA simulation with the configuration of sN N = 200
GeV Cu+Cu collisions.
invariant mass distribution of the cross pairs from the Dalitz and double
Dalitz decays. The relative scale between ⇡ 0 and ⌘ is normalized by the ⇡ 0
to meson ratios measured by the PHENIX experiment. Further, each decay
modes are weighted by their branching ratios.
Reproduced invariant mass shapes of the ⇡ 0 and ⌘ cross pairs for minimum
bias events are shown in Fig. 3.14. The lower side peak is produced from⇡ 0 decays, while the higher side peak arises from ⌘ decays. The invariant
mass distributions are produced for each centrality bin with four transverse
momentum region for like- and unlike-sign pairs.

1CHAPTER 3. ANALYSIS

3.10

85

Background normalization

We explain the background normalization in this section. The backgroundshapes evaluated in the previous sections are normalized to the foreground
distribution. The normalization is done by a four-component fit, which issimultaneously fit to the foreground distribution FG by the background comJT
XC.
ponents, BGCM , BGJT
near , BGaway , and BG
FG++,=nCM BGCM++,

near+ nJPnear BGJP++,JP

+ nJPaway BG++,away + nXC BGXC++,

= BGSUM++,(3.32)

where nCM , nJPnear , nJPaway , and nXC are the normalization factor to be evaluated by the fit. In the fit, jet-induced pairs from the same-jet (near-side)and the back-to-back jet (away-side) are treated separately because the e↵ectof jet quenching is assumed to be di↵erent. If partons pass-through createdhot-and-dense matter in the heavy-ion collision, they might lose their energy,
called the jet quenching phenomenon. Therefore, it is reasonable to assume
that the same- and back-to-back jets’ normalization factor is di↵erent. The
fit is applied to both like-sign BG and BG++ distributions simultaneously.
The four-component fit is done with the transverse momentum 1 < pT < 5
GeV/c for each centrality bin. Figure 3.15 shows the like-sign and unlikesign invariant mass distributions of the foreground FG together with thenormalized background BGSUM for minimum bias events. The normalized
BGSUM has a good agreement to the data for like-sign pairs. Meanwhile, there
is a significant deviation between the BGSUM
and the foreground distribution+of unlike-sign pairs below the 0.3 GeV/c2 region. This deviation contributes
from the signal and the known hadron decays described in Sec. 3.13.
The calculated normalization factors are applied to the normalizationfor each transverse-momentum range. Further, the calculated normalization
factors in like-sign distributions are employed for the scaling of unlike-sign
background distributions. Figures 3.16, 3.17, and 3.18 show the results on
the fits for minimum bias, 0–40%, and 40–94% centrality events, respectively.
The top panels in each figure represent the like-sign invariant mass distributions of the data together with the normalized background components, andthe bottom panels express the unlike-sign distributions. The total evaluatedbackgrounds BGSUM are compatible with the foreground distributions FG for
like-sign electron pairs.

CHAPTER 3. ANALYSIS(a)

Cu+Cu, sNN=200GeV
e−e− + e+e+: 1<pT<5GeV/c

3

Number of pairs

10

86

102

FG− −+FG++
SUM
BGSUM
− − +BG++

FG/BGSUM

10
1.40
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

(b)

(c)

mee (GeV/c 2 )Cu+Cu, sNN=200GeV
e+e−: 1<pT<5GeV/c

Number of pairs

104
103
102

FG+ −
BGSUM
+−

10
FG/BGSUM

0

10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

(d)

1
0

mee (GeV/c 2 )Figure 3.15: Like-sign and unlike-sign electron-pair invariant-mass distributions of the data together with evaluated backgrounds for Cu+Cu minimum
bias events.

3.11

Data-driven approach

We explain the data-driven approach, which is another method for background estimation in this section. This method is mainly applied for a crosscheck of the background estimation in this study. The data-driven approachis a well-known technique as the like-sign subtraction method [83]. The
method demonstrates the background distribution by the foreground-likesign electron pairs corrected the acceptance e↵ect. The like-sign foregroundCHAPTER 3. ANALYSIS
10102

e−e−+e+e+: 1.5<p <2.0

FG
SUM

BG

fit

MX
BG+ −
XC
BG+ −
JT
BG+ −

1

0.2

104

0.4

1

e+e−: 1.0<p <1.5

0

0.2

0.6
0.8
1
mee (GeV/c2)

102
10
1

T

10−2

10−1

10
1

10

0

0.2

0.4

0.6
0.8
1
mee (GeV/c2)

e+e−: 2.0<p <3.0

10
1

0.4

0.6
0.8
1
mee (GeV/c2)

0

0.2

0.4

0.6
0.8
1
mee (GeV/c2)

e+e−: 3.0<p <5.0
T

10
1

10−1

10−2

10−2
0.2

10−30

102

T

10−1

−2

0.6
0.8
1
mee (GeV/c2)

10−2
0

102

10−1
0.4

T

1

10−1

103

e+e−: 1.5<p <2.0103
Number of pairs

0.4

102

0.2

1

10−1

0.6
0.8
1
mee (GeV/c2)T0e−e−+e+e+: 3.0<p <5.0

T

10−1

103

Number of pairs10e−e−+e+e+: 2.0<p <3.0

10

Number of pairs

100

Number of pairs

Number of pairs

102

T

Number of pairs

T

Number of pairs

Cu+Cu, sNN=200GeV, MB
e−e−+e+e+: 1.0<p <1.5

Number of pairs

103

87

0.2

0.4

0.6
0.8
1
mee (GeV/c2)

10−3
0

0.2

0.4

0.6
0.8
1
mee (GeV/c2)

Figure 3.16: Like-sign and unlike-sign electron-pair invariant-mass distributions of the data together with evaluated backgrounds for Cu+Cu minimum
bias events.
10
Cu+Cu, sNN=200GeV, 0-40%e−e−+e+e+: 1.0<p <1.5102e−e−+e+e+: 1.5<p <2.0

SUM

BG

fit

MX
BG+ −
XC
BG+ −
JT
BG+ −

1

Number of pairs

Number of pairs

FG

10

10

T

Number of pairs

T

102

10

1

e−e−+e+e+: 2.0<p <3.0

1

10−1

10−2

10−1
−2

e+e−: 1.0<p <1.5
T

0

0.2

0.4

0.6
0.8
1
mee (GeV/c2)

e+e−: 1.5<p <2.0103
Number of pairs

103
Number of pairs

0.6
0.8
1
mee (GeV/c2)

10
1

10
1

10
0.6
0.8
1
mee (GeV/c2)0e+e−: 2.0<p <3.0
T

10
1

0.2

0.4

0.6
0.8
1
mee (GeV/c2)

0

10−30

0.2

0.4

0.6
0.8
1
mee (GeV/c2)

e+e−: 3.0<p <5.0

102

T

10
1

10−1

10−2

10−2

−2

0.4

0.6
0.8
1
mee (GeV/c2)

10−1

10−1
0.2

103

0.4

102

10−1

0

0.2

T

102

102

0

Number of pairs

104

0.4

Number of pairs

0.2

T

1

10−1

10
0

e−e−+e+e+: 3.0<p <5.0T

Number of pairs

103

0.2

0.4

0.6
0.8
1
mee (GeV/c2)

10−3
0

0.2

0.4

0.6
0.8
1
mee (GeV/c2)

Figure 3.17: Like-sign and unlike-sign electron-pair invariant-mass distributions of the data together with evaluated backgrounds for Cu+Cu 0–40%
centrality events.
pairs are only composed of background components, and the like-sign andCHAPTER 3. ANALYSIS

T

e−e−+e+e+: 1.5<p <2.0

fit

MX

BG+ −

XC
BG+ −
JT
BG+ −

10−4
−5

Number of pairs

SUM

BG

10−3

10−2

10−2

FG

10−2

10−3

10−3

10−4

10−4

10−5

10−5

10

0.2

0.4

0.6
0.8
1
mee (GeV/c2)

e+e−: 1.0<p <1.5

103

T

10
1

0.4

0.6
0.8
1
mee (GeV/c2)

e+e−: 1.5<p <2.0
T

102
10
1

10

0.2

0.4

0.6
0.8
1
mee (GeV/c2)

e+e−: 2.0<p <3.0

102

T

1

10

10−4

10−5

10−5

0

0.6
0.8
1
mee (GeV/c2)

10−3

−4

10−4

0.4

10−2

−3

10

10−3

0.2

10−1

−1

10−2

−2

10−6
0

10

10

10−1

10−5
0

0.2

103

Number of pairs

Number of pairs

1020

Number of pairs

0

T

10−1

10−1

10−1

e−e−+e+e+: 2.0<p <3.0

1

T

1

1

Number of pairs

10

Cu+Cu,− −sNN+=200GeV,
40-94%
e e +e e+: 1.0<p <1.5
Number of pairs

10

88

0.2

0.4

0.6
0.8
1
mee (GeV/c2)

10−6
0

0.2

0.4

0.6
0.8
1
mee (GeV/c2)

Figure 3.18: Like-sign and unlike-sign electron-pair invariant-mass distributions of the data together with evaluated backgrounds for Cu+Cu 40–94%
centrality events.
unlike-sign pairs have di↵erent detector acceptance. Therefore, the like-sign
foreground distribution corrected with the detector acceptance can reproduce
the unlike-sign background distribution completely. However, this approach
has a statistical limitation that occurs by the experimental data statistics;
hence, we employ the method as a cross-check for the background estimation.
We compare the reproduced background shape for unlike-sign electron pairs,
BGsum+ , from the simulation-based approach to the background reproducedby the data-driven approach.
The unlike-sign background can be made inferences from the like-sign
foreground pairs. The relative detector acceptance is di↵erent between the
combination of electric-charge sign pairs because the particle trajectory’s
curvature depends on their charge. Therefore, the acceptance correction
must be considered to reproduce the unlike-sign background from the like-CHAPTER 3. ANALYSIS
10

18200GeV Cu+Cu (MinBias)

9161.0<p <1.5GeV/c

8

T

Alpha

Alpha

12
CB+ − /(CB + + +CB− − )

10
6

3

4

2

2

1
0.2

0.4
0.6
0.8
mee (GeV/c2)

0
0

1

15
10

4
5

2
0.2

0.4
0.6
0.8
mee (GeV/c2)

0
0

1

0.2

0.4
0.6
0.8
mee (GeV/c2)

200GeV Cu+Cu (0-40%)9161.0<p <1.5GeV/c

8

T

Alpha

Alpha

CB+ − /(CB + + +CB− − )

10
6

3

4

2

2

1

0
0

0
0

0.2

0.4
0.6
0.8
mee (GeV/c2)

1

3.0<p <5.0GeV/c

T

T

10

20

8

15

6
10
4
5

2
0.2

0.4
0.6
0.8
mee (GeV/c2)

0
0

1

0.2

0.4
0.6
0.8
mee (GeV/c2)

10

18200GeV Cu+Cu (40-94%)

9

16

1.0<p <1.5GeV/c

8

T

14

Alpha

Alpha

CB+ − /(CB + + +CB− − )

10
6

3

4

2

2

12

1.5<p <2.0GeV/c

T

10

0.4
0.6
0.8
mee (GeV/c2)

1

0
0

20

8

15

6
10

3.0<p <5.0GeV/c
T

4
5

2

1
0.2

1

25

2.0<p <3.0GeV/c

T

5
4

0.4
0.6
0.8
mee (GeV/c2)

30

6

8

0.2

14

7

12

0
0

1

Alpha

20

2.0<p <3.0GeV/c

T

5
4

1

25

12

1.5<p <2.0GeV/c

6

8

0.4
0.6
0.8
mee (GeV/c2)

30

7

12

0.2

14

Alpha

14

0
0

1

10

18

0
0

8

Alpha

20

T

20

6

Alpha

0
0

3.0<p <5.0GeV/c

T

10

5
4

2.0<p <3.0GeV/c

T

6

8

25

12

1.5<p <2.0GeV/c

7

Alpha

14

30
14

Alpha

20

89

0.2

0.4
0.6
0.8
mee (GeV/c2)

1

0
0

0.2

0.4
0.6
0.8
mee (GeV/c2)

1

0
0

0.2

0.4
0.6
0.8
mee (GeV/c2)

Figure 3.19: Acceptance correction factor ↵ as a function of electron-pairinvariant mass for each transverse momentum and centrality
sign pairs. The correction factor ↵ is express as
BGsum= ↵acc. (FG++ + FG+).

(3.33)The background in unlike-sign pairs is reproduced by multiplying the sumof like-sign foregrounds by the acceptance-correction factor. The ↵ factor is
calculated as the ratio of like- and unlike-sign pairs in mixed pairs evaluatedin Sec. 3.9.1, and it is represented as↵acc =

BGCM +
BGCM ++ + BGCM.

(3.34)

1

CHAPTER 3. ANALYSIS

90

The acceptance-correction factors, ↵, for each transverse momentum range
are evaluated as a function of electron-pair invariant mass. The factors arecalculated as a function of the invariant mass in this analysis, although thedetector acceptance naturally depends on both invariant mass and transverse
momentum. We confirm that ↵(mee ) is enough for the acceptance correction, not ↵(mee , pT ) with the simulation. To confirm the ↵(mee ) factor works
well, the Dalitz decay simulation for ⇡ 0 and ⌘ is adopted. We compare theinvariant mass distributions produced in the simulation with the acceptancecorrected foreground, ↵(mee )FG, in like-sign pairs and the cross pairs, BGXC .
The ↵(mee )FG distribution reproduces the BGXC well. Therefore, we employ↵(mee ) as the correction factor. Figure 3.19 shows the acceptance-correction
factors for three centrality classes independently; minimum bias, 0–40%, and
40–94%. Figure 3.20 shows the invariant mass distributions for both likesign and acceptance-corrected like-sign foreground pairs with three centrality classes. The acceptance-corrected distributions have been seen the shapemodification around the 1 GeV/c2 in 1.0 < pT < 1.5 GeV/c, as well as othertransverse momentum ranges. These corrected distributions are employed
for the cross-check described in the next section.
The background-subtracted distributions are obtained from the subtraction of acceptance-corrected like-sign distribution from the unlike-sign foreground distribution. Figure 3.21 shows the subtracted invariant-mass distribution, together with the unlike-sign foreground FG+ and ↵(mee )FG++,for three centrality classes.

3.12

Cross-check for background evaluation

We validate the background distributions reproduced by the simulation-based
approach using the data-driven approach as a cross-check. The evaluatedbackground BGSUM
are compared with the acceptance-corrected like-sign+
foreground distributions, FG and FG++ .
The comparisons are shown in Figs. 3.22, 3.23, and 3.24 for minimum
bias, 0–40%, 40–94% centrality events, respectively. The invariant mass
distributions by both the simulation-based and the data-driven approaches
are consistent within the statistical errors. The simulation-based approachyields a smaller statistical uncertainty than another one, especially at hightransverse-momentum. Therefore, we employ the simulation-based approachto the background estimation in this study.

CHAPTER 3. ANALYSIS

104

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103

103

102

102

10

10

104

T

103

103

102

102

10
1

1

−1

−1

−1

−1

0.4 0.6 0.8
mee (GeV/c2)

1

10− 2
0

104

10
0.2

0.4 0.6 0.8
mee (GeV/c2)

1

10− 2
0

105
200GeV Cu+Cu (0-40%)
1.0<p <1.5GeV/c

104

T

103

102

102

Counts

103

10

10
0.2

0.4 0.6 0.8
mee (GeV/c2)

1

10− 2
0

105
104

1.5<p <2.0GeV/c
T
FG++ , −−
α × FG++ , −−

10

104

2.0<p <3.0GeV/c
T

103

103

102

102

10

1

1

1

10− 1

10− 1

10− 1

10− 1

1

10− 2
0

105
200GeV Cu+Cu (40-94%)
1.0<p <1.5GeV/c

10− 2
0

0.2

0.4 0.6 0.8
mee (GeV/c2)

1

10− 2
0

10

4

10

3

103

102

102

10

10

10

3

10

3

102

102

Counts

1

105

4

10

0.4 0.6 0.8
mee (GeV/c2)

105

4

T

0.2

1.5<p <2.0GeV/c
T
FG++ , −−
α × FG++ , −−

10

104

2.0<p <3.0GeV/c
T

10

1

1

1

10− 1

10− 1

10− 1

10− 1

0.2

0.4 0.6 0.8
mee (GeV/c2)

1

10− 2
0

0.2

0.4 0.6 0.8
mee (GeV/c2)

1

10− 2
0

3.0<p <5.0GeV/c
T

0.2

0.4 0.6 0.8
mee (GeV/c2)

1

0.2

0.4 0.6 0.8
mee (GeV/c2)

1

3.0<p <5.0GeV/c
T

10− 2
0

0.2

0.4 0.6 0.8
mee (GeV/c2)

Figure 3.20: The invariant mass distributions for the like-sign foregrounds
and their acceptance-corrected distributions in three centrality bins: (top)minimum bias, (middle) 0–40%, and (bottom) 40–94%.

3.13

1

10

1

10− 2
0

0.4 0.6 0.8
mee (GeV/c2)

105

Counts

0.4 0.6 0.8
mee (GeV/c2)

Counts

0.2

0.2

10

1

10− 2
0

T

105

Counts100.2

3.0<p <5.0GeV/c

10

1

105

Countsα × FG++ , −−105
2.0<p <3.0GeV/c

1

10− 2
0

Counts

104

Counts10105
1.5<p <2.0GeV/c
T
FG++ , −−Counts105
200GeV Cu+Cu (MinBias)
1.0<p <1.5GeV/c

CountsCounts

104

Counts105

91

Correlated pairs from hadronic decay

The hadron decay electron-pairs are the remaining background after subtracting the above combinatorial, jet-induced, and correlated cross pair backgrounds. The virtual photon signal is extracted as excess over the hadron
decay pairs. This background source is the known hadron decays electronpairs, which are correlated. The pairs are called hadronic cocktail or continuum. The cross pairs described in Sec. 3.9.3 are also originated from thehadron decays, but they are not physical pair, whereas the hadronic cocktail

1

CHAPTER 3. ANALYSIS

104

T

103

103

102

102

10

104

T

103

103

102

102

10
1

1

−1

−1

−1

−1

0.4 0.6 0.8
mee (GeV/c2)

1

10− 2
0

104

10
0.2

0.4 0.6 0.8
mee (GeV/c2)

1

10− 2
0

105
200GeV Cu+Cu (0-40%)
1.0<p <1.5GeV/c

104

T

103

102

102

Counts

103

10

10
0.2

0.4 0.6 0.8
mee (GeV/c2)

1

10− 2
0

105
104

1.5<p <2.0GeV/c
T
FG+−
Acc.Corr FG+ + , − −Subtracted

10

104

2.0<p <3.0GeV/c
T

103

103

102

102

10

1

1

1

10− 1

10− 1

10− 1

10− 1

1

10− 2
0

105
200GeV Cu+Cu (40-94%)
1.0<p <1.5GeV/c

10− 2
0

0.2

0.4 0.6 0.8
mee (GeV/c2)

1

10− 2
0

10

4

10

3

103

102

102

10

10

10

3

10

3

102

102

Counts

1

105

4

10

0.4 0.6 0.8
mee (GeV/c2)

105

4

T

0.2

1.5<p <2.0GeV/c
T

FG+−
Acc.Corr FG+ + , − −Subtracted

10

104

2.0<p <3.0GeV/c
T

10

1

1

1

10− 1

10− 1

10− 1

10− 1

0.2

0.4 0.6 0.8
mee (GeV/c2)

1

10− 2
0

0.2

0.4 0.6 0.8
mee (GeV/c2)

1

10− 2
0

1

3.0<p <5.0GeV/c
T

0.2

0.4 0.6 0.8
mee (GeV/c2)

1

0.2

0.4 0.6 0.8
mee (GeV/c2)

1

3.0<p <5.0GeV/c
T

10

1

10− 2
0

0.4 0.6 0.8
mee (GeV/c2)

105

Counts

0.4 0.6 0.8
mee (GeV/c2)

Counts

0.2

0.2

10

1

10− 2
0

T

105

Counts100.2

3.0<p <5.0GeV/c

10

1

105

Counts10105
2.0<p <3.0GeV/c

1

10− 2
0

Counts

104

Counts10105
1.5<p <2.0GeV/c
T
FG+−
Acc.Corr FG+ + , − −Subtracted

Counts105
200GeV Cu+Cu (MinBias)
1.0<p <1.5GeV/c

CountsCounts

104

Counts

105

92

10− 2
0

0.2

0.4 0.6 0.8
mee (GeV/c2)

Figure 3.21: The invariant mass distribution of electron pairs for the unlikesign foregrounds, the acceptance-corrected like-sign pairs, and the data after
subtracting background by the data-driven approach with three centrality
bins: (top) minimum bias, (middle) 0–40%, and (bottom) 40–94%.
is a physical pair.
The hadronic cocktail components are reproduced by EXODUS and PISA
simulations, which are the same Monte Carlo simulation for evaluating thecorrelated cross-pair background in Sec. 3.9.3. The considered hadron decay
modes are summarized in Table 3.6.
The PHENIX experiment has successfully reproduced the invariant yieldof ⇡ 0 meson in 200 GeV Cu+Cu collisions. The modified Hagedorn function

1

CHAPTER 3. ANALYSIS

Like-sign subtraction
BGSUM fit
BGCM
+−
BGXC
+−
BGJT
+−

10
1

0

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

SUM

0.1

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
mee (GeV/c2)

1

T

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
mee (GeV/c2)

3.0<p <5.0GeV/c
T

10−2
10−3

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

/FG

0.2

SUM

0.1

BG

/FG
SUM

0.1

10−1

10−2

BG

1.40
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6

Number of pairs

Number of pairs

2.0<p <3.0GeV/c

10−1

0

1

10

1

1.40
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6

T

10

0

102
10

1.5<p <2.0GeV/c

10−1

BG

BG

SUM

/FG

10−1
1.40
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6

102

T

Number of pairs

Number of pairs

102

103

Cu+Cu, sNN=200GeV, MB
1.0<p <1.5GeV/c

/FG

103

93

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
mee (GeV/c2)

1.40
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
mee (GeV/c2)

Figure 3.22: The comparison of invariant mass distributions between theacceptance-corrected foreground like-sign and BGSUM
evaluated by the++,SUM
simulation-based approach with the BG++, /FG for Cu+Cu minimum bias
pevents at sN N = 200 GeV.
can parametrize this invariant yield:⇣⌘ nd3(apT +bp2T ) + p /p=Ae.
(3.35)T0
dp3
The transverse invariant-mass scaling generates the invariant yield of otherhadrons, and it can be express as:
E

✓
q
p
d3
1(a m2T m2 0 +b(m2T m2 0 )⇡⇡E 3 =A e) + m2Tdp

m2⇡0 /p0◆ n.

(3.36)

Table 3.9.3 lists the Hagedorn function parameters for Minimum Bias,
0–40%, and 40–94% centrality classes. It is important to note that the large

CHAPTER 3. ANALYSIS

94

Table 3.6: Considered decay modes and their branching ratios [84] in the
hadronic cocktail simulation by EXODUS
Mother particle
⇡0
⌘
!
⌘0

⇢

Decay modes⇡ 0 ! + e+ e
⇡ 0 ! e+ e + e+ e
⌘ ! + e+ e
⌘ ! e+ e + e+ e
! ! e+ e! ! ⇡ 0 + e+ e
⌘ 0 ! + e+ e
! e+ e! ⌘ + e+ e
⇢ ! e+ e

Branching ratio %1.174
3.34 ⇥ 10 3
6.90 ⇥ 10 1
2.40 ⇥ 10 3
7.28 ⇥ 10 3
7.7 ⇥ 10 2
9.0 ⇥ 10 22.954 ⇥ 10 2
1.15 ⇥ 10 2
4.72 ⇥ 10 3

Table 3.7: Meson to ⇡ 0 ratios and their uncertainties [85]particlemeson/⇡ 0
uncertainty

⌘
0.48
±0.03

!
0.90
±0.06

⌘0
0.25
±0.075

0.40
±0.12

⇢
1.00
±0.30

CHAPTER 3. ANALYSIS

Like-sign subtraction
BGSUM fit
BGCM
+−
BGXC
+−
BGJT
+−

10
1

0

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

SUM

0.1

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
mee (GeV/c2)

1

T

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
mee (GeV/c2)

3.0<p <5.0GeV/c
T

10−2
10−3

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

/FG

0.2

SUM

0.1

BG

/FG
SUM

0.1

10−1

10−2

BG

1.40
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6

Number of pairs

Number of pairs

2.0<p <3.0GeV/c

10−1

0

1

10

1

1.40
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6

T

10

0

102
10

1.5<p <2.0GeV/c

10−1

BG

BG

SUM

/FG

10−1
1.40
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6

102

T

Number of pairs

Number of pairs

102

103

Cu+Cu, sNN=200GeV, 0-40%
1.0<p <1.5GeV/c

/FG

103

95

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
mee (GeV/c2)

1.40
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
mee (GeV/c2)

Figure 3.23: The comparison of invariant mass distributions between theacceptance-corrected foreground like-sign and BGSUM
evaluated by the++,SUM
simulation-based approach with the BG++, /FG for Cu+Cu 0–40% cenp
trality events at sN N = 200 GeV.
uncertainty in the absolute scale parameter A does not a↵ect the extraction of
direct virtual-photon component because the shape of the hadronic cocktail
is only entered into the determination.
Once the function evaluates the hadron transverse-momentum spectra,
electron pair spectra originated from the hadrons can be given by decay
kinematics and branching ratios implemented in the EXODUS simulation.
Generated electrons arisen from hadron decays in EXODUS are passed
through the PHENIX GEANT3 simulation, PISA, to simulate detector response and consider the detector acceptance. The same electron identification and pair-cuts are applied, and electron-pair invariant-mass distributions
are reproduced. The relative scale between hadrons is normalized by theCHAPTER 3. ANALYSIS

Like-sign subtraction
BGSUM fit
BGCM
+−
BGXC
+−
BGJT
+−

1

10−1

0

0.2

0.3

0.4

0.5

0.6

0.7

T

1

10−2
0.8

0.9

1

SUM

0.1

1.5<p <2.0GeV/c

10−1

BG

BG

SUM

/FG

10−2
1.40
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6

10

T

Number of pairs

Number of pairs

10

102

Cu+Cu, sNN=200GeV, 40-94%
1.0<p <1.5GeV/c

/FG

102

96

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
mee (GeV/c2)

1.40
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
mee (GeV/c2)

102

Number of pairs

10

2.0<p <3.0GeV/c
T

1

10−1

BG

SUM

/FG

10−2
1.40
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
mee (GeV/c2)

Figure 3.24: The comparison of invariant mass distributions between theacceptance-corrected foreground like-sign and BGSUM
evaluated by the++,SUM
simulation-based approach with the BG++, /FG for Cu+Cu 40–94% cenp
trality events at sN N = 200 GeV.
meson-to-pion ratios listed in Table 3.7 and branching ratios listed in Table
3.6.
The invariant mass distribution of simulated electron-pair from known
hadron decays are merged as a hadronic cocktail shown in Fig. 3.25. The
cocktail distribution is represented in a solid black line, while each component
is expressed in colored lines.

3.14

Open heavy flavor contribution

An additional background contribution is open heavy flavor decays that produce correlated electron pairs. It is a semi-leptonic decay of charm hadrons,

CHAPTER 3. ANALYSIS

104
103
Counts

2

10

10

105

Cocktail
0
Cu+Cu, sNN=200GeV, MB πηω
1.0 < p < 1.5 GeV/cTη'φρ
Cocktail Simulation

104
103

1

1
10

−2

10−2

10

0.4
0.6
mee (GeV/c2)

104
2.0 < p < 3.0 GeV/c
T

2

10

10

0.8

10−30

1

103

10

10−2
1

0.8

1

Cocktail
π0
η
ω
η'
φ
ρ

1

10−2
0.8

T

10

10−1

0.4
0.6
mee (GeV/c2)

3.0 < p < 5.0 GeV/c

2

10−1

0.2

0.4
0.6
mee (GeV/c2)

104

1

10−30

0.2

105

Cocktail
π0
η
ω
η'
φ
ρ

Counts0.2

105Counts10

Cocktail
π0
η
ω
η'
φ
ρ

−1

10

103

T

10

−1

10−30

1.5 < p < 2.0 GeV/c

2

Counts

105

97

10−30

0.2

0.4
0.6
mee (GeV/c2)

0.8

1

Figure 3.25: The invariant mass shape of a hadronic cocktail evaluated byp
the EXODUS and PISA simulation for sN N = 200 GeV Cu+Cu collisions.
The black lines represent the summed shape of cocktail components. The
colored dashed lines express each cocktail components from ⇡ 0 to ⇢ meson.
and the contribution is the so-called cc contribution.
The PYTHIA and PISA simulations evaluated the open heavy flavor contribution for the p+p collision system condition. The evaluated contribution
is scaled by the number of collisions Ncoll by the d+Au results [83]. The cc̄
contribution and the background-subtracted invariant mass distributions areshown in Fig. 3.26. The contribution is small and hiding behind the hadronic
cocktail in the invariant mass region interested in this study below mee = 0.3
GeV/c2 . The cc̄ contribution becomes dominant in the high invariant-mass

CHAPTER 3. ANALYSIS

98

104

Cu+Cu, sNN=200GeV

103

e+e−: 1<p <5GeV/c
T

ccbar

102

Number of pairs

SUM

FG+ −-BG
BG

10
1

10−1
10−2
10−3
0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

−5

Ratio

(FG+ −-BGSUM)/BGccbar

−10

−15

−20
0

0.1

0.2

0.3

0.4

0.5

0.6

mee (GeV/c2)

0.7

0.8

0.9

1

Figure 3.26: The evaluated cc̄ contribution together with the backgroundsubtracted distribution
region due to their large opening angle. The contribution is less than 0.1%
at most in the mass region mee < 0.3 GeV/c2 , even if the 100% uncertainty
from the model dependence is considered.

3.15

Determination of direct photon fraction

In this section, we describe the extraction of the direct virtual-photon signal.
The virtual photon composition is extracted as an excess over the hadronic
cocktail after subtracting the background components.

CHAPTER 3. ANALYSIS

99

Virtual photons are measured by fitting on the invariant mass spectra ofelectron pairs for 0.12 < mee < 0.3 GeV/c2 which is almost above the neutralpion invariant-mass. The very low mass region is derived from neutral pions;
therefore, the signal-to-background ratio can be improved in the intended
mass region.
The fit function on the invariant mass spectra is given by
fFG (mee ) = (1r ) fc (mee ) + r fdir (mee ) + fBG (mee )(3.37)

where r is the only fit parameter which is called direct photon fraction,
fc and fBG are the hadronic cocktail invariant-mass shape and the fixed
contribution BGSUM , respectively, and fdir is the expected mass shape of
direct photons. The invariant mass shape of fc and fdir is independently
normalized to the foreground in the invariant mass < 30 MeV/c2 .
A similar fitting procedure is employed in the previous studies, although
there are a few di↵erences. In the previous studies, the fit function is given
byfFG BG (mee ) = (1r ) fc (mee ) + r fdir (mee ) .

(3.38)The hadronic cocktail is only included in the function since the BGSUM andthe open heavy flavor contributions are subtracted before the fit. Moreover,the fit in this study is applied by a log-likelihood fit in order that the fitting
works correctly even though limited statistics, especially at higher transverse
momentum region.
The relation between real photon and the associated electron pair productions can be expressed as
2

dN
2↵ 1
=
dmee dpT
3⇡ mee

s

1

4m2e
2
Mee

✓

2m2
1 + 2eMee◆

S (mee , pT )dN
dpT

(3.39)

where ↵ is the fine structure constant, and S (mee , pT ) is a process-dependent
factor. The factor S (mee , pT ) took account of di↵erences between real photon and virtual photon productions, such as form factors and phase space.
S (mee , pT ) becomes negligible in the high transverse momentunm (pTmee ),and the factor becomes 1 as mee ! 0. In addition, the electron pair invariant

CHAPTER 3. ANALYSIS

100

mass Mee should be greater than electron mass me . Therefore, Equation 3.41
can simplifies as
dN 2
2↵ 1 dN'.
dmee
3⇡ Mee dpT
Number of pairs

105(3.40)

Cu+Cu, sNN=200GeV, MB
1<p <5GeV/c

104

T

fη'

103

fη' / Sη' = fdir
102

10

1
0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 2 1mee (GeV/c )Figure 3.27: The expected invariant-mass shape for direct virtual photon inp
Cu+Cu collisions at sN N = 200 GeV. The expected shape is calculatedusing ⌘ 0 in the hadronic cocktail simulation.
The direct virtual photon’s mass-shape is evaluated using the ⌘ 0 Dalitzdecay component in the cocktail simulation. The decay rate of Dalitz decay
for pseudo-scaler mesons can be expressed by
dN 2
2↵ 1
=
dmee dpT
3⇡ mee

s

1

4m2e
2
Mee

✓

2m2
1 + 2e
Mee

◆

|F m

2

✓

| 1

m2
Mh2

◆3

dN
dpT
(3.41)(mee , pT )

⇣
⌘3
⇣
⌘3
m2
m2
where S (mee , pT ) = |F (m2 ) | 1 M, and 1 M
term in S (mee , pT )22hhis a suppression factor which arises due to the finite invariant mass of theCHAPTER 3. ANALYSIS

101

parent particles [86]. Therefore, the mass shape for the virtual photons canbe evaluated byfdir (mee ) = f⌘0 (mee ) /S⌘0 (mee ) .

(3.42)The expected invariant-mass shape for direct virtual-photons together withthe ⌘ 0 meson are shown in Fig. 3.27.
Figures 3.28, 3.29, and 3.30 show the electron pair invariant mass distributions with the fit results by Eq. 3.37 for minimum bias, 0–40%, and
40–94% centralities, respectively. The black markers represent the measured
foreground electron pairs, and the shaded red regions are the evaluated background distribution. The hadronic cocktail distribution are represented by
the dotted blue lines, while the fit results are shown by the solid red lines.
The fit for mass distributions are performed within an invariant mass range
0.1 < mee < 0.3 GeV/c2 for several transverse momentum bins separately.
Direct photon fractions expected by a next-to-leading-order (NLO) perturbativequantum-chromodynamics (pQCD) calculation are compared to the data.
The definition of the direct photon fraction in which all contributions arise
from the pQCD processes are expressed by
r =

NpQCD
NpQCD
=
.
Ninclusive
Ndecay + NpQCD(3.43)The expectations from NLO pQCD calculation for Cu+Cu collisions are calculated by the Ncoll scaling, and it is given by⇣⌘
centrality
Min.Bias
NpQCD Ncoll/Ncollrcentrality = centrality,(3.44)
Min.Bias
Ndecay+ NpQCD (N centrality /Ncoll)
where NpQCD is given by
NpQCD =

rMin.Bias
Ndecay ,1 rMin.Bias(3.45)and Ndecay denotes decay photon invariant yields evaluated by the Monte
Carlo simulations described in the below section.

CHAPTER 3. ANALYSIS

102

5

10

200GeV Cu+Cu MB, 1.0<p <1.5GeV/c

104

T

3

10

102

104

3

102
10
1

0.1

0.2

0.3

0.4
0.5
mee (GeV/c2)

0

10

102

Data
fc
f BG
(1-r γ )f c+r γ f dir +f BG
r γ =0.064±0.032
χ2/NDF=70.2/39

10

0.3

0.4
0.5
mee (GeV/c2)

T

Data
fc
f BG
(1-r γ )f c+r γ f dir +f BG
r γ =0.168±0.072
χ2/NDF=23.2/39

10

10
1

10− 1

1
10− 100.2

200GeV Cu+Cu MB, 3.0<p <5.0GeV/c

2

Counts per 5MeV/c2

Counts per 5MeV/c2

10

0.1

3

200GeV Cu+Cu MB, 2.0<p <3.0GeV/c
T

3

Data
fc
f BG
(1-r γ )f c+r γ f dir +f BG
r γ =0.116±0.027
χ2/NDF=31.9/39

10

10
1
0

200GeV Cu+Cu MB, 1.5<p <2.0GeV/c
T

Counts per 5MeV/c2

Counts per 5MeV/c2

104

Data
fc
f BG
(1-r γ )f c+r γ f dir +f BG
r γ =0.045±0.022
χ2/NDF=47.2/39

0.1

0.2

0.3

0.4
0.5
mee (GeV/c2)

10− 20

0.1

0.2

0.3

0.4
0.5
mee (GeV/c2)

Figure 3.28: The e+ e pair mass distributions in Cu+Cu Minimum Bias collisions for four transverse momentum regions. The data (closed circles), thefit function (red curve), hadronic contribution (blue curve), and the background BGSUM .

3.16

Systematic uncertainties

In this section, we describe the possible sources of systematic errors andexplain how to evaluate the uncertainties. We take into account the following
sources of systematic uncertainties.
• Background normalization• Particle composition in hadronic cocktail

CHAPTER 3. ANALYSIS

103

5

10

200GeV Cu+Cu 0-40%, 1.0<p <1.5GeV/c

104

T

3

10

102

104

3

10

102

10
1
0

1
0.1

0.2

0.3

0.4
0.5
mee (GeV/c2)

0

102

Data
fc
f BG
(1-r γ )f c+r γ f dir +f BG
r γ =0.090±0.038
χ2/NDF=85.1/39

10

0.2

0.3

0.4
0.5
mee (GeV/c2)

10200GeV Cu+Cu 0-40%, 3.0<p <5.0GeV/c
T

2

10

10

Data
fc
f BG
(1-r γ )f c+r γ f dir +f BG
r γ =0.217±0.085
χ2/NDF=21.3/39

1

10− 1

1
10− 100.1

3200GeV Cu+Cu 0-40%, 2.0<p <3.0GeV/c

Counts per 5MeV/c2

Counts per 5MeV/c2

10

Data
fc
f BG
(1-r γ )f c+r γ f dir +f BG
r γ =0.127±0.032
χ2/NDF=30.9/39

10

T

3

200GeV Cu+Cu 0-40%, 1.5<p <2.0GeV/c
T

Counts per 5MeV/c2

Counts per 5MeV/c2

104

Data
fc
f BG
(1-r γ )f c+r γ f dir +f BG
r γ =0.044±0.025
χ2/NDF=46.0/39

0.1

0.2

0.3

0.4
0.5
mee (GeV/c2)

10− 20

0.1

0.2

0.3

0.4
0.5
mee (GeV/c2)

Figure 3.29: The e+ e pair mass distributions in Cu+Cu 0–40% collisions forfour transverse momentum regions. The data (closed circles), the fit function(red curve), hadronic contribution (blue curve), and the background BGSUM .
• Hadronic cocktail normalization• Fitting range for r calculation
Each systematic uncertainty is obtained from the Root-Mean-Square errorof the results in the direct photon fractions, r .

CHAPTER 3. ANALYSIS
104

104

200GeV Cu+Cu 40-94%, 1.0<p <1.5GeV/c

3

10

T

Counts per 5MeV/c2

10

102
10
1

200GeV Cu+Cu 40-94%, 1.5<p <2.0GeV/c
T

Data
fc
f BG
(1-r γ )f c+r γ f dir +f BG
r γ =0.061±0.046
χ2/NDF=47.0/39

102Counts per 5MeV/c2

Data
fc
f BG
(1-r γ )f c+r γ f dir +f BG
r γ =0.065±0.034
χ2/NDF=36.8/39

3

10
1

10− 1

10− 10

0.1

0.2

0.3

0.4
0.5
mee (GeV/c2)

0

0.1

0.2

0.3

0.4
0.5
mee (GeV/c2)

3

10200GeV Cu+Cu 40-94%, 2.0<p <3.0GeV/c
T

2

Counts per 5MeV/c2

10

10

Data
fc
f BG
(1-r γ )f c+r γ f dir +f BG
r γ =0.087±0.054
χ2/NDF=30.1/39

1

10− 1
10− 20

0.1

0.2

0.3

0.4
0.5
mee (GeV/c2)

Figure 3.30: The e+ e pair mass distributions in Cu+Cu 40–94% collisions
for three transverse momentum regions. The data (closed circles), the fit
function (red curve), hadronic contribution (blue curve), and the background
BGSUM .

3.16.1

Background normalization uncertainties

First systematic uncertainty is in the background normalization of the fourcomponent fit. The normalization factors of background components lead toa systematic error. To evaluate the systematic error related to the normalization, we vary the fitting parameters one by one to shift ± 1 sigma.
The uncertainty evaluation procedure is as follows: First of all, we shift
one of the fitting parameters obtained from the four-component fit by one
sigma. Second, shifted parameters are fixed, and a three-component fit isCHAPTER 3. ANALYSIS

105

applied to the invariant-mass foreground distribution. Third, we subtract
the background and compare the cocktail distribution to evaluate the direct
photon fraction. Lastly, the above processes are repeated for all of the fitting
parameters.

3.16.2

Particle composition uncertainties

The second systematic uncertainty is particle composition, which is the uncertainty of neutral pion to meson ratios. We need to estimate the impact of
the ratio uncertainties on the results.
We evaluate the systematic error with the following procedure. First, we
shift one ratio by ±1 from the nominal ratio and create a cocktail distribution. Secondly, we calculate r with the obtained cocktail distribution.
Finally, we repeat the above processes for all meson to neutral pion ratios.
This procedure is employed independently to the collision centrality. Table
3.7 shows the meson to neutral pion ratios with uncertainty. We employ theratios and uncertainties for this systematic error estimation.

3.16.3

Uncertainty in hadronic cocktail normalization

The hadronic cocktail normalization is the other origin of systematic error.
We use the invariant mass region of 0.03 GeV/c2 as the nominal normalization region. The low mass region of the electron-pair invariant-mass isdominantly originated from ⇡ 0 Dalitz decays, and electron pairs are a↵ectedby the finite mass resolution. Therefore, it is crucial to evaluate the e↵ect of
the normalization region.
To evaluate the systematic error, we vary the mass region for the normalization. The evaluation procedure is as follows: Firstly, we apply the
0.03±0.01 GeV to the cocktail normalization. Then, we calculate r with
the normalized cocktail distribution. This procedure is employed independently to the collision centrality.

3.16.4

Uncertainty in the fitting range for r

The final source of systematic uncertainty is the fitting range of r . Thisfitting is for the extraction of direct photon fraction. The nominal fitting
range in the invariant mass distribution is 0.12 < mee < 0.3 GeV/c2 , but
this range may a↵ect the direct photon fraction.

CHAPTER 3. ANALYSIS

106

To evaluate the fitting’s uncertainty, we shift the upper and lower limitof the fitting range slightly and apply the six kinds of fitting ranges in theinvariant mass distributions. We calculate the r in each fitting range andestimate the systematic error.

3.16.5

Summary of systematic uncertainties

We explain the four kinds of systematic errors in the above subsections. We
evaluate the total systematic error by calculating the Root Mean Square
Error of these four uncertainties. The total systematic errors are calculated
for each transverse momentum bin and centrality class.

Chapter 4
Results and Discussion
4.1

Direct photon fraction

Direct photon fractions have been measured by the virtual photon methodpin Cu+Cu collisions at sN N = 200 GeV. The results are presented as afunction of transverse momentum for three centrality bins: minimum bias, 0–40%, and 40–92% centrality events. The direct photon fractions are obtained
as excess over the hadronic cocktail as described in the previous chapter.
Figure 4.1 shows the direct photon fractions r for three centrality bins.
The data points are presented with both statistical and systematic uncertainties. The results are compared with the expectations by next-to-leadingorder (NLO) perturbative-quantum-chromodynamics (pQCD) calculations
with the three curves of the NLO pQCD calculations corresponding to thetheory scales µ = 0.5pT , pT , and 2.0pT . The direct photon fractions of thedata exceed the NLO pQCD calculations, especially minimum bias and central collisions.
Comparison with other collision systems
The direct photon fraction has been measured by the virtual photon methodpin several collision systems at sN N = 200 GeV. Figure 4.2 shows direct
photon fractions as a function of transverse momentum measured by thevirtual photon method in p+p, d+Au, Cu+Cu, and Au+Au in minimum
bias events. The error bars denote the statistical uncertainty, while the error
boxes represent the systematic uncertainty. The data points are comparedwith the NLO pQCD calculations with three theoretical scales.
107CHAPTER 4. RESULTS AND DISCUSSION

0.3

0.3

0.3

(a) Cu+Cu (MB)(b) Cu+Cu (0-40%)sNN=200GeV

0.25
rγ = direct γ / inclusive γ

108(c) Cu+Cu (40-94%)

0.25

0.25

NLO pQCD 0.2

0.2|y|<0.35
0.2µ = 1.0p
Tµ = 0.5p
T 0.15µ = 2.0p

0.15

0.15

T

0.1

0.1

0.1

0.05

0.05

0.05

0

0

0

1

2

3
4
p (GeV/c)
T

5

6

1

2

3
4
p (GeV/c)
T

5

6

1

2

3
4
p (GeV/c)

5

6

T

Figure 4.1: Direct photon fraction measured with the virtual photon methodp
as a function of transverse momentum in Cu+Cu collisions at sN N = 200
GeV
The p+p and d+Au results show agreements with the NLO pQCD calculations, whereas the Cu+Cu and Au+Au results show excess over the theoretical expectations. Direct photons in small collision systems originate frominitial hard scattering since the hot medium is not created in the collisions.
In heavy-ion collision systems, there is a contribution of thermal radiationfrom the created medium. The excess in Cu+Cu collisions is more modest
than that in Au+Au. It is possibly due to a smaller volume of the createdmatter.

4.2

Direct photon spectra

The direct photon spectra are calculated from the direct photon fractions
and the decay photon yields. The decay photon yields are obtained fromCHAPTER 4. RESULTS AND DISCUSSION(b) d+Au (MB)(a) p+p
0.2109(c) Cu+Cu (MB)(d) Au+Au (MB)

0.2

0.2

0.15

0.15

0.15

0.1

0.1

0.1

0.1

0.05

0.05

0.05

0.05

0

0

0

0

rγ = direct γ /inclusive γ

0.2

sNN=200GeV|y|<0.35
NLO pQCDµ = 1.0p
Tµ = 0.5p
Tµ = 2.0p

0.15

T

1

2

3

4

p (GeV/c)
T

5

6 1

2

3

4

p (GeV/c)
T

5

6 1

2

3

4

p (GeV/c)
T

5

6 1

2

3

4

5

6

p (GeV/c)T

Figure 4.2: Direct photon fraction measured with the virtual photon methodpfor di↵erent collision systems in sN N = 200 GeV: (a) p+p collisions [40], (b)d+Au collisions [40], (c) Cu+Cu collisions by this work, and (d) Au+Au collisions [39]. Expectations from NLO pQCD calculations [87] are also shownby curves.
the EXODUS simulation. EXODUS simulates the hadron decays with photons. The considered hadrons and their decay modes are tabulated in Table
4.1. The input shape of the transverse momentum distribution for the ⇡ 0meson is a modified Hagedorn function, and the shapes for other mesons are
obtained from the transverse invariant-mass scaling. The evaluated decay
photon spectra for three centrality classes are shown in Fig. 4.3. The total decay photon spectra are denoted by the black line, while colored lines
indicate decay photon contributions from each hadron decay.
Direct photon spectra are obtained by multiplying the direct photon frac-

CHAPTER 4. RESULTS AND DISCUSSION

110

Table 4.1: Considered hadrons and their decay modes in the decay photon
simulation by EXODUS. Branching ratios are from the Particle Data Group[84].
Mother particle
⇡0
⌘

!

⌘0

Decay modes
Branching ratio
2(98.823 ± 0.034)%
e+ e(1.174 ± 0.035%
2
39.41 ± 0.20)%+⇡ ⇡(4.22 ± 0.88)%
e+ e(6.9 ± 0.4) ⇥ 10 33⇡ 0
(32.68 ± 0.23)%
0⇡ 2(2.7 ± 0.5) ⇥ 10 4⇡+⇡ ⇡0(89.2 ± 0.7)%
0 +
⇡ e e
(7.7 ± 0.6) ⇥ 10 40⇡(9.28 ± 0.28)%
2(2.20 ± 0.08)%+e e< 9 ⇥ 10 4!
(2.75 ± 0.23)%⇢(29.1 ± 0.5)%
0 0
⇡ ⇡ ⌘
(22.2 ± 0.8)%

CHAPTER 4. RESULTS AND DISCUSSION

102

102

102

(b) Cu+Cu 0-40%(a) Cu+Cu MB
10111(c) Cu+Cu 40-94%

1010Decay γ sum
1
π0
η
10
η'
ω

Decay γ sum
1
π0
η
10
η'
ω

10− 2

10− 2

10− 2

10− 3

10

10− 4

10− 4

10− 5

10

10− 6

10

10− 7

10− 7

1
10− 1

Ed3N/dp3 (GeV-2c3)

−1

10− 8

10

−1

−3

10

−3

10− 4

−5

10

−6

−5

10

−6

10− 7

−8

1 1.5 2 2.5 3 3.5 4 4.5 5

Decay γ sum
π0
η
η'
ω

10

−8

1 1.5 2 2.5 3 3.5 4 4.5 5

1 1.5 2 2.5 3 3.5 4 4.5 5p (GeV/c)p (GeV/c)p (GeV/c)

T

T

T

p
Figure 4.3: Decay photon spectra in Cu+Cu collisions at sN N = 200 GeV
for minimum bias, 0–40%, and 40–94% centrality classes calculated by the
EXODUS simulation.
tion by the decay photon spectrum. The calculation is given by:
dN directrdN decay
=
dpT
1 r
dpT

(4.1)

where r is the direct photon fraction defined by:r =direct.
inclusive(4.2)

CHAPTER 4. RESULTS AND DISCUSSION112

The direct photon invariant yield is obtained from the following equation:
N directd3 N
1 dN direct
1
1
E 3 =
=
(4.3)
dpT
2⇡pT dpT dy2⇡pT Nevents pT y
where Nevents is the number of events for each centrality, and pT and y
are the given transverse momentum and rapidity bin, respectively.
p
Figure 4.4 shows the direct photon spectra in Cu+Cu collisions at sN N =200 GeV for minimum bias, 0–40%, and 40–94% centralities. The direct
photon spectrum in Cu+Cu minimum bias collisions is compared to the TAA
scaled p+p results and its parameterized function. The scaling parameter TAA
is evaluated from the Glauber calculations. The spectra in other centralities
are compared with the parameterized function. The scaled p+p results [40]nare parameterized by a modified power-law function App (1 + pT 2 /Bpp ) pp .
The fit function is an empirical parametrization, but it describes the p+p
results well, especially at the low transverse-momentum region. The direct
photon spectra in Cu+Cu collisions have a clear enhancement from the binary scaled p+p results.
Spectrum comparison with Au+Au collision system
The direct photon spectra in Cu+Cu collisions are compared to the Au+Au
presults at sN N = 200 GeV. The Npart in Cu+Cu 0–40% and 40–94% centralities are comparable to the Au+Au 40–60% and 60–92% centralities. The
Npart of 0–40% and 40–94% centralities are 66.4 and 11.6, while those for
Au+Au collisions are 56.0 (40–60%) and 12.5 (60–92%).
The spectra in Au+Au collisions are scaled by the Npart ratios, and thescaled spectra are shown with the open square markers in Fig. 4.4. The
spectra in Cu+Cu collisions are consistent with the Au+Au results within
the uncertainties.
Temperature estimation
It is known that the excess yield of the direct photon spectrum indicatesthe contribution from thermal photons arisen from Quark-Gluon Plasma;
therefore, the inverse slope of the spectrum implies the e↵ective temperatureof the created matter. The spectrum is parameterized as:
✓
◆
✓
◆npp
pT
p2T
A exp
+ TAA App 1 +
.
(4.4)
T
Bpp

CHAPTER 4. RESULTS AND DISCUSSION(b) Cu+Cu 0-40%(a) Cu+Cu MB
Cu+Cu
1

1

TAA×p+p
TAA×p+p fit
-p /B

10− 1

113

Ae T +TAA×p+p fit 10(c) Cu+Cu 40-94%

Au+Au 40-60%
Normalized to Npart
1
Au+Au 40-60%: Npart=56.0
Cu+Cu 0-40%: Npart=66.4
10− 1

10− 2

10− 2

10− 2

10− 3

10

10− 4

10− 4

10− 5

10

Ed3N/dp3 (GeV-2c3)

−1

−3

T

−3

10− 4

−5

1 1.5 2 2.5 3 3.5 4 4.5 5p (GeV/c)

10

Au+Au 60-92%
Normalized to Npart
Au+Au 60-92%: Npart=12.5
Cu+Cu 40-94%: Npart=11.7

10−5

1 1.5 2 2.5 3 3.5 4 4.5 5

1 1.5 2 2.5 3 3.5 4 4.5 5p (GeV/c)p (GeV/c)T

T

Figure 4.4: Direct photon spectra in Cu+Cu collisions for (a) minimum bias,(b) 0–40%, and (c) 40–94% centrality events. The Cu+Cu minimum bias
result is shown together with the TAA scaled p+p spectra and its fit results.
The central and peripheral results for Cu+Cu collisions are compared to thep+p parameterized function and the Npart scaled Au+Au peripheral results.
Furthermore, the inverse slopes of the exponential function fit to the data
give the e↵ective temperature.
The function consists of two terms. The first term denotes an exponentialfunction with the free parameters A and T . The parameter T is the inverse
slope, and it implies the e↵ective temperature of the created matter. The
second term of the function represents the scaled p+p parameterization. The
parameters in the second term are calculated by the fit on the measured direct

CHAPTER 4. RESULTS AND DISCUSSION

114

p
photon spectra in p+p collisions at s = 200 GeV. The data points aremeasured by the virtual photon method at the low transverse-momentum
region pT < 6 GeV/c, and the real photon measurement results are also
shown together at the high transverse-momentum region 4 < pT < 10 GeV/c.
The inverse slope are 285 ± 53 (stat) ± 57 (syst) MeV/c for minimum bias
collisions, 333 ± 72 (stat) ± 45 (syst) MeV/c for 0–40% centrality events, and237 ± 117 (stat) ± 212 (syst) for 40–94% centrality events, respectively.

450
400

Effective temperature

Teff (MeV/c)

350
300
250
200
150

sNN = 200GeV

100

Cu+Cu
Au+Au

50
0

10

Npart

102

Figure 4.5: The e↵ective temperature as a function of Npart for Cu+Cu andp
Au+Au collisions at sN N = 200 GeV
The Npart dependence of the e↵ective temperature is investigated shownin Fig. 4.5. The measured temperature is compared to the Au+Au results at
p
sN N = 200 GeV. The Cu+Cu data points present in the small-Npart region.
There is no clear Npart -dependence on the e↵ective temperature in the same
collision energy.

CHAPTER 4. RESULTS AND DISCUSSION

4.3

115

Rapidity density

Integrated direct photon yields called the rapidity densities are further investigated in Cu+Cu collisions. The rapidity density at the mid-rapidity is
calculated by summing the direct photon yields in given transverse momentum bins considered with the bin width correction:
dN
dy
i
Cbw

= 2⇡

X

i
pT i y i Cbw
pT i ,(4.5)

piT >1GeV/c=

Z pT .max
pT .min⇥⇤ffit (pT ) dpT / ffit(pT i ) pT i ,(4.6)

where y i and pT i are the direct photon yield and transverse momentum
bin-width for the ith pT bin, respectively. ffit (pT ) is the fit function to thedata points of direct photon spectra.
Figure 4.6 shows the rapidity densities in Cu+Cu collisions with threepcentrality bins at sN N = 200 GeV as functions of Npart . The rapidity
density tends to increase logarithmically as a function of Npart . The rapidity
density clearly increase with Npart , whereas the e↵ective temperature areapproximately 250 MeV/c independent Npart . The Cu+Cu rapidity densities
are compared with the Au+Au results at the same collision energy [42]. A
simple power-law function with the fixed power of 1.25 is employed to fit both
the Cu+Cu and Au+Au results, and the function is reported in Ref. [44].
The Cu+Cu data give the data points in the small Npart region. The simple
function works well to describe the Npart dependence. The direct photon
rapidity density for the di↵erent collision system-size at the same collisionenergy seems to follow the identical scaling. It suggests that the sourcesof low transverse-momentum direct photons are no qualitative change forpdi↵erent centrality and system size at sN N = 200 GeV.
Comparison to other collision systems
The Cu+Cu rapidity density results are further compared to the other collision systems with di↵erent collision energies and collision sizes. Figure 4.7
shows the integrated direct-photon yields (pT > 1.0 GeV/c) as a functionof dNch /d⌘ for various collision systems, including the Cu+Cu results [44].
dNch /d⌘ is a charged particle multiplicity. It is roughly proportional to Npart

CHAPTER 4. RESULTS AND DISCUSSION

sNN=200GeV, mid-rapidity

1

10−1

T

dN/dy(p >1GeV/c)

10

116

Au+Au
Cu+Cu

10−2

10−3

10

102

Npart

Figure 4.6: Rapidity densities of the direct photon yield for pT > 1 GeV/c
as functions of Npart and dNch /d⌘ together with the Au+Au results. The
power-law functions are the fit results for the Au+Au data.
for fixed beam energy, and it does not saturate unlike Npart . dNch /d⌘ signifies the system size at the hadronization. The rapidity densities in heavy-ion
collisions are fitted by a power-law function with a fixed power of 1.25. The
power-law function describes the dNch /d⌘ dependence of the rapidity densities for heavy-ion collisions well. The rapidity density of the fit to p+p
data and pQCD calculations seem to be the similar power to the heavy-ion
collision resutls, although the yield is smaller.
The rapidity densities in the heavy-ion collision results measured in thepwide range of the collision energy from sN N = 39 to 2760 GeV, and di↵erent collision systems follow the same scaling behavior. Even if the numberof charged particles is the same, the initial conditions of the QGP should bedi↵erent for di↵erent collision energies. If thermal photons are the dominantsource at the low transverse-momentum region, the result suggests that thermal photons are emitted near the QGP-hadron transition. The direct photon
spectrum itself has a large yield, suggesting an early contribution. However,CHAPTER 4. RESULTS AND DISCUSSION

117

its integral, rapidity density implies that low transverse-momentum direct
photons arise from the collision’s late stage. Besides, the simple power-law
function, which is only two parameters, empirically describes the heavy-ion
collision data very well. It suggests that some fundamental commonality is
EVIEW LETTERS
123, the022301(2019)
underlying
production
mechanism of the direct photon production.

pT belowoccurs for
GeV=c thee apparent
ENIX [8]fit ranges

pﬃﬃﬃﬃﬃﬃﬃﬃ
sNN ish pT ,theCD calcuher thanlculations
ge to thenth of theing the in-102

A+A/p+p → γ dir + X

Pb+Pb, sNN = 2760 GeV
Au+Au, sNN = 200 GeV

10PHENIX

α = 1.25

Au+Au, sNN = 62.4 GeV
Au+Au, sNN = 39 GeV

1

Cu+Cu, sNN = 200 GeV
p+p, s = 200 GeV

T

dNγ /dy (1.0 < p < 5.0 GeV/c)

ield is theoduced by) calculaale of μ ¼
ormalized
from [55].
p þ p data
GeV=c, thegnificantly
ut follows
dependent

10− 1

10− 2
Ncoll scaled prompt photons
p+p fit, s = 200 GeV
pQCD, s = 2760 GeV
pQCD, s = 200 GeV
pQCD, s = 62.4 GeV

10− 3
10− 4
1

10

dNch/dη

102

103

η≈0

Figure 4.7: Rapidity densities of direct photons with pT > 1 GeV/c as a
FIG.
3. Integrated direct photon yield (pT >range
1.0 GeV=c)vsfunction of dNch /d⌘. The rapidity densities cover the wideof collisionpdN
for dataFig.
The
dashedlineof isa powerenergiessN N sets= 39shownto 2760 in
GeV
and1.thecollision
nucleiAu+Au,
ch =dη,from
Pb+Pb,and Cu+Cu.
rapidity
data arefittedby aupper
power-lawlaw
fit witha fixedTheslopeof density
α ¼ 1.25.
The
twolimitsfunction
with
the
fixed
↵
=
1.25.
[44]
correspond to the data in 20%–40% and 40%–80% Pb þ Pb
pﬃﬃﬃﬃﬃﬃﬃﬃ
collisions at sNN ¼ 2760 GeV. The integrated yields of the fit
to p þ p data and of the pQCD calculations are shown as well,both scaled by N coll [21,51].

200 GeV data at the same dN ch =dη. The N coll scaled pQCD
calculation is about 30% below the data, which may not besignificant considering the 25% systematic uncertainty on
the calculation.

Chapter 5
Summary and Conclusion
We have studied the production of low transverse-momentum direct photonspin Cu+Cu collisions at sN N = 200 GeV. We have measured direct photons
by the virtual photon method with the PHENIX experiment at the RHIC
collider in Brookhaven National Laboratory.
The direct photon fraction as a function of transverse momentum is obtained for three centrality classes: minimum bias, 0–40% and 40–94%. The
measured fractions are compared to the expectations from next-to-leadingorder (NLO) perturbative-quantum-chromodynamics (pQCD) calculations.
The results have an excess over the NLO pQCD calculations in all centrality
classes. The excess appears the contribution of thermal photons from thehot medium. The Cu+Cu results are compared to the results in p+p, d+Au,p
and Au+Au collisions at sN N = 200 GeV. An excess over the theoretical
calculations is seen in the Cu+Cu and Au+Au results, whereas the p+p andd+Au results correspond with the calculations. The excess in the Cu+Cu
results is relatively modest compared to the Au+Au results. It is possible
due to a smaller volume of the created medium.
Direct photon spectra have been measured, and these are compared withthe binary scaled p+p results. The Cu+Cu spectra have an excess yield
above the scaled p+p, as well as in the Au+Au collisions. The Cu+Cu spectra are also compared with the Au+Au results scaled by the Npart ratio, andthe spectra are consistent within the uncertainties. An exponential fit to theexcess yield gives inverse slopes of 285±53(stat)±57(syst) MeV/c for minimum bias collisions and 333±72(stat)±45(syst) MeV/c for the most central
0–40%, and 237±117(stat)±66(syst) MeV/c for 40–94% centralities. The
calculated inverse slopes indicate the e↵ective temperature of the created118

CHAPTER 5. SUMMARY AND CONCLUSION

119

medium, and no Npart dependence is found in the temperature at the givenpcollision energy of sN N = 200 GeV.
The Npart dependence of the direct photon rapidity density is further investigated. The Cu+Cu results are compared with the Au+Au results. The
Cu+Cu data points help to look at the dependence in the small Npart region. An increasing trend for Npart is reported in Au+Au collisions, and the
Cu+Cu results follow the same Npart dependence. A simple power-law function empirically describes the dependence with a fixed power of 1.25. This
result suggests that the principal source of low transverse-momentum direct
photons is no qualitative change. Moreover, the collision energy dependenceof the direct-photon rapidity density is discussed, and the charged-particle
multiplicity (dNch /d⌘) dependency is shown. The Cu+Cu results provide
new data points in the small dNch /d⌘ region. The rapidity density for lowtransverse-momentum direct photons in heavy-ion collisions follow the samedNch /d⌘ scaling in the wide range of collision energy between 39 to 2760
GeV. This result implies that the direct photon sources are similar acrossthe wide collision energy region. Even if dNch /d⌘ is the same, the initialconditions should be di↵erent if the collision energy is di↵erent. Therefore,
the scaling suggests that the low transverse-momentum direct photons areproduced near the QGP-hadron transition.
This thesis provides the collision system-size dependence of low transversemomentum direct-photon production. The Cu+Cu results improve the knowledge of the direct photon production, especially in the small Npart anddNch /d⌘ regions. Theoretical models qualitatively express the direct photon
production; however, quantitative understanding has not yet been achieved.
The rapidity density of direct photons follows the unified scaling regardless ofcollision system size and energy. The Cu+Cu collisions provide new results
in a small dNch /d⌘ region, but there is still a gap between the p+p collision
results. The PHENIX experiment has taken the data for small collision systems, such as p+Au and 3 He+Au collisions to understand the direct photon
production in smaller dNch /d⌘ region than the Cu+Cu peripheral collisions.
The studies of direct photon production in small collision systems have begun, and it will help quantitative understanding of low transverse-momentum
direct photon production.

Acknowledgements
I would like to express the most profound appreciation to my supervisor,
Prof. K. Shigaki. He gave me continuous guidance and support. He also gaveme an excellent opportunity to join the PHENIX collaboration. Without his
agreement of my travel to Brookhaven National Laboratory, I would not havefinished this thesis. I would like to heartfelt appreciate Prof. Y. Yamaguchi,
who advises and support my thesis work. I would never finish this thesis
without his valuable advice and discussions. I would also like to express mydeepest gratitude to Dr. Y. Akiba for his support. He gave me insightfulcomments and generous support. His book on Quark-Gluon Plasma wasalso an excellent reference for this thesis. I am grateful to Assoc. Prof. K.
Homma for his insightful suggestions for this thesis. He also taught me muchknowledge and technical skills of the Beam-Beam Counter in the PHENIX
experiment.
I must gratefully acknowledge Dr. H. En’yo for the financial support
during JRA at RIKEN. Without his help, I would not have completed thisthesis. I would like to thank Prof. T. Sugitate. He taught me Quark-Gluon
Plasma and the history of particle physics. I would also like to acknowledge
Assoc. Prof. T Miyoshi for his comment on my thesis and presentation.
I express my sincere thanks to the member of the Paper Preparation
Group 200 in the PHENIX collaboration. I owe a significant debt to Prof.
R. Seto. I would also like to thank the PHENIX collaboration. I havegreatly benefited from the conveners of the physics working group meetings,
including Prof. V. Riabov and Dr. T. Sakaguchi. Those people give me
constructive comments and warm encouragement. I also appreciate Dr. C.
H. Pinkenburg, Dr. C. Mickey, and Mr. S. Stoll for their cooperation in the
BBC operation and maintenance.
I would like to show my most tremendous appreciation to Dr. Y. Nakamiya,
Mr. D. Watanabe, Dr. K. M. Kijima, Dr. M. Ouchida, and Mr. M. Nihashi,
120

CHAPTER 5. SUMMARY AND CONCLUSION

121

who taught me much knowledge and many technical skills. In particular, Mr.
M. Nihashi gave me a lot of supports for life at BNL. I would like to o↵er myspecial thanks to all the people who worked together at BNL and RIKEN.
Thanks to them, I was able to enjoy BNL and RIKEN life.

Appendix A
Data table
Table A.1: Direct photon fraction in Cu+Cu minimum bias
pT
1.0< pT <1.5GeV/c
1.5< pT <2.0GeV/c
2.0< pT <3.0GeV/c
3.0< pT <5.0GeV/c

r
0.045
0.116
0.064
0.168

Stat. error
0.022
0.027
0.032
0.072

Syst. error
0.548
0.231
0.334
0.195

Table A.2: Direct photon fraction in Cu+Cu 0–40% centralitypT
1.0< pT <1.5GeV/c
1.5< pT <2.0GeV/c
2.0< pT <3.0GeV/c
3.0< pT <5.0GeV/c

r
0.044
0.127
0.090
0.217

122

Stat. error
0.025
0.032
0.038
0.085

Syst. error
0.618
0.259
0.315
0.213

APPENDIX A. DATA TABLE

123

Table A.3: Direct photon fraction in Cu+Cu 40–94% centralitypT
1.0< pT <1.5GeV/c
1.5< pT <2.0GeV/c
2.0< pT <3.0GeV/c

r
0.065
0.061
0.088

Stat. error
0.034
0.046
0.060

Syst. error
0.350
0.357
0.434

Table A.4: Direct photon yield in Cu+Cu minimum bias
pT
1.18741.70062.29153.4444Mean
0.0121337
0.00304398
0.000287172
3.24082e-05

Stat. error
0.00611175
0.000811146
0.000153236
1.65889e-05

Syst. error
0.00635632
0.000621467
8.98173e-05
5.26481e-06

Table A.5: Direct photon yield in Cu+Cu 0–40% centrality
pT
1.18751.70082.28983.445

Mean
0.0289627
0.00805553
0.00097946
0.000104529

Stat. error
0.0172251
0.00229759
0.000454379
5.22027e-05

Syst. error
0.017096
0.00181826
0.000280948
1.74203e-05

Table A.6: Direct photon yield in Cu+Cu 40–94% centrality
pT
1.18791.70342.297

Mean
0.00478253
0.000411663
0.000116383

Stat. error
0.00266948
0.000329365
8.59435e-05

Syst. error
0.00156414
0.000137916
4.5993e-05

APPENDIX A. DATA TABLE

124

Table A.7: Direct photon rapidity density in Cu+Cu collisions
Centrality
dN/dy
Minimum Bias 0.0670627
0–40%
0.169709
40–94%
0.0217306

Stat. error Syst. error
0.0233227 0.0239785
0.0657873 0.0646457
0.0101927 0.00592101

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公表論文
題目：Low-momentum direct-photon measurement in Cu+Cu collisions at sNN= 200 GeV
著者：A. Adare et.al., （別紙、共著者リスト①参照）
Physical Review C 98, 054902 (2018)参考論文(1) 題目：Azimuthally anisotropic emission of low-momentum direct photons in Au+Au
collisions at sNN = 200 GeV
著者：A. Adare et.al., （別紙、共著者リスト②参照）

Physical Review C 94, 064901 (2016)(2) 題目：Dielectron production in Au+Au collisions at sNN = 200 GeV
著者：A. Adare et.al., （別紙、共著者リスト③参照）

Physical Review C 93, 014904 (2016)