̞. ૉཻࢠཧ࿦άϧʔϓ‫ڭ‬त ੴ‫ ڮ‬Ԇ޾ɺۚ୩ ࿨ࢸɺ᤽૿ Յ৳।‫ڭ‬त ੴ௩ ੒ਓɺ୩‫ ޱ‬༟հɺࢁ࡚ ߶ɺ٢ߐ ༑রɺࠜଜ ӳࠀॿ‫ ڭ‬ҏෑ ‫ޗ‬࿠ɺେ໺ ߒ࢙ɺࠤ౻ ༐ೋɺໟར ݈࢘‫ࢉܭ‬Պֶ‫ڀݚ‬ηϯλʔ٬һ‫ڀݚ‬һ ੨໦ ৻໵ʢ‫౎ژ‬େֶ‫ૅج‬෺ཧֶ‫ڀݚ‬ॴʣ‫ڀݚ‬һ ුా ঘ࠸ɺ໦ଜ ఩࢜ɺ ᜊ౻ ՚ɺࠤʑ໦ ݈ࢤɺ‫׈‬઒ ༟հɺଜ໦
‫ٱ‬঵ɺେֶӃੜ ʢ9 ໊ʣʲਓࣄҟಈʳۚ୩࿨ࢸ‫ڭ‬त͕਺ཧ෺࣭‫ܥ‬௕Λୀ೚͠ɺૉཻࢠ࿦‫ࣨڀݚ‬ͷ‫ڭ‬तʹ෮‫ͨ͠ؼ‬ʢ2015 ೥
4 ݄ 1 ೔ʣɻ୩‫ޱ‬༟հത͕࢜‫ࢉܭ‬Պֶ‫ڀݚ‬ηϯλʔ।‫ڭ‬तʹঢ೚ͨ͠ʢ2016 ೥ 1 ݄ 1 ೔ʣɻʲ‫׆ڀݚ‬ಈʳૉཻࢠཧ࿦άϧʔϓʹ͓͍ͯ͸ɺຊ೥౓΋ɺ֨ࢠ৔ͷཧ࿦ͱ௒‫ݭ‬ཧ࿦ͷ 2 ͭͷ෼໺Ͱ‫׆ڀݚͳൃ׆‬ಈ͕ߦͳΘΕͨɻ֨ࢠ৔ͷཧ࿦άϧʔϓ͸ɺ‫ࢉܭ‬Պֶ‫ڀݚ‬ηϯλʔͱີ઀ͳ࿈‫ܞ‬ͷ΋ͱɺ֨ࢠ QCDͷେ‫ܕ‬γϛϡϨʔγϣϯ‫ڀݚ‬Λਪਐ͍ͯ͠Δɻ֨ࢠ৔ͷཧ࿦άϧʔϓͷ‫ऀڀݚ‬ͷେ൒͕ࢀՃ͢ΔओཁϓϩδΣΫτͰ͋Δ HPCI ઓུϓϩάϥϜ෼໺̑‫ڀݚ‬։ൃ՝୊ 1
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ͨɻ2016 ೥ळ͔Β JCAHPCʢ࠷ઌ୺‫ڞ‬ಉ HPC ‫ج‬൫ࢪઃɿஜ೾େֶͱ౦‫ژ‬େֶ྆‫ػ‬ؔͷ‫ڭ‬৬һ͕த৺ͱͳΓઃ‫͢ܭ‬ΔεʔύʔίϯϐϡʔλγεςϜΛઃஔ͠ɺ࠷ઌ୺
ͷେ‫ن‬໛ߴੑೳ‫جࢉܭ‬൫ΛߏஙɾӡӦ͢ΔͨΊͷ૊৫ʣʹ͓͍ͯ Oakforest-PACSʢϐʔΫԋࢉੑೳ 25PFLOPS ͷ௒ฒྻΫϥελ‫ػࢉܭ‬ɺʮ‫ژ‬ʯΛ௒͑Δࠃ಺࠷ߴੑೳ
γεςϜͱͳΔ‫ࠐݟ‬Έʣ͕Քಇ༧ఆͰ͋Γɺ͜Εʹ޲͚ͯ PACS Collaboration Λ૊৫͠ɺ४උ‫ڀݚ‬Λ։͍࢝ͯ͠Δɻ͜Εͱฒߦͯ͠ɺ༗‫ݶ‬Թ౓ɾ༗‫ ౓ີݶ‬QCD ͷ‫ݚ‬‫ڀ‬ɺςϯιϧωοτϫʔΫ‫ࢠ֨ͮ͘جʹࣜܗ‬ήʔδཧ࿦ͷ‫ڀݚ‬ɺඪ४ཧ࿦Λ௒͑Δ
෺ཧͷ୳‫Ͳͳٻ‬ɺ‫׆ڀݚͳൃ׆‬ಈΛߦͬͨɻ͞Βʹɺ֨ࢠ QCD ഑Ґ΍ͦͷଞͷσʔλΛ‫ڞ‬༗͢ΔҝͷσʔλάϦου ILDG/JLDG ͷߏஙɾ੔උΛਪਐͨ͠ɻ
ࠃ಺ͷ‫ࢉܭ‬Պֶશମͷಈ޲ͱͯ͠ɺ2015 ೥౓Ͱऴྃͨ͠ HPCI ઓུϓϩάϥϜͷ
‫ͯ͠ͱܧޙ‬ɺ2016 ೥౓͔Βʮϙετʮ‫ژ‬ʯͰॏ఺తʹऔΓ૊Ή΂͖ࣾձతɾՊֶత
՝୊ʯʹؔ͢ΔΞϓϦέʔγϣϯ։ൃɾ‫ڀݚ‬։ൃ͕࢝·ͬͨɻ‫ ࡏݱ‬9 ͭͷॏ఺՝୊͕ઃఆ͞Ε͓ͯΓɺ9 ൪໨ͷ՝୊Ͱ͋ΔʮӉ஦ͷ‫ج‬ຊ๏ଇͱਐԽͷղ໌ʯ͕ૉཻࢠ
෺ཧɾ‫֩ࢠݪ‬෺ཧɾӉ஦෺ཧ෼໺͕ର৅ͱ͢Δ‫ૅج‬Պֶత‫ڀݚ‬՝୊Ͱ͋Δɻͦͷ‫׆‬ಈ͸ɺhttp://www.jicfus.jp/jp ʹৄ͍͠ɻ－1－௒‫ݭ‬ཧ࿦άϧʔϓ͸‫ݭ‬ͷ৔ͷཧ࿦ɺߦྻ໛‫ܕ‬ɺήʔδɾॏྗରԠͱ͍͏ 3 ͭͷ ؔ࿈͢ΔςʔϚΛத৺ͱͯ͠‫ڀݚ‬ΛਐΊ͍ͯΔɻࠓ೥౓͸ത࢜‫ڀݚ‬һͷ໦ଜࢯɾଜ໦
ࢯ͕ՃΘͬͨ͜ͱʹΑΓɺ‫ڀݚ‬ͷ෯͕޿͕ͬͨɻ‫ݭ‬ͷ৔ͷཧ࿦ͱ࣍‫ݩ‬ਖ਼ଇԽɺ‫ݭ‬ͷ৔ͷཧ࿦ͷ࣍‫ݩ‬ਖ਼ଇԽͱϧʔϓৼ෯ɺήʔδ-ॏྗ૒ରੑͱՄੵ෼ੑʹ‫߹݁ڧͮ͘ج‬ήʔδཧ࿦ͷ‫ڀݚ‬ɺίώʔϨϯτঢ়ଶΛ༻͍ͨߦྻ‫ز‬Կͷ‫ڀݚ‬౳ɺ௒‫ݭ‬ཧ࿦ʹؔ࿈
͢Δ༷ʑͳ෼໺ʹ͍ͭͯͷ‫ڀݚ‬Λߦͬͨɻʲ̍ʳ ֨ࢠ৔ͷཧ࿦ʢۚ୩ ࿨ࢸɺ᤽૿ Յ৳ɺੴ௩ ੒ਓɺ୩‫ ޱ‬༟հɺࢁ࡚ ߶ɺ٢ߐ ༑রɺࠜଜ ӳࠀɺුా ঘ࠸ɺࠤʑ໦ ݈ࢤɺ‫׈‬઒ ༟հ)(1) HPCI ઓུϓϩάϥϜ෼໺ 5 ʹ͓͚Δ‫ڀݚ‬։ൃ՝୊෼໺ 5ʮ෺࣭ͱӉ஦ͷ‫ߏͱݯى‬଄ʯͷઓུ໨ඪ͸ɺϏοάόϯʹ࢝·ΔӉ஦ͷྺ࢙ʹԙ͚Δɺૉཻࢠ͔Β‫ݩ‬ૉ߹੒ɺ੕ɾۜՏ‫ܗ‬੒ʹࢸΔ෺࣭ͱӉ஦ͷ‫ݯى‬ͱߏ଄Λɺෳ਺ͷ֊૚Λ‫ࢉܭ͙ܨ‬Պֶతख๏Ͱ౷Ұతʹཧղ͢Δ͜ͱʹ͋Δɻ͜ͷ໨ඪΛ໨ࢦͯ͠ 4 ͭͷ‫ڀݚ‬։ൃ՝୊͕ઃఆ͞Ε͓ͯΓɺͦͷ͏ͪͷҰ͕ͭʮ֨ࢠ QCD ʹΑΔ෺ཧ఺ͰͷόϦΦϯؒ૬‫༻࡞ޓ‬ͷܾఆʯͰ͋Δɻຊ՝୊͕
໨ࢦ͢΋ͷ͸ɺ֨ࢠ QCD ‫ࢉܭ‬ͷඍࡉԽͱϚϧνεέʔϧԽΛ‫͢ͱݤ‬Δ৽͍͠
ల։Ͱ͋ΔɻඍࡉԽͱ͸ɺΞΠιεϐϯରশੑͷഁΕͷޮՌΛऔΓೖΕͨ‫ࢉܭ‬΍ɺ௿ΤωϧΪʔͷϋυϩϯߏ଄‫ࢉܭ‬Λҙຯ͢ΔɻଞํɺϚϧνεέʔϧԽͱ͸ɺ֨ࢠ QCD Λ༻͍ͨ‫֩ࢠݪ‬ͷ௚઀ߏ੒ʹΑͬͯͦͷଋറΤωϧΪʔΛ‫ٻ‬ΊͨΓɺ͋Δ͍͸֩ࢠؒͷ༗ޮϙςϯγϟϧΛௐ΂ͨΓ͢Δ͜ͱΛҙຯ͢Δɻલऀ͸ɺࢁ࡚ɾ᤽૿Λத৺ͱͨ͠άϧʔϓʹΑͬͯਪਐ͞Ε͓ͯΓɺ‫ऀޙ‬͸ HAL
QCD Collaboration ͕औΓ૊ΜͰ͍ΔΞϓϩʔνͰ͋Δʢ‫ޙ‬ड़ʣɻʮ‫ژ‬ʯͰੜ੒͞Εͨ഑ҐΛ༻͍ͨ‫ج‬ຊ෺ཧྔ‫ࢉܭ‬ʮ‫ژ‬ʯͰ͸ɺDDHMCʢDomain-Decomposed Hybrid Monte Carloʣ๏Λ༻͍
ͯɺ964 ͷ֨ࢠαΠζɺ0.1 fm ఔ౓ͷ֨ࢠִؒΛ࣋ͭɺ2+1 ϑϨʔόʔʢmu =md ̸= ms ʣQCD ͷήʔδ഑ҐΛੜ੒ͨ͠ɻ͜ͷ഑Ґͷ࠷େͷಛ௃͸ɺ(9fm)3
ͱ͍͏ैདྷʹͳ͍ѹ౗తͳେ͖͞ͷۭؒମੵͰ͋Δɻͦͷ࠷େͷར఺͸ɺෳ਺ͷ֩ࢠ͔Β‫֩ࢠݪ‬Λ௚઀ߏ੒͢Δ͜ͱ͕ՄೳʹͳΔ͜ͱ΍ɺ཭ࢄԽ͞ΕͨӡಈྔͷࠁΈ෯͕ࡉ͔͘ͳΔ͜ͱʹΑͬͯɺϋυϩϯ‫ܗ‬ঢ়Ҽࢠͷӡಈྔۭؒʹ͓
͚Δਫ਼ີͳղੳ͕ՄೳͱͳΔ͜ͱͰ͋Δɻ഑Ґੜ੒͸ 2014 ೥౓ॳΊʹऴྃ͠ɺ
HA-PACSʢ‫ࢉܭ‬ϊʔυ਺ 332ɺGPU ෦ϐʔΫԋࢉੑೳ 1.048PflopsɺCPU ෦ϐʔΫԋࢉੑೳ 0.118PflopsʣΛ༻͍ͯϋυϩϯ࣭ྔͳͲͷ‫ج‬ຊ෺ཧྔͷଌఆΛߦ͖ͬͯͨɻ2015 ೥౓͸ɺϋυϩϯ࣭ྔɺΫΥʔΫ࣭ྔɺٖεΧϥʔதؒࢠ่յఆ਺ͳͲͷ‫ج‬ຊతͳ෺ཧྔͷ‫ʹࢉܭ‬ରۭͯ࣌ؒ͠ฒਐରশੑΛར༻ͨ͠౷‫ܭ‬ਫ਼౓ͷ޲্Λ໨ࢦͨ͠ɻਤ 1 ͸෺ཧ఺Ͱͷϋυϩϯ࣭ྔ‫ࢉܭ‬ͷ࠷ऴ݁ՌΛ࣮‫ݧ‬஋ͱൺֱͨ͠΋ͷͰ͋Δɻ͜͜Ͱ͸ɺΫΥʔΫ࣭ྔ (mu = md ̸= ms ) ͱ֨ࢠִؒΛܾΊΔͨΊͷ 3 ͭͷ෺ཧྔͱͯ͠ɺπ தؒࢠ࣭ྔʢmπ ʣɺK தؒࢠ࣭ྔʢmK ʣɺΩ όϦΦϯ࣭ྔʢmΩ ʣΛ࠾༻͍ͯ͠Δɻ

－2－

0.16
0.14

(mH/mΩ)lat / (mH/mΩ)exp − 1

0.12
0.10
0.08
0.06
0.04
0.02
0.00
-0.02
-0.04
-0.06
-0.08
-0.10

π

K

ρ K* φ

N Λ Σ

Ξ

Δ

∗

Σ

Ξ

∗

Ω

ਤ 1: 2+1 ϑϨʔόʔ֨ࢠ QCD ‫Ͱࢉܭ‬ಘΒΕͨϋυϩϯ࣭ྔͱ࣮‫ݧ‬஋ͱͷൺֱɻനൈ͖γϯϘϧ͸ΫΥʔΫ࣭ྔͱ֨ࢠִؒΛܾΊΔͨΊͷ෺ཧΠϯϓοτΛද͢ɻ҆ఆཻࢠ (‫͍ڧ‬૬‫่Ͱ༻࡞ޓ‬յ͠ͳ͍) ͸࣮‫ݧ‬஋ͱ‫ࠩޡ‬ͷൣғͰҰக͍ͯ͠Δ
ͷʹରͯ͠ɺෆ҆ఆཻࢠ (‫͍ڧ‬૬‫่Ͱ༻࡞ޓ‬յ͢Δ ρ ΍ ∆ ͳͲ) ͸ɺ‫ࠩޡ‬ͷൣғΛ௒࣮͑ͯ‫ݧ‬஋ͱͷ༗ҙͳζϨ͕‫ͯݟ‬औΕΔɻ͜Ε͸ɺ‫͍ͯ͠༻࠾ࡏݱ‬Δϋυϩϯ࣭ྔͷ‫ํࢉܭ‬๏͕ෆ҆ఆཻࢠʹରͯ͠͸༗ޮͰͳ͍͜ͱΛද͓ͯ͠Γɺ͜Ε΄Ͳ໌֬ʹ࣮ূ͞Εͨྫ͸ੈքͰॳΊͯͰ͋Δɻ͜ͷଞɺϋυϩϯ࣭ྔͷ‫ͱࢉܭ‬ฒߦͯ͠ɺٖεΧϥʔதؒࢠͷ่յఆ਺ɺΧΠϥϧઁಈ࿦ʹ͓͚Δ௿ΤωϧΪʔఆ਺ɺ֩ࢠͷγάϚ߲ͳͲͷ‫ࢉܭ‬΋࣮ߦ͠ɺେม‫ڵ‬ຯਂ͍݁ՌΛಘͯ
͍Δʢ࿦จ 8ʣɻɹ(2) K தؒࢠ่յৼ෯ͷ‫ڀݚ‬ૉཻࢠඪ४໛‫ʹܕ‬͸ɺੲ͔Βͷະղܾͳ໰୊Ͱɺ͔ͭཧ࿦ͷ‫ۃ͍͓ͯʹূݕ‬Ίͯॏཁͳ໰୊͕࢒͞Ε͍ͯΔɻK தؒࢠ่յͰͷ ∆I = 1/2 ଇͷղ໌ͱɺCPඇอଘύϥϝʔλ (ϵ′ /ϵ) ͷཧ࿦͔Βͷ༧ଌͰ͋Δɻ͜ΕΒͷ໰୊ʹ͸ɺK தؒࢠ͕ೋͭͷ π தؒࢠʹ่յ͢Δ৔߹ͷ่յৼ෯ͷ‫͕ࢉܭ‬ඞཁͰ͋Δɻ
ੴ௩ɺ٢ߐΒ͸ɺ֨ࢠ QCD ʹΑΓ่յৼ෯Λ֨ࢠ QCD ʹΑΓ਺஋‫͠ࢉܭ‬ɺ໰୊ͷ‫ڀݚ‬Λߦͬͨɻπ தؒࢠ࣭ྔ mπ = 280 MeV ͷ‫Ͱݩ‬ɺऴঢ়ଶͷ π தؒࢠ͕ӡಈྔΛ΋͍ͨͳ͍৔߹ͷ‫ࢉܭ‬Λ‫׬‬੒ͤͨ͞ (จ‫ݙ‬.9)ɻ͜ͷ‫ʹࢉܭ‬ΑΓɺ∆I = 1/2 ଇͷஹީΛ‫ݟ‬Δ͜ͱ͕Ͱ͖ͨɻCP ඇอଘύϥϝʔλ (ϵ′ /ϵ) ʹؔͯ͠͸౷‫͕ࠩޡܭ‬ඇৗʹେ͖͘ɺ‫ࢉܭ‬ͷվળ͕ඞཁͰ͋Δ͜ͱ͕෼͔ͬͨɻ
͜ͷ‫ڀݚ‬Λ‫ʹݩ‬ɺ‫ࢉܭ‬ΛӡಈྔΛ΋ͭ‫࣮ݱ‬ͷ่յͷ৔߹ʹ֦ு͠ɺ৴པੑͷߴ͍ৼ෯Λ‫ٻ‬ΊΔ‫ڀݚ‬Λ։࢝ͨ͠ɻ‫ࡏݱ‬ɺ่յৼ෯ͷ‫ࢉܭ‬ͷͨΊʹɺ৽ͨͳήʔδ഑ҐΛੜ੒͠ɺຊ֨‫ࢉܭݧࢼ͚ͨ޲ʹࢉܭ‬Λߦ͍ͬͯΔɻ(3) ༗‫ݶ‬Թ౓ɾ༗‫ ౓ີݶ‬QCD ͷ‫ڀݚ‬ʢWHOT-QCD Collaborationʣ

－3－ۚ୩ɺ୩‫ޱ‬Β͸ɺ৽ׁେֶߐ৲৴࢘।‫ڭ‬तɺ޿ౡେֶകా‫࢜و‬।‫ڭ‬तɺ‫۝‬भେֶླ໦ത‫ڭ‬तΒͱͷ‫ڞ‬ಉ‫Ͱڀݚ‬ɺWilson ‫ܕ‬ΫΥʔΫʹΑΔ༗‫ݶ‬Թ౓ɾີ౓̦
̘̙ͷ‫ڀݚ‬ΛҾ͖ଓ͖ਪਐͨ͠ɻ
վྑ Wilson ΫΥʔΫʹΑΔ NF = 2 + 1 QCD ͷ෺ཧ఺ۙ๣ʹ͓͚Δঢ়ଶํఔࣜͷͨΊͷ഑Ґੜ੒Λ‫ܧ‬ଓͯ͠ਪਐ͢Δͱͱ΋ʹɺঢ়ଶํఔࣜͷධՁʹඞཁͳϕʔλؔ਺Λ QCD ͷଟม਺ۭؒͰਫ਼౓Αܾ͘ఆ͢Δख๏ͱͯ͠ɺଟॏ఺࠶ॏ
Έ෇͚๏ʹΑΔϕʔλؔ਺ධՁͷࢼ‫ݧ‬Λߦͬͨɻ͞ΒʹɺGradient Flow ๏Λ༻͍ͨ༗‫ݶ‬Թ౓ঢ়ଶํఔࣜͷධՁΛɺಈతΫΥʔΫΛ‫ؚ‬Ή QCD Ͱ࣮ߦ͢Δ࠷ॳͷ‫ڀݚ‬Λ։࢝͠ɺࢼ‫ڀݚݧ‬ͷ݁ՌΛಘͨɻ
0.14451.7

1.69

κ=0.1400
κ=0.1425
κ=0.1440
simulation point
multi point

mPS/mV=0.70
mPS/mV=0.72
mPS/mV=0.74
mPS/mV=0.76

0.144
0.1435

P

κ

0.143

1.68

0.1425
0.142

1.67

1.66

0.1415
0.141

0.14

0.142

κ

0.144

1.81

1.815

1.82
β

1.825

1.83

1.835

ਤ 2: NF = 2 QCD ʹ͓͚Δଟॏ఺࠶ॏΈ෇͚๏ͷ‫[ ڀݚ‬࿦จ 11] ɻࠨਤɿվྑϓϥέοτ P =c0 W 1×1 + 2c1 W 1×2 ͷ‫ظ‬଴஋ͷ β = 1.825. ʹ͓͚Δ κ ґଘੑɻࠇ‫ؙ‬͸ɺ̏ͭͷγϛϡϨʔγϣϯ఺ʹ͓͚Δ‫؍‬ଌ݁Ռɻࢵɺ྘ɺ੨͸ɺ̏఺ͦΕͧΕͷσʔλʹΑΔ୯७ͳ࠶ॏΈ෇͚๏ͷ݁ՌɻʮॏͶ͋Θͤ໰୊ʯͷͨΊʹɺύϥϝʔλΛେ͖͘ಈ͔͢ͱ୯७ͳ࠶ॏΈ෇͚๏Ͱ͸‫؍‬ଌ݁ՌΛ࠶‫ͳ͖Ͱݱ‬͍͜ͱ͕Θ͔Δɻ੺͸ɺ̏఺ͷσʔλΛଟॏ఺࠶ॏΈ෇͚๏ʹΑΓ݁߹ͯ͠‫݁ͨ͠ࢉܭ‬Ռɻ‫؍‬ଌ݁ՌΛεϜʔεʹ‫͗ܨ‬ɺ޿͍ύϥϝʔλྖҬͰਫ਼౓ͷߴ͍‫͕ࢉܭ‬ՄೳͱͳΔɻɹӈਤɿmPS /mV ͷ݁Ռ͔Β‫ٻ‬Ίͨ౳෺ཧઢ (LCP)ɻmPS /mV ͕ 1 ʹ͍ۙ΄ͲΫΥʔΫ࣭ྔ͕େ͖͍৔߹ʹ૬౰͢Δɻ

ଟॏ఺࠶ॏΈ෇͚๏ʹΑΔ QCD ϕʔλؔ਺༗‫ݶ‬Թ౓ɾ༗‫ ౓ີݶ‬QCD ͷঢ়ଶํఔࣜ΍෺ཧྔͷԹ౓ɾີ౓ґଘੑΛ‫͢ࢉܭ‬ΔͨΊʹ͸ɺཧ࿦ͷύϥϝʔλۭؒ಺ͷʮ౳෺ཧઢʢLine of Constant Pjhysics:
LCPʣʯʢಉҰͷ෺ཧ‫ܥ‬Λ༷ʑͳ֨ࢠִؒͰද‫ݱ‬ʣͱɺLCP ্Ͱύϥϝʔλͷ֨ࢠִؒґଘੑΛ͋ΒΘ͢ʮϕʔλؔ਺ʯͷ৘ใ͕ඞཁͰ͋ΔɻQCD ͸ɺήʔδ݁߹ఆ਺ (β) ͱෳ਺ͷΫΥʔΫ࣭ྔ (κ) ΍Խֶϙςϯγϟϧ (µ) Λ‫ج‬ຊύϥϝʔλͱ͕ͯ࣋ͭ͠ɺଟ࣍‫ݩ‬ͷύϥϝʔλۭؒͰ LCP ΍ϕʔλؔ਺Λਫ਼౓Α͘ධՁ͢Δ͜ͱ͸؆୯Ͱ͸ͳ͍ɻͦΕΛղܾ͢ΔͨΊʹʮଟॏ఺࠶ॏΈ෇͚๏ʢmulti-point reweighting ๏ʣʯΛ‫ݕ‬౼͠ɺີ౓θϩͷ NF = 2 QCD ͷ৔߹ʹࢼ‫ڀݚݧ‬Λߦͬͨʢ࿦จ 10,11ʣɻ‫ܥ‬ͷύϥϝʔλґଘੑΛௐ΂Δ༗ྗͳํ๏ͱͯ͠ɺ࠶ॏΈ෇͚๏ʢreweighting๏ʣ͕Α͘࢖ΘΕΔ͕ɺ༗‫ݶ‬Թ౓ɾ༗‫ ౓ີݶ‬QCD ͷ‫Ͱڀݚ‬ཁ‫͞ٻ‬ΕΔΑ͏ͳɺ－4－

(mVa)dβ/d(mVa)

-0.5
-0.6

0.03

mPS/mV=0.70
mPS/mV=0.72
mPS/mV=0.74
mPS/mV=0.76
Nf=2 1 loop
Nf=0 1 loop

0.025(mVa)dκ/d(mVa)

-0.4

-0.7
-0.8
-0.9
-1

0.02
0.015
0.01
mPS/mV=0.70
mPS/mV=0.72
mPS/mV=0.74
mPS/mV=0.76

0.005

1.81

1.815

1.82

1.825

1.83

0
1.835

β

1.81

1.815

1.82
β

1.825

1.83

1.835

ਤ 3: ଟॏ఺࠶ॏΈ෇͚๏ʹΑΔɺNF = 2 QCD ͷϕʔλؔ਺ a(dβ/da)ʢࠨਤʣͱ a(dκ/da)ʢӈਤʣɻmV a Λۙ๣Ͱ݁߹ύϥϝʔλͷ̎࣍ϑΟοτͨ݁͠Ռʹ‫ͨ͠ࢉܭ͍ͯج‬΋ͷɻࠨਤͷഁઢ͸ɺ

NF = 0 ͱ 2 ͷ৔߹ͷઁಈ̍࣍ͷ݁Ռɻ[࿦จ 11]ύϥϝʔλۭؒͷ޿͍ྖҬʹԠ༻͢Δ͜ͱʹ͸ࠔ೉͕൐͏ɻਤ 2 ࠨʹɺվྑϓϥέοτ P ͷ κ ґଘੑΛࣔ͢ɻࠇ‫ؙ‬͸̏ͭͷγϛϡϨʔγϣϯ఺ʹ͓͚Δ‫؍‬ଌ݁ՌͰɺࢵɺ྘ɺ੨͸ɺͦΕͧΕͷγϛϡϨʔγϣϯ఺ͷσʔλΛ࢖ͬͯ࠶ॏΈ෇͚๏Λ࢖ͬͯ‫ ͨ͠ࢉܭ‬P ͷ κ ґଘੑͷ༧‫ݴ‬Λ͋ΒΘ͢ɻύϥϝʔλΛେ͖͘ಈ͔͢ͱ‫؍‬ଌ݁ՌΛ࠶‫͕ͱ͍͜ͳ͖Ͱݱ‬Θ͔Δɻ‫ࠩޡ‬ධՁ΋৴པੑ͕௿
͘ɺ͜ͷ·· LCP ΍ϕʔλؔ਺ͷ‫ͱ͜͏࢖ʹࢉܭ‬͸೉͍͠ɻ͜Ε͸ɺ࠶ॏΈ෇͚๏ʹඞཁͳώετάϥϜΛɺ֤γϛϡϨʔγϣϯ఺Ͱͷ‫ظ‬଴஋ۙ๣Ͱ͔͠৴པͰ͖ΔධՁ͕Ͱ͖ͣɺ‫ظ‬଴஋͕େ͖͘ಈ͘ࣄʹରԠ͢ΔΑ͏ͳύϥϝʔλͷେ͖ͳมԽʹରԠͰ͖ͳ͍ࣄʹΑΔʢʮॏͶ͋Θͤ໰୊ʯʣɻ
ଟॏ఺࠶ॏΈ෇͚๏Ͱ͸ɺॏͶ͋Θͤ໰୊Λղܾ͢ΔͨΊʹɺෳ਺ͷγϛϡϨʔγϣϯσʔλΛ౷߹ͯ͠࠶ॏΈ෇͚͢Δɻਤ 2 ࠨਤʹɺ̏ͭͷγϛϡϨʔγϣϯΛ߹Θͤͯଟॏ఺࠶ॏΈ෇͚๏ʹΑΓ‫݁ͨ͠ࢉܭ‬ՌΛ੺ઢͰࣔ͢ɻ‫؍‬ଌ݁Ռʢࠇ‫ؙ‬ʣΛεϜʔεʹ‫͗ܨ‬ɺγϛϡϨʔγϣϯ఺ͷؒͷྖҬ΋‫ؚ‬Ίɺ޿͍ύϥϝʔλྖҬͰ৴པੑͱਫ਼౓ͷߴ͍݁Ռ͕ಘΒΕͨɻ͜ΕʹΑΓɺLCP ͱ
ϕʔλؔ਺ͷ‫ʹࢉܭ‬ඞཁͳɺύϥϝʔλۭؒͷ޿͍ྖҬͰͷਫ਼౓ͷߴ͍ଌఆ͕ՄೳͱͳΔɻͦΕʹ‫ ͨ͠ࢉܭ͍ͯͮج‬NF = 2 QCD ͷ LCP ͱϕʔλؔ਺Λɺਤ 2 ӈਤͱਤ 3 ʹࣔ͢ɻ

NF = 2 + 1 ෺ཧ఺ QCD ͱ༗‫ ౓ີݶ‬QCD
͜ͷख๏ΛԠ༻ͯ͠ NF = 2 + 1 ෺ཧ఺ QCD ΍༗‫ ౓ີݶ‬QCD Λ‫͢ڀݚ‬Δͨ
Ίͷ४උ΋ਐΊ͍ͯΔʢ࿦จ 12ʣɻզʑ͕։ൃͨ͠Δ‫ݻ‬ఆ֨ࢠִؒΞϓϩʔνʹ‫͖ͮج‬ɺPACS-CS ͷθϩԹ౓γ
ϛϡϨʔγϣϯͱಉ͡γϛϡϨʔγϣϯɾύϥϝʔλΛ࢖ͬͯɺT = 140–500
MeV ʹ૬౰͢Δ༗‫ݶ‬Թ౓഑ҐΛ‫ܥ‬౷తʹ஝ੵ͍ͯ͠Δɻ͜Ε·Ͱʹੜ੒ͨ͠༗‫ݶ‬Թ౓഑ҐͱɺPACS-CS ͕ެ։͍ͯ͠ΔθϩԹ౓഑Ґ΍ reweighting factorΛ༻͍ͯɺPlaquette ‫ظ‬଴஋ɺPolyakov loop ‫ظ‬଴஋ɺ͞Βʹঢ়ଶํఔࣜͷ‫ܭ‬ࢉͰඞཁͱͳΔ QCD ࡞༻ͷ coupling parameter ඍ෼ͷࢼ‫ࢉܭݧ‬Λ͓͜ͳ͍ɺ

－5－‫ظ‬଴͢ΔৼΔ෣͍Λ֬ೝͨ͠ʢਤ 4 ࠨਤʣɻ͜ΕΛൃలͤ͞ɺଟॏ఺࠶ॏΈ෇͚๏΍ Gradient Flow ๏Λ༻͍ͨ෺ཧ఺Ͱͷϕʔλؔ਺ͷධՁ͕࣍ͷ՝୊Ͱ
͋Δɻ
25

0.03
<Polyakov loop>

phys. pnt.
PRD85(094508)

0.3

20

0.2
0.02

15
0.1
0

10
0.5

1

1.5

0.01

5
0

Tr0
0
0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0

100 200 300 400 500 600 700

ਤ 4: ࠨਤɿ෺ཧ఺ʹ͓͚Δ༗‫ݶ‬Թ౓ QCD ͷ഑ҐͰ‫ ͨ͠ࢉܭ‬Polyakov loop ‫ظ‬଴஋ͷԹ౓ґଘੑɻҎલͷ‫ʹࢉܭ‬ΑΔൺֱతॏ͍ΫΥʔΫ࣭ྔͰͷ݁Ռ΋ࣔ͢ɻΫΥʔΫ࣭ྔ͕ܰ͘ͳΔͱ૬సҠԹ౓͕
Լ͕Δࣄ͕෼͔Δɻ[࿦จ 11] ɹӈਤɿGradient Flow ๏ʹΑΔ NF = 2 + 1 QCD ঢ়ଶํఔࣜʢதؒ
݁Ռʣɻॎ࣠͸ ϵ/T 4 ɺԣ࣠͸ T [MeV]ɻ੺‫ ؙ͕‬Gradient Flow ๏ͷ݁ՌͰɺࠇࡾ֯͸ T -ੵ෼๏ʹΑΔҎલͷ݁Ռɻ

Gradient Flow ๏ʹΑΔ NF = 2 + 1 QCD ঢ়ଶํఔࣜ
ۙ೥ QCD ೤ྗֶྔͷ৽͍͠‫ํࢉܭ‬๏ͱͯ͠ gradient flow Λ༻͍ͨํ๏͕஫
໨Λཋͼ͍ͯΔɻ͜ͷํ๏Ͱ͸‫܁‬Γࠐ·ΕͨΤωϧΪʔӡಈྔςϯιϧΛ֨ࢠ্Ͱ௚઀‫͢ࢉܭ‬Δ͜ͱ͕ՄೳʹͳΓɺΤωϧΪʔີ౓ͳͲͷঢ়ଶํఔࣜΛ‫ࢉܭ‬
͢Δ͜ͱ͕Ͱ͖Δɻ͞Βʹ gradient flow ʹΑΔΫʔϦϯάͷޮՌʹΑͬͯɺ೤ྗֶྔʹ͓͚Δ‫ࠩޡ‬ͷେ෦෼Λ઎ΊΔήʔδ഑Ґͷ༳Β͕͗ԡ͑͞ΒΕɺैདྷͷੵ෼๏Λϕʔεͱͨ͠‫ࢉܭ‬ख๏ʹൺ΂ͯɺߴਫ਼౓ͷ‫͕ࢉܭ‬ՄೳʹͳΔ͜ͱ͕‫ظ‬଴͞Ε͍ͯΔɻ͜Ε·ͰʹΫΤϯνۙࣅͰ͸ gradient flow Λ༻͍ͨ‫ߦ͕ࢉܭ‬ΘΕ͓ͯΓɺͦͷ༗ޮੑ͕ࣔ͞Ε͍ͯΔɻಈతΫΥʔΫΛ‫ؚ‬Ή࡞༻Ͱͷ gradient flow ͷఆࣜԽ͸ɺM. Lüscher ʹΑΓߦΘΕ͓ͯΓɺfull QCD ͰͷΤωϧΪʔӡಈྔςϯιϧͷධՁํ๏΋ H. Makino ͱ H. Suzuki ͷ࿦จͰ։ൃ͞Ε͍ͯΔɻ͞ΒʹɺɺΧΠϥϧΦʔμʔύϥϝʔλ΍Ґ૬਺ͷධՁ΋ gradient flow ʹΑΓ༰қʹͳΔͱ‫ظ‬଴͞Ε͓ͯΓɺ૬ߏ଄ͳͲͷ‫ʹڀݚ‬΋େ͖ͳਐల͕‫ظ‬଴͞ΕΔɻզʑ͸ɺ͜ΕΒΛ࢖ͬͯಈతΫΥʔΫΛ‫ؚ‬Ή (2+1)-flavor QCD ʹ͓͚Δ gradient flowΛ༻͍ͨ QCD ೤ྗֶྔͷ‫ࢉܭ‬Λ໨తͱͯ͠ɺ‫ڀݚ‬ΛਐΊ͍ͯΔɻͦͷͨΊͷ‫ࢉܭ‬ίʔυΛɺ Bridge++Λϕʔεʹ։ൃͨ͠ɻ
࠷ॳͷεςοϓͱͯ͠ɺmPS /mV = 0.65 ͷ΍΍ॏ͍ΫΥʔΫ࣭ྔྖҬͰ NF =2 + 1 QCD ͷঢ়ଶํఔࣜͷ‫ڀݚ‬Λ։࢝ͨ͠ɻ‫ݻ‬ఆ֨ࢠִؒ๏Λ࠾༻͠ɺCPPACS Collaboration Ͱੜ੒ͨ͠θϩԹ౓഑Ґͱಉ͡γϛϡϨʔγϣϯɾύϥ－6－ϝʔλΛ༻͍ɺT = 170–700MeV ʹ૬౰͢Δ༗‫ݶ‬Թ౓഑ҐΛੜ੒͍ͯ͠Δɻਤ
4 ӈਤʹɺgradient flow Λ༻͍ͨঢ়ଶํఔࣜ‫ࢉܭ‬ͷதؒ݁ՌΛࣔ͢ɻMakinoiSuzuki ʹΑΔঢ়ଶํఔࣜʢΤωϧΪʔɾӡಈྔςϯιϧʣͷධՁํ๏Ͱ͸ɺflow
time t ʹ͍ͭͯθϩͷ‫ݶۃ‬Λ֎ૠ͢Δඞཁ͕͋Δ͕ɺNt ≈ 4 ͷߴԹ֨ࢠҎ֎Ͱ͸ɺ҆ఆͨ݁͠ՌΛಘΔ͜ͱ͕ग़དྷͨɻਤ 4 ӈਤͰɺ੺‫ ؙ͕‬Gradient Flow๏ʹΑΔΤωϧΪʔີ౓ͷ݁ՌͰɺࠇࡾ֯͸ɺT -ੵ෼๏ʹΑΓզʑ͕Ҏલ‫ܭ‬ࢉͨ݁͠ՌͰ͋ΔɻGradient Flow ๏ʹΑΔӈ୺ͷσʔλʢNt = 4ʣͱͦͷ࣍ͷσʔλʢNt = 6ʣͰ͸ɺt → 0 ͷ֎ૠʹෆఆੑ͕༗Δ͕ɺͦͷ‫ܥ‬౷‫ࠩޡ‬͸Τϥʔόʔʹ‫·ؚ‬Ε͍ͯͳ͍ɻ࿈ଓ‫ݶۃ‬Ҏ֎Ͱ Gradient Flow ๏ͱ T -ੵ෼๏͕Ұக͢Δඞવੑ͸ͳ͍͕ɺ༗‫ݶ‬ͷ֨ࢠ্Ͱ྆ऀ͕΄΅Ұக͍ͯ͠Δ͜ͱ͸ɺํ๏ͷ༗༻ੑΛ͍ࣔࠦͯ͠Δɻ

Gradient Flow ๏ʹΑΔ‫ؒ࣌ࢉܭ‬͸ɺT -ੵ෼๏ΑΓେ͖͘࡟‫͞ݮ‬Ε͍ͯΔɻ࣍ͷ໨ඪ͸ɺҟͳΔ֨ࢠִؒͰͷಉ༷ͷ‫ࢉܭ‬Λߦ͍ɺ࿈ଓ‫ݶۃ‬Λௐ΂Δ͜ͱͰ͋
Δɻ࠷ऴతʹ͸ɺ෺ཧ఺Ͱͷ༗‫ݶ‬Թ౓഑ҐΛ༻͍ͨΤωϧΪʔӡಈྔςϯιϧͷଌఆΛ໨ࢦ͍ͯ͠Δɻ(4) ֨ࢠ QCD ʹΑΔอଘిՙͷ༳Β͗ͱ૬ؔͷ‫ڀݚ‬
s1/2 [GeV]
NN

200

62.4

39

27

19.6

11.5 7.7(MQ/σ2Q )/(MP/σ2P )

0.25

QCD:

(Tf,0, κf2=0)(Tf,0,κf2=0.02)

0.2

STAR: pmax
=2.0 GeVt

0.15

PHENIX/STAR2.0

pmax=0.8 GeVt

0.1(MP/σ2P)2

0.05
0

0.2

0.4

0.6

0.8

1

ਤ 5: ૯ిՙ༳Β͗ͷฏ‫ͱۉ‬෼ࢄͷൺͱ૯ཅࢠ਺༳Β͗ͷฏ‫ͱۉ‬෼ࢄͷൺͷൺͷ࣮‫ݧ‬஋ʢγϯϘϧʣͱ֨ࢠ QCD ‫ࢉܭ‬ʢόϯυ‫ͼٴ‬ઢʣͱͷൺֱɻด͡ࠐΊɾඇด͡ࠐΊ૬సҠͷલ‫Ͱޙ‬͸ɺ‫ܥ‬ͷࣗ༝౓͕ϋυϩϯ͔ΒΫΥʔΫʹมԽ͢Δɻอଘిՙͷ༳Β͗΍ͦΕΒͷؒͷ૬ؔ͸ɺ͜ͷࣗ༝౓ͷมԽʹහ‫͋Ͱײ‬Γɺ૬సҠͷੑ࣭Λৄࡉʹௐ΂Δͷʹ༗༻Ͱ͋Δɻ
େ໺͸ɺFrithjof Karsch ࢯΛத৺ͱ͢Δ BNL-Bielefeld-CCNU CollaborationʹࢀՃ͠ɺ2+1 ϑϨʔόʔͷ Highly Improved Staggered Quark ࡞༻Λ༻͍ͨ
֨ࢠ QCD γϛϡϨʔγϣϯʹΑΓɺ༷ʑͳอଘిՙͷ༳Β͗‫ͦͼٴ‬ΕΒͷؒͷ૬ؔʹؔ͢Δ‫ڞ‬ಉ‫ڀݚ‬Λߦͬͨɻ͜͜ͰɺγϛϡϨʔγϣϯ͸ෳ਺ͷ֨ࢠִؒʹͯߦ͍ɺ࿈ଓ‫ݶۃ‬Λͱͬͨɻ·ͣɺ300–700MeV ͷߴԹྖҬʹ͓͍ͯɺu,d,s ΫΥʔΫʹର͢Δର֯‫ͼٴ‬ඇର֯ΫΥʔΫ਺‫ײ‬ड཰Λ 4 ࣍ͷΦʔμʔ·Ͱ‫ͨ͠ࢉܭ‬ɻͦͯ͠ɺಘΒΕͨ݁ՌΛ͍͔ͭ͘ͷઁಈ‫ͱࢉܭ‬ൺֱ͠ɺ‫ʹ͍ޓ‬Α

－7－͘Ұக͢Δ͜ͱΛࣔͨ͠ʢ࿦จ 14ʣɻ·ͨɺԹ౓ͱԽֶϙςϯγϟϧʹؔ͢Δ
ςΠϥʔల։Λ༻͍ͯɺ૯όϦΦϯ਺‫ͼٴ‬૯ిՙͷ༳Β͗ͷฏ‫ͱۉ‬෼ࢄΛ‫ࢉܭ‬ͨ͠ɻͦͯ͠ɺͦͷ݁ՌΛ STAR ‫ ͼٴ‬PHENIX ࣮‫ݧ‬ͷ݁Ռͱൺֱ͠ɺόϦΦϯԽֶϙςϯγϟϧ͕ 0 ͷ‫Ͱݶۃ‬ͷ freeze-out Թ౓Λܾఆ͢Δͱͱ΋ʹɺॳΊ
ͯɺfreeze-out line ͷ‫ݶ੍ʹ཰ۂ‬Λ༩͑ͨʢ࿦จ 16ʣɻ(5) ༗‫ݶ‬Թ౓֨ࢠ QCD ʹΑΔΫΥʔίχ΢ϜফࣦͱॏΫΥʔΫ༌ૹͷ‫ڀݚ‬
model
3a

BGM

2βa

2βb

2αb

1βb

2αa

1βa

1αa

1αb

0
1

κ/T

T ~ 1.5 Tc

2
3

3
4
strategy (i)strategy (ii)5

ਤ 6: ༷ʑͳϞσϧʹ‫ͮ͘ج‬εϖΫτϧؔ਺ͷϑΟοτ͔ΒಘΒΕͨॏΫΥʔΫӡಈྔ֦ࢄ܎਺ͷ݁Ռɻփ৭ͷόϯυ͸࠷ऴ݁ՌΛࣔ͢ɻΫΥʔίχ΢Ϝ͸νϟʔϜ΍ϘτϜͱ͍ͬͨॏΫΥʔΫͱͦͷ൓ΫΥʔΫͷଋറঢ়ଶͰ͋ΔɻRHIC ΍ LHC Ͱͷ૬ର࿦తॏΠΦϯিಥ࣮‫͚͓ʹݧ‬ΔΫΥʔίχ΢Ϝੜ੒ྔͷ཈੍͸ɺΫΥʔΫɾάϧΦϯɾϓϥζϚ (QGP) ੜ੒Λࣔ͢ॏཁͳγάφϧͷҰͭͰ͋ΓɺΫΥʔίχ΢ϜͷߴԹഔ࣭தͰͷৼΔ෣͍Λཧ࿦తʹཧղ͢Δ͜ͱ͸ɺ࣮‫݁ݧ‬ՌΛઆ໌͢Δ্ͰඇৗʹॏཁͰ͋Δɻ·ͨɺ
QGP ͷྲྀମྗֶతͳੑ࣭΋஫໨͞Ε͓ͯΓɺྲྀମϞσϧʹ‫݁ݧ࣮ͮ͘ج‬Ռͷઆ໌ʹ͸ɺQGP தͰͷॏΫΥʔΫ༌ૹ‫ݱ‬৅ͷཧ࿦తཧղ͕ඞཁෆՄܽͰ͋Δɻେ໺͸ɺYork େͷ Anthony Francis ࢯɺBielefeld େͷ Olaf Kaczmarek ࢯɺBernେͷ Mikko Laine ࢯ‫ ͼٴ‬Jülich ‫ࢉܭ‬ηϯλʔͷ Thomas Neuhaus ࢯΒͱ‫ʹڞ‬ɺ࠷େ 1923 ×48 ͱ͍͏ඇৗʹେ͖ͳ֨ࢠΛ༻͍ͯ pure SU(3) ͷ֨ࢠ QCD γ
ϛϡϨʔγϣϯΛߦ͍ɺ࿈ଓ‫͚͓ʹݶۃ‬Δ৭ిՙ૬ؔؔ਺Λ‫ͨ͠ࢉܭ‬ɻͦͯ͠ɺ͜ͷ૬ؔؔ਺ʹର༷ͯ͠ʑͳϞσϧʹ‫ͮ͘ج‬ϑΟοτΛߦ͍ɺεϖΫτϧ
ؔ਺Λ‫͠ࢉܭ‬ɺͦͷθϩप೾਺ۙ๣ͷৼΔ෣͍͔ΒॏΫΥʔΫӡಈྔ֦ࢄ܎
਺ (κ) Λ‫ੵݟ‬΋ͬͨɻͦͷ݁Ռɺ૬సҠԹ౓ͷ໿ 1.5 ഒͷԹ౓ (T ) ʹ͓͍ͯɺ
κ/T 3 = 1.8 − −3.4 ͱ͍͏஋Λಘͨʢ࿦จ 15ʣɻ·ͨɺHeng-Tong Ding ࢯɺOlaf Kaczmarek ࢯɺSwagato Mukherjee ࢯ‫ ͼٴ‬Hai-Tao Shu ࢯΒͱͷ‫ڞ‬ಉ‫ݚ‬‫ʹڀ‬ΑΓɺ૬ؔؔ਺͔ΒεϖΫτϧؔ਺Λ‫͢ࢉܭ‬Δํ๏ͱͯ͠ɺ֬཰࿦తͳख
๏Λಋೖ͠ɺΫΥʔίχ΢ϜͷεϖΫτϧؔ਺ͷ‫༷͚ͨ޲ʹࢉܭ‬ʑͳ༧උత‫ܭ‬－8－๞c٥ϕ c
ǈչ  

eYSz

eYz4

eYzf
eYz4
eYSz
eYS4
eYlz
eYSl
eYS:
eYSf
ࢉΛߦͬͨʢ࿦จ eYzf
17ʣɻࠓ‫ޙ‬͸ɺΑΓৄࡉͳ‫ܥ‬౷‫ࠩޡ‬ͷ‫ূݕ‬΍‫ط‬ଘͷํ๏ͱͷc٥ൺֱ౳ͱ‫ʹڞ‬ɺ༷ʑͳԹ౓ʹ͓͚ΔΫΥʔίχ΢ϜͷεϖΫτϧؔ਺Λ‫ࢉܭ‬
FIG. 4. Results ͠ɺΫΥʔίχ΢ϜͷফࣦԹ౓΍ॏΫΥʔΫ֦ࢄ܎਺ͷਪఆΛߦ͏ɻfor the critical endpoints in the plane of 1/l and 1/s (black open circles). Also shown (red squares) are theϕpoints where zero temperature simulations are carried out to calculate hadron masses. SU(3)-symmetric line is drawn in pink,while for green and blue lines the sum of three quark masses is constant.

(6) 3 ϑϨʔόʔɾ2+1 ϑϨʔόʔ༗‫ݶ‬Թ౓ QCD ʹ͓͚Δ૬ߏ଄ʢ᤽૿ʣ
zY:9

zY:z

ဣǦա ǟި֮ ӝ

zYk9

zYkz
3N0URCNjc
lN0 03<a33 URIwY ~j
ka0 03<a33 URIwY ~j:j@ 03<a33 URIwY ~j
ǈչ  

zYl9

zYlz

ASYf
AlYz
AlYl

zYlz

zYl9

zYkz

ဣǦա ǟࠀ ӝ

zYk9

zY:z

cIRU3

ASY4

AlY:
zY:9

p
p
2
2
FIG. 5. CEL in ਤ
the 7:
plane
alongରশ఺ʢ
CEL calculatedbyη ʣΛද͢ɻthe fit in eq. (7). Pink linem2πof-m( 2η tฏ໘ʹ͓͚Δྟքऴઢɻ௚ઢ͸SU(3)mπ = m0 m⇡ ) and ( t0 m⌘s ) and the slope
denotes the line of SU(3) symmetry ( Nf = 3). Three types of polynomial fitting results are overlapping in upper plot.

Թ౓ T ͱΫΥʔΫԽֶϙςϯγϟϧ µ Λؔ਺ͱ͢Δ QCD ͷ૬ਤΛ֬ఆͤ͞
QCD γϛϡϨʔγϣϯʹ͓͚Δ࠷େͷ໨ඪͷҰͭͰ͋Δɻ᤽
[11] X. -Y. Jin, Δ͜ͱ͸ɺ֨ࢠ
Y. Kuramashi, Y. Nakamura,
S. Takeda and A. Ukawa, Phys. Rev. D 91, 014508 (2015) [arXiv:1411.7461[hep-lat]].
૿͸ɺཧ‫ࢉܭݚ‬Պֶ‫ߏػڀݚ‬ʢAICSʣͷӉ઒෭‫ߏػ‬௕ɺதଜ‫ڀݚ‬һɺۚ୔େ[12] K. Rajagopal, appearing in Quark-Gluon Plasma 2, edited by R. Hwa, World Scientific, 1995, [arXiv:hep-ph/9504310].
[13] X. -Y. Jin, ֶ෢ాॿ‫͓ڭ‬ΑͼถࠃΞϧΰϯψࠃཱ‫ॴڀݚ‬ͷ
Y. Kuramashi, Y. Nakamura, S. Takeda and A. Ukawa, Phys.Jin
Rev.
D 92, 114511 (2015) [arXiv:1504.00113‫ڀݚ‬һΒͱͷ‫ڞ‬ಉ‫ڀݚ‬ͷ΋
ͱɺO(a) վྑΛࢪͨ͠ Wilson-Clover ΫΥʔΫ࡞༻ͱ Iwasaki ήʔδ࡞༻Λ༻͍ͯɺT ɺµɺΫΥʔΫ࣭ྔ mq ͷύϥϝʔλۭؒʹ͓͚Δ 3 ϑϨʔόʔ QCD
ͷྟքऴઢͷܾఆʹऔΓ૊ΜͰ͖ͨɻઌͣɺ࠷ॳͷεςοϓͱͯ͠ µ = 0ʢີ౓θϩʣʹ͓͚Δ 3 ϑϨʔόʔ QCD ʹ͓͚Δྟքऴ఺Λܾఆͨ͠ʢ࿦จൃද
ࡁʣɻΘΕΘΕ͕༻͍ͨํ๏͸ɺઑ౓ (kurtosis) ަࠥ๏ͱ‫ݺ‬͹ΕΔ༗‫ݶ‬αΠζεέʔϦϯάղੳख๏ͷҰछͰ͋ΓɺҰ࣍૬సҠྖҬʹ͓͚Δ෺ཧྔ෼෍ͷઑ౓ͱΫϩεΦʔόʔଆͷରԠ෺͕ɺҟͳΔۭؒମੵґଘੑΛ࣋ͭੑ࣭Λར༻͠
͍ͯΔɻຊ‫ڀݚ‬͸ɺੈքͰॳΊͯ 3 ϑϨʔόʔ QCD ʹ͓͚Δྟքऴ఺ͷܾఆʹ੒ޭͨ͠΋ͷͰ͋ΓɺQCD ͷ૬ߏ଄Λཧղ͢Δ্Ͱͷඇৗʹॏཁͳૅੴͱͳ͍ͬͯΔɻ
࣍ͷεςοϓ͸ 3 ϑϨʔόʔ QCD ͔Β 2+1 ϑϨʔόʔ QCD ΁ͷ֦ுͰ͋Δ͕ɺΘΕΘΕ͸ઌͣ 3 ϑϨʔόʔ QCD ͷ‫݁ࢉܭ‬ՌΛ༻͍ͨ reweighting ๏ʹΑͬͯɺ3 ϑϨʔόʔ QCD ͷྟքऴ఺ۙ๣ͷྟքऴઢͷৼΔ෣͍Λௐ΂ͨɻͨͩ͠ɺࠓճ͸ʮ࣌ؒํ޲ʯͷ֨ࢠαΠζΛ NT = 6 ʹ‫ݻ‬ఆ͍ͯ͠Δɻਤ 7 ͸ɺ
m2π -m2η ฏ໘ʹ͓͚Δ SU(3) ରশ఺ۙ๣ͷྟքऴઢͷৼΔ෣͍Λϓϩοτͨ͠

－9－

ਤ 8:

ΫΥʔΫԽֶϙςϯγϟϧ µ/T ͷؔ਺ͱͯ͠ͷΫΥʔΫ਺ີ౓ͷ̎࣍ΩϡϜϥϯτ

2⟨N̂ ⟩c /(V T 3 ). άϥϑ͸্͔ΒߴԹଆɿβ = 2.1 (orange), 1.9 (red), 1.7 (magenta), 1.5 (green),
1.3 (dark green), 1.1 (blue), 0.9 (black)ɿ௿Թଆɻ΋ͷͰ͋Δɻࢵ৭ͷ௚ઢ͸ SU(3) ରশͳ఺Λද͓ͯ͠ΓɺͦΕΛԣ੾Δྟքऴઢͷ܏͖͸ཧ࿦తʹ −2 ʹͳΔ͸ͣͰ͋Δ͕ɺΘΕΘΕͷ݁Ռ΋ྑ͍ਫ਼౓Ͱͦ
ΕΛ࠶‫͍ͯ͠ݱ‬Δɻ(7) ༗‫ ౓ີݶ‬QCD ͷ‫ڀݚ‬ླ໦ͱ୩‫ޱ‬͸ࡕେͷதଜ७ࢯɺཱ‫ڭ‬େͷԬকଠ࿠ࢯΒͱ‫ڞ‬ಉͰ͢ΔΧϊχΧϧ
๏Λ༻͍ͨ༗‫ ౓ີݶ‬QCD ͷ‫ڀݚ‬Λߦͬͨɻ༗‫ ࢠ֨౓ີݶ‬QCD ʹ͸ෳૉ࡞༻ͷ໰୊ɺ‫ͦͼٴ‬ͷ೿ੜͱͯ͠ͷූ߹໰୊ͱ‫ݺ‬͹ΕΔະղܾͷ໰୊͕͋Δɻ͜ͷෳૉ࡞༻ͷ໰୊Λ௚઀ճආ͢Δํࡦͱͯ͠ɺ
ΧϊχΧϧ෼഑ؔ਺ΛϑΨγςΟʔల։ͷ܎਺ͱͯ͠௚઀‫͢ࢉܭ‬ΔΧϊχΧϧ
๏ͱ‫ݺ‬͹ΕΔख๏Λ࠾༻ͨ͠‫ڀݚ‬Λߦͬͨɻಛʹॏ͍ΫΥʔΫʹରͯ͠༗ޮͳ
hopping parameter ల։Λ࠾༻͢Δ͜ͱͰɺ޿͍Թ౓ྖҬͰΧϊχΧϧ෼഑ؔ਺ͷ‫ࢉܭ‬Λߦͬͨɻ෺ཧྔͱͯ͠͸ɺΫΥʔΫ਺ີ౓ͱͦͷߴ࣍ͷΩϡϜϥϯτͷ‫ࢉܭ‬ΛओʹߦͬͨɻಛʹΫΥʔΫ਺ͷ༳Β͗ʹ૬౰͢Δ̎࣍ͷΩϡϜϥϯτʹ͸ T < Tc ͷ௿Թଆʹ͓͍ͯ૬సҠʹಛ༗ͳϐʔΫߏ଄͕‫ݱ‬Ε͍ͯΔ͜ͱ͕‫ͯݟ‬औΕΔ (ਤ 8)ɻ
ߋʹ̎࣍ͱ̍࣍ͷΩϡϜϥϯτͷൺ ⟨N̂ 2 ⟩c /⟨N̂ ⟩ ʹ͍ͭͯ‫ࢉܭ‬Λߦͬͨ (ਤ 9)ɻ
͜Ε͸ϋυϩϯϨκφϯεΨε໛‫ͼٴܕ‬ΫΥʔΫΨε໛‫ͱܕ‬ͷൺֱ͕໌֬ͳ
ྔͰ͋Δ͕ɺ஫໨͢΂͖ϙΠϯτ͸ɺಛʹ T < Tc ͷ௿ԹଆͰͷৼΔ෣͍Ͱ͋
Δɻ௿ີ౓ଆͰ͸ϋυϩϯ໛‫ܕ‬ͷ༧‫ͱݴ‬Α͘Ұக͍ͯ͠ΔҰํͰɺີ౓Λ্͛ͯߦ͘ʹैͬͯɺϋυϩϯ໛‫͔ܕ‬Β͸ͣΕͯɺΫΥʔΫ໛‫ܕ‬ͷ༧‫͍ͯͮۙʹݴ‬͍༷͘ࢠ͕‫ͯݟ‬औΕΔɻߴԹଆͰ͸Ұ؏ͯ͠ΫΥʔΫ໛‫ܕ‬ͷ༧‫ͱݴ‬Α͘Ұக͍ͯ͠Δ͜ͱͱൺֱ͢Δͱ͜Ε͸ஶ͍͠ҧ͍Ͱ͋Δɻ͜Ε͸ɺ௿ԹଆͰີ౓Λ্͛ͯߦ͘ʹैͬͯɺQCD ૬ਤͷΫΥʔΫͷด͡ࠐΊʖඇด͡ࠐΊ૬సҠͷ‫ڥ‬քΛ·͍ͨͰߦ͘‫ݱ‬৅ͱߟ͑ΒΕΔɻ࠷‫࣍̎ʹޙ‬ͷΩϡϜϥϯτʹ‫ݱ‬ΕͨϐʔΫͷҐஔ͔Β QCD ͷ૬ਤΛྨਪͨ͠΋ͷ͕ਤ 10 Ͱ͋Δɻ－10－ਤ 9: όϦΦϯԽֶϙςϯγϟϧ µB /T ͷؔ਺ͱͯ͠ͷΫΥʔΫ਺ͷ̎࣍ΩϡϜϥϯτͱΫΥʔΫ਺ͷൺ ⟨N̂ 2 ⟩c /⟨N̂ ⟩. ϋυϩϯϨκφϯεΨε໛‫ܕ‬ʢ੨ઢʣ‫ͼٴ‬ΫΥʔΫΨε໛‫ܕ‬ʢ੺ઢʣͱͷൺֱΛߦ͍ͬͯΔɻ

ਤ 10: ΫΥʔΫ਺༳Β͗ʹ‫ݱ‬ΕΔϐʔΫͷҐஔ͔Βྨਪͨ͠ QCD ૬ਤɻ－11－

(8) ςϯιϧωοτϫʔΫ‫ࢠ֨ͮ͘جʹࣜܗ‬ήʔδཧ࿦ͷ‫ڀݚ‬
֨ࢠ QCD ‫Ͱࢉܭ‬͸ɺۙ೥ͷ‫ػࢉܭ‬ೳྗͷ޲্΍৽‫ن‬ΞϧΰϦζϜͷ։ൃɾվྑͷ݁Ռɺࣗવքͷͷ uɺdɺs ΫΥʔΫ࣭ྔ্ͰͷγϛϡϨʔγϣϯ΍ɺߋʹ͸ܰ‫֩ࢠݪ‬ͷଋറΤωϧΪʔ‫Ͱ·ࢉܭ‬΋͕ՄೳͱͳΓͭͭ͋ΔɻͦͷҰํͰɺղܾ͢΂͖௕೥ͷ՝୊͕ͦͷ··࢒͞Ε͍ͯΔ͜ͱ΋ࣄ࣮Ͱ͋Δɻ࠷΋ॏཁͳ՝୊͸ɺϑΣϧϛΦϯ‫ܥ‬Λѻ͏ࡍͷෛූ߸໰୊͓Αͼෳૉ࡞༻Λ࣋ͭ‫ܥ‬ͷγϛϡϨʔγϣϯͰ͋Δɻ͜ΕΒ͸ɺ͍ܰΫΥʔΫͷμΠφϛΫεɺStrong CP໰୊ɺ༗‫ ౓ີݶ‬QCD ͷ‫͍͓ͯʹڀݚ‬ආ͚ͯ௨Εͳ͍໰୊Ͱ͋ΔɻΘΕΘΕ͸ɺۙ೥෺ੑ෺ཧ෼໺ͰఏҊ͞ΕͨςϯιϧωοτϫʔΫ‫ͮ͘جʹࣜܗ‬෼഑ؔ਺ͷ਺஋‫ࢉܭ‬ख๏Λ֨ࢠήʔδཧ࿦΁Ԡ༻͠ɺϞϯςΧϧϩ๏ʹ‫ى‬Ҽ͢Δෛූ߸໰୊͓Αͼෳૉ࡞༻໰୊Λղܾ͠ɺ͜Ε·Ͱͷ֨ࢠ QCD ‫͕ࢉܭ‬੒͠ಘͳ͔ͬͨ
৽ͨͳ෺ཧ‫ڀݚ‬ͷ։୓Λ໨ࢦ͍ͯ͠Δɻ
Dcut=100.160

4
K=0.14990
K=0.14991
3.5

0.155

3

0.150

X

Kc

2.5

0.145

2

0.140
1.5

0.135
1

0.130

0.5
0

5

10

15

20
iteration

25

30

35

40

0

2

4

6

Dcut

8

10

12

ਤ 11: 10244 ֨ࢠαΠζʹ͓͚Δ 4 ࣍‫ݩ‬ΠδϯάϞσϧͷ૬సҠԹ౓ͷܾఆɻࠨਤɿDcut =10 ʹ͓͚Δςϯιϧͷ‫ݻ‬༗஋ͷॖॏ౓ʹΑΔߴԹ૬ʢॖॏ౓ 1ʣͱ௿Թ૬ʢॖॏ౓ 2ʣͷಉఆɻӈਤɿసҠԹ౓ͷ Dcut ґଘੑɻ੨͍ԣઢ͸ϞϯςΧϧϩ๏ʹΑΔ‫݁ࢉܭ‬ՌΛද͢ɻ͜Ε·Ͱɺ᤽૿ͱཧ‫ࢉܭݚ‬Պֶ‫ߏػڀݚ‬ʢAICSʣͷਗ਼ਫಛผ‫ڀݚ‬һ͸ɺςϯιϧ‫܁‬ΓࠐΈ‫܈‬ΛάϥεϚϯ਺΋ѻ͑ΔΑ͏ʹ֦ு͠ʢάϥεϚϯςϯιϧ
‫܁‬ΓࠐΈ‫܈‬ʣɺ ੈքͰॳΊͯϑΣϧϛΦϯೖΓͷήʔδཧ࿦΁ͷԠ༻ʹ੒ޭͨ͠ɻ۩ମతʹ͸ɺάϥεϚϯςϯιϧ‫܁‬ΓࠐΈ‫܈‬Λ༻͍ͯɺθ ߲͕༗Δ৔߹ͱ
ແ͍৔߹ͷ 1 ϑϨʔόʔͷ 2 ࣍‫ ࢠ֨ݩ‬Schwinger Ϟσϧʢ2 ࣍‫ ࢠ֨ݩ‬QEDʣʹ͓͚Δ૬ߏ଄Λௐ΂ͨʢ࿦จൃදࡁʣɻ͜ͷ‫ʹڀݚ‬ΑΓɺάϥεϚϯςϯιϧ
‫܁‬ΓࠐΈ‫͕܈‬ɺ‫ࡏݱ‬ͷ֨ࢠ QCD ‫๊͕͑ࢉܭ‬Δෛූ߸໰୊΍ෳૉ࡞༻໰୊Λղܾ͍ͯ͠Δ͜ͱΛࣔ͢͜ͱʹ੒ޭͨ͠ɻࠓ‫ޙ‬͸ɺ࠷ऴ໨ඪͰ͋Δ 4 ࣍‫ ݩ‬QCD
΁ͷԠ༻ʹ޲͚ɺ(i) ඇՄ‫׵‬ήʔδཧ࿦΁ͷ֦ுɺ(ii) ߴ࣍‫ݩ‬Ϟσϧ΁ͷԠ༻ɺ(iii) ෺ཧྔ‫ࢉܭ‬ͷͨΊͷख๏։ൃɺͱ͍͏ 3 ͭͷ՝୊ʹऔΓ૊Ήඞཁ͕͋Δɻ
2015 ೥౓ʹ͓͍ͯಛʹਐల͕͋ͬͨ‫ڀݚ‬͸ɺςϯιϧ‫܁‬ΓࠐΈ‫܈‬Λ༻͍ͨ 4 ࣍‫ݩ‬ΠδϯάϞσϧͷղੳͰ͋Δɻਤ 11 ͸ɺ10244 ֨ࢠαΠζʹ͓͚Δ 4 ࣍‫ݩ‬ΠδϯάϞσϧͷ૬సҠԹ౓‫ࢉܭ‬Λද͍ͯ͠Δɻઌͣɺ֤ Dcutʢςϯιϧ‫܁‬ΓࠐΈ‫ࢉܭ͍͓ͯʹ܈‬ਫ਼౓Λίϯτϩʔϧ͢Δύϥϝʔλʣʹ͓͍ͯɺςϯιϧ‫ݻ‬༗஋ͷॖॏ౓Λௐ΂Δ͜ͱʹΑͬͯ૬సҠԹ౓Λܾఆ͢ΔɻࠨਤͰ͸ Dcut =10－12－ͷྫΛϓϩοτ͍ͯ͠Δɻͦͷ‫ޙ‬ɺ૬సҠԹ౓ͷ Dcut ґଘੑʹ͓͍ͯऩଋͷ༷ࢠΛௐ΂Δ͜ͱʹΑͬͯɺ࠷ऴతͳ૬సҠԹ౓Λܾఆ͢Δʢӈਤʣɻ੨͍ԣ
ઢ͸ϞϯςΧϧϩ๏ͷ݁ՌΛද͍ͯ͠Δ͕ɺςϯιϧ‫܁‬ΓࠐΈ‫܈‬ͷ݁Ռ΋͍ۙ஋ʹऩଋ͍ͯ͠Δ͜ͱ͕Θ͔Δɻͨͩ͠ɺैདྷͷϞϯςΧϧϩ‫͚͓ʹࢉܭ‬Δ࠷େ֨ࢠαΠζ͸ 804 Ͱ͋ΓɺࠓճͷΘΕΘΕͷ‫͚͓ʹࢉܭ‬Δ 10244 ֨ࢠαΠζʹൺ΂ͯඇৗʹখ͍͞ɻςϯιϧ‫܁‬ΓࠐΈ‫͚͓ʹ܈‬Δ‫ࢉܭ‬ίετͷମੵґଘੑ͸ର਺తͰ͋Γɺ͜ͷ఺΋ϞϯςΧϧϩ๏ʹ͘Β΂ͯѹ౗తͳ༏ҐੑΛ࣋ͭಛ௃ͷҰͭͰ͋Δɻ(9) ֨ࢠ QCD ʹΑΔΫΥʔΫΛࣗ༝౓ͱͨ͠‫֩ࢠݪ‬ͷ௚઀ߏ੒᤽૿ɺࢁ࡚͸ཧ‫ࢉܭݚ‬Պֶ‫( ߏػڀݚ‬AICS) ͷӉ઒෭‫ߏػ‬௕ͱͷ‫ڞ‬ಉ‫ʹڀݚ‬ΑΓɺ2010 ೥ੈքͰॳΊͯ֨ࢠ QCD ʹΑΔϔϦ΢Ϝ‫֩ࢠݪ‬ͷߏ੒ʹ੒ޭ͠ɺͦͷͷͪ 2 ֩ࢠ‫ܥ‬ͷଋറঢ়ଶͰ͋Δॏཅࢠͷߏ੒ʹ΋੒ޭͨ͠ɻ͜ΕΒͷ‫ܭ‬ࢉ͸ɺ‫ࢉܭ‬ίετΛ཈͑ΔͨΊʹΫΣϯνۙࣅ͔ͭॏ͍ΫΥʔΫ࣭ྔΛ༻͍ͨࢼ‫ݧ‬తͳ΋ͷͰ͋ͬͨɻͦͷ‫ޙ‬ɺਅۭภ‫ޮۃ‬ՌΛऔΓೖΕͨ 2+1 ϑϨʔόʔQCD γϛϡϨʔγϣϯΛߦ͍ɺۙࣅΛഉͨ͠ΑΓ‫ੈ࣮ݱ‬քʹ͍ۙঢ়‫Ͱگ‬ͷϔϦ΢Ϝ‫͓֩ࢠݪ‬Αͼ 2 ֩ࢠ‫ܥ‬ͷଋറΤωϧΪʔ‫ʹࢉܭ‬੒ޭͨ͠ɻͨͩ͠ɺ͜ͷ‫ ࢉܭ‬͸ π தؒࢠ࣭ྔ 0.5 GeV ૬౰ͷΫΥʔΫ࣭ྔΛ༻͍ͨ΋ͷͰ͋Γɺ෺ཧ఺ (π தؒࢠ࣭ྔ 0.14 GeV ʹ૬౰) ΑΓ΋͔ͳΓॏ͍ɻͦͷͨΊɺ෺ཧ఺΁޲͚ͨΫΥʔΫ࣭ྔґଘੑΛௐ΂ΔͨΊʹɺ޿ౡେֶ ੴ઒݈Ұ।‫ڭ‬तΛ‫ڞ‬ಉ‫ʹऀڀݚ‬Ճ͑ɺπ தؒࢠ࣭ྔ 0.3 GeV ૬౰ͷΫΥʔΫ࣭ྔͰͷ‫ࢉܭ‬Λ਱ߦͨ͠ɻ͜ͷ‫ڀݚ‬੒Ռ͸ɺຊ೥౓ɺֶज़࿦จʹ‫͞ࡌܝ‬Εͨ (࿦จ 22, 23)ɻ͜ͷ੒ՌΛ౿·͑ɺʮ‫ژ‬ʯͰੜ੒͞Εͨ 964 ֨ࢠαΠζͷήʔδ഑ҐΛ༻͍ͨ෺ཧ఺Ͱ
ͷܰ‫֩ࢠݪ‬ଋറΤωϧΪʔ‫ࢉܭ‬Λߦͳ͍ͬͯΔɻ3 He ‫֩ࢠݪ‬ͷଋറΤωϧΪʔʹରԠ͢Δ༗ޮΤωϧΪʔࠩͷதؒ݁ՌΛਤ 12 ʹࣔ͢ɻ෺ཧ఺Ͱͷ‫Ͱࢉܭ‬͸౷‫ࠩޡܭ‬Λ཈͑Δ͜ͱ͕ඇৗʹ೉͍ͨ͠Ίɺ‫ݱ‬ஈ֊Ͱ͸౷‫ܭ‬తʹ༗ҙͳ݁Ռ͸ಘΒΕ͍ͯͳ͍͕ɺࠓ‫ޙ‬౷‫ࠩޡܭ‬Λখ͘͢͞ΔͨΊͷ‫ࢉܭ‬Λ‫ܧ‬ଓ͍ͯ͘͠ɻ

experiment

0.04

3

He ∆E

0.02

0

-0.02

-0.04
0

4

8

t

12

16

20

ਤ 12: 3 He ‫֩ࢠݪ‬ͷ༗ޮΤωϧΪʔࠩɻԣ࣠͸‫ؒ࣌ڏ‬ɺ࣮ઢ͸࣮‫ݧ‬஋ɻେ͖ͳ‫ྖؒ࣌ڏ‬ҬͰɺ༗ޮΤωϧΪʔ͕ࠩఆ਺ʹͳΕ͹ɺͦͷ஋͕ଋറΤωϧΪʔʹରԠ͢Δɻ(10) ֨ࢠ QCD Λ༻͍ͨ֩ࢠߏ଄‫ڀݚ‬－13－ཅࢠͱதੑࢠ (֩ࢠ) ͸ΫΥʔΫͷଋറঢ়ଶͰ͋Γɺͦͷߏ଄Λৄࡉʹௐ΂ΔͨΊʹ͸ɺ‫͍ڧ‬૬‫༻࡞ޓ‬ͷୈҰ‫ݪ‬ཧ‫͋Ͱࢉܭ‬Δ֨ࢠ QCD Λ༻͍ͨ‫͕ࢉܭ‬ඞཁ
Ͱ͋Δɻ͜Ε·Ͱʹ֨ࢠ QCD Λ༻͍ͯɺ֩ࢠߏ଄ʹؔ܎͢Δ֩ࢠ‫ܗ‬ঢ়Ҽࢠͷ‫ͳߦ͕ڀݚ‬ΘΕ͖͕ͯͨɺඇৗʹྑ͍ਫ਼౓Ͱଌఆ͞Ε͍ͯΔ࣮‫ݧ‬஋Λ࠶‫͖Ͱݱ‬͍ͯͳ͍ɻ͜ͷ࣮‫ݧ‬஋ͱͷෆҰகͷओͳ‫ݪ‬Ҽ͸ɺ‫͍༻ʹࢉܭ‬ΒΕͨΫΥʔΫ࣭ྔ͕‫࣮ݱ‬ͷ΋ͷΑΓ΋େ͖͍ͨΊͰ͋Δͱߟ͑ΒΕ͍ͯΔɻ
᤽૿ɺࢁ࡚͸ɺ޿ౡେֶ ੴ઒݈Ұ।‫ڭ‬तɺ౦๺େֶ ࠤʑ໦উҰ।‫ڭ‬तɺཧ‫ݚ‬‫ࢉܭ‬Պֶ‫( ߏػڀݚ‬AICS) Ӊ઒෭‫ߏػ‬௕ͱͱ΋ʹɺPACS Collaboration ʹ͓͍ͯɺ͜ͷ‫ݪ‬ҼΛऔΓআ͍ͨ‫͋Ͱࢉܭ‬Δɺ‫࣮ݱ‬ͷΫΥʔΫ࣭ྔʹ‫ۃ‬Ί͍ͯۙύϥϝʔλ (π தؒࢠ࣭ྔ 145MeV) Ͱͷ֩ࢠ‫ܗ‬ঢ়Ҽࢠ‫ࢉܭ‬Λߦͳͬͨʢ࿦จ 23ʣɻ
ਤ 13 ͸ి‫ؾ‬త֩ࢠ‫ܗ‬ঢ়Ҽࢠͷதؒ݁ՌͰ͋Δɻ͜Ε·Ͱͷ‫݁ࢉܭ‬Ռͱ͸ҟͳΓɺ࣮‫ݧ‬஋ʹྑ͘Ұகͨ݁͠Ռ͕ಘΒΕ͍ͯΔɻࠓ‫ޙ‬΋͜ͷ‫ࢉܭ‬ΛਐΊɺ࣓‫ؾ‬త‫ܗ‬ঢ়Ҽࢠ΍࣠ੑΧϨϯτʹؔ܎͢Δ‫ܗ‬ঢ়Ҽࢠͷ‫ڀݚ‬Λߦͳ͍ͬͯ͘༧ఆͰ
͋Δɻ
1.2
Experimentmπ=0.145 GeV

2GE(q )/GE(0)

1
0.8
0.6
0.4
0.2
0

0

0.1

0.2
2

2

q [GeV ]ਤ 13: ి‫ؾ‬త֩ࢠ‫ܗ‬ঢ়Ҽࢠɻԣ࣠͸ӡಈྔҠߦɺഁઢ͸࣮‫ݧ‬஋Λද͢(11) ૉཻࢠඪ४໛‫ܕ‬Λ௒͑ͨཧ࿦ͷ୳ࡧ΢ΥʔΩϯάςΫχΧϥʔ໛‫ܕ‬͸ૉཻࢠඪ४໛‫ܕ‬Λ௒͑ͨཧ࿦ͷ༗ྗͳީิ
Ͱ͋Δɻ͜ͷ໛‫ܕ‬͸ɺ‫߹݁ڧ‬ήʔδཧ࿦ͷμΠφϛΫεʹΑΓɺૉཻࢠඪ४໛
‫Ͱܕ‬͸खͰ༩͑ΒΕ͍ͯͨిऑରশੑͷࣗൃతഁΕͷ‫ݯى‬Λઆ໌Ͱ͖Δɻ͠
͔͠ɺ͜ͷ໛‫ܕ‬Λߏங͢ΔͨΊʹඞཁͳ‫߹݁ڧ‬ήʔδཧ࿦ʹ͸ɺۙࣅత‫ܗڞ‬ରশੑΛ࣋ͭͳͲɺಛघͳ৚͕݅՝͞Ε͍ͯΔɻࢁ࡚͸໊‫ݹ‬԰େֶૉཻࢠӉ஦‫ى‬‫( ߏػڀݚݯ‬KMI) Λத৺ͱͨ͠ LatKMI Collaboration ͷ‫ऀڀݚ‬ɺࢁ࿬޾Ұಛผ‫ڭ‬तɺ੨໦อಓ।‫ڭ‬तΒͱ‫ʹڞ‬ɺ֨ࢠήʔδཧ࿦Λ༻͍ͨ਺஋‫͔ࢉܭ‬ΒɺͦͷΑ͏ͳ৚݅Λຬͨ͢ήʔδཧ࿦͕ଘࡏ͢Δ͔ͷ୳ࡧΛߦͬͨɻ͜Ε·Ͱͷ 4
ʢ࿦จ 24ʣɺ 8ɺ 12 ϑϨʔόʔ SU(3) ήʔδཧ࿦ͷ‫͔ڀݚ‬Βɺ8 ϑϨʔόʔཧ࿦͕ͦΕΒ৚݅Λຬͨ͢Մೳੑ͕͋ΔࣄΛࣔͨ͠ʢ࿦จ 25ʣɻͦͷՄೳੑΛ͔֬ΊΔͨΊɺ༷ʑͳϋυϩϯ࣭ྔʢ࿦จ 26ʣɺS ύϥϝʔλʢ࿦จ 27ʣɺτϙϩδΧϧνϟʔδʹؔ܎ͨ͠෺ཧྔʢ࿦จ 28 , 29ʣΛ‫͠ࢉܭ‬ɺ8 ϑϨʔόʔཧ࿦ͷੑ࣭ΛΑΓ໌֬ʹཧղ͢ΔͨΊͷ‫ڀݚ‬Λߦͬͨɻ－14－

(12) ίϯϑΥʔϚϧཧ࿦ͷ਺஋త‫ڀݚ‬ૉཻࢠඪ४໛‫ܕ‬Λӽ͑Δཧ࿦ͷީิͰ͋Δ΢ΥʔΩϯάςΫχΧϥʔ໛‫ܕ‬͸ɺίϯϑΥʔϚϧରশੑΛ΋ͬͨཧ࿦Λϕʔεʹߏங͞ΕΔͱߟ͑ΒΕ͍ͯΔɻ
WMFQCD Collaboration (‫( ࡚ؠ‬ஜ೾ɾKEK)ɺੴ઒ (޿ౡ)ɺதࢁ (Walter Burke
Institute), ໺ळ, Cossu (KEK)ɺ٢ߐ) ͸ɺQCD తͳ৔ͷཧ࿦ (Nf ‫ݸ‬ͷ‫ج‬ຊද‫ݱ‬ͷϑΣϧϛΦϯ͕݁߹ͨ͠ SU(3) ήʔδཧ࿦) ͷίϯϑΥʔϚϧରশੑʹؔ
͢Δཧ࿦ߏ଄ͷղ໌Λ໨తʹ‫ڀݚ‬Λߦ͍ͬͯΔɻ‫܁‬ΓࠐΈ‫܈‬౳ʹ‫ͮ͘ج‬ཧ࿦తͳߟ࡯ͱɺͦΕΛ‫͢ূݕ‬Δҝͷ֨ࢠγϛϡϨʔγϣϯΛ‫ڀݚ‬खஈͱ͍ͯ͠Δɻલ೥౓·Ͱʹɺʮ༗‫ݶ‬ͷ IR cutoﬀ Λ࣋ͭίϯϑΥʔϚϧཧ࿦ʯͱ͍͏ɺ৽֓
೦Λఏএ͠ɺͦͷཧ࿦ͷಛ௃Λ໌Β͔ʹ͖ͯͨ͠ɻͭ·Γɺ• ήʔδ݁߹ఆ਺͕ IR fixed point (੺֎‫ݻ‬ఆ఺) Λ࣋ͭཧ࿦Λɺ༗‫ݶ‬ͷ IR
cutoﬀ Λۭ࣋ͭ࣌ʢྫ͑͹ɺۭؒํ޲ͷαΠζ͕༗‫ۭ࣌ͳݶ‬ʣ্Ͱఆࣜ
Խ͢ΔͱɺIR cutoﬀ ͕ແ͍ཧ࿦Ͱ͸ϑΣϧϛΦϯ࣭ྔ mf ͕θϩͰͷΈ࣮‫͢ݱ‬Δ conformal ରশੑ͕ɺ༗‫ݶ‬ͷ mf ΁޿͕Γɺʮด͡ࠐΊ૬ʯͱ΋ʮඇด͡ࠐΊ૬ʯͱ΋ҟͳΔʮconformal ྖҬʯ͕ଘࡏ͢Δ͜ͱɺ• ʮconformal ྖҬʯͰͷ meson ఻ൖؔ਺ G(t) (ۭؒӡಈྔ p⃗ = 0) ͸ɺม‫ܗ‬౬઒‫ܕ‬G(t) ∼ C exp(−mt)/tαͱͳΔʢด͡ࠐΊ૬Ͱ͸ࢦ਺ؔ਺‫ ܕ‬G(t) ∼ C exp(−mt)ʣ͜ͱɺ

• conformal ྖҬͷਅۭ͸ɺۭؒํ޲ͷ Polyakov Loop ͕ඇࣗ໌ͳ Z(3) Ґ૬Λ΋ͭ ”twisted Z(3) vacuum” Ͱ͋Δ͜ͱ
Λཧ࿦తɾ਺஋తʹࣔͨ͠ɻʢ‫ऀ̎ޙ‬͸ɺconformal ྖҬͷಛ௃ɻʣQCD తཧ࿦ͷཧ࿦ߏ଄ͱͯ͠͸ɺ• Nf = 7, 8, 12, 16 ͷ‫Ͱܥ‬ίϯϑΥʔϚϧྖҬ͕ଘࡏ͢Δ͜ͱ͔Βɺ QCD
తཧ࿦ʢθϩԹ౓ʣͷ conformal window ͸ Nf = 7 − 16 Ͱ͋Δ͜ͱɺ

• Nf = 2 ͷ༗‫ݶ‬Թ౓ QCD ʹ͓͍ͯ΋ɺߴԹ૬ʹ conformal ྖҬ͕ଘࡏ͢Δ͜ͱͳͲΛ໌Β͔ʹͨ͠ɻຊ೥౓͸ɺθϩԹ౓ͷ QCD తཧ࿦ʹରͯ͠ɺIR fixed point Λಉఆ͢Δ৽ख๏ΛఏҊ͠ɺNf = 7, 8, 12, 16 ͷ֨ࢠγϛϡϨʔγϣϯͰ࣮ࡍʹ IR fixed point Λ‫ٻ‬Ίͨʢ࿦จ 30ʣɻ৽ख๏͸ɺ‫܁‬ΓࠐΈ‫ͮ͘جʹ܈‬ɻαΠζʢIR cutoﬀʣͷҟͳΔ্ۭ࣌ͷ meson ఻ൖؔ਺ʹؔ͢Δ‫܁‬ΓࠐΈ‫ํ܈‬ఔ͔ࣜΒग़ൃ͠ɺ఻ൖؔ਺
ʢ͔Βఆٛ͞ΕΔ༗ޮ࣭ྔ m(t)ʣͷεέʔϦϯάଇ͕ಋ͔ΕΔɻͭ·Γɺm(t)͸ɺ࣌ؒ t ʢͱ༗ޮ࣭ྔࣗ਎ʣΛαΠζͰεέʔϧ͢ΔͱɺIR fixed point ্(mf = 0) Ͱ͸ɺαΠζʹґଘ͠ͳ͍Ϣχόʔαϧͳؔ਺ͱͳΔɻ͜ͷख๏ͷ‫ূݕ‬ͷͨΊɺNf = 7, 8, 12, 16 ͷཧ࿦ʹରͯ͠ɺIwasaki ήʔδ࡞༻ͱ WilsonϑΣϧϛΦϯ࡞༻Λ༻͍ͨ֨ࢠγϛϡϨʔγϣϯΛ̏ͭͷ֨ࢠαΠζ 83 × 32,
123 × 48, 163 × 64 Ͱɺ݁߹ఆ਺Λม͑ͳ͕Βߦ͍ɺʮಛఆͷ݁߹ఆ਺ͷ࣌ʢͷ－15－

Έʣɺεέʔϧͨ͠ meson ༗ޮ࣭ྔ͕αΠζʹΑΒͳ͍ʯ͜ͱΛࣔͨ͠ɻͭ·ΓɺIR fixed point ΛಉఆͰ͖ͨɻ఻ൖؔ਺ͷεέʔϦϯάଇ͔Βɺҟৗ࣭ྔ࣍‫ݩ‬Λ‫ٻ‬ΊΔࣄ͕Ͱ͖Δ͕ɺ਺஋తʹҙຯͷ͋Δ݁ՌΛಘΔʹ͸ɺΑΓେ͖ͳαΠζͷ‫͕ࢉܭ‬ඞཁͰ͋Γɺࠓ‫ޙ‬ͷ՝୊Ͱ͋Δɻ

Nf = 2 ߴԹ૬ͷίϯϑΥʔϚϧతੑ࣭ͷղ໌ʹ͍ͭͯ΋ਐల͕͋ͬͨ (࿦จ32)ɻࡢ೥౓·Ͱ͸ɺ࣌ؒํ޲ (Թ౓ํ޲ʣͷαΠζ Lt ͕ ۭؒํ޲ͷαΠζLs ΑΓେ͖͍‫ʹܥ‬ରͯ͠ɺconformal ྖҬͷଘࡏΛ͖͕ࣔͯͨ͠ɺਖ਼͍͠༗
‫ݶ‬Թ౓‫͋Ͱܥ‬Δ Lt < Ls ͷ‫ʹܥ‬ରͯ͠΋ conformal ྖҬ͕ଘࡏ͢ΔࣄΛࣔͨ͠ɻ۩ମతʹ͸ɺPolyakov loop ͱ meson ༗ޮ࣭ྔΛଌఆ͠ɺmf = 0 ͰɺZ(3)twisted state ͕࣮‫͍ͯ͠ݱ‬ΔࣄΛࣔͨ͠ɻࠓ೥౓͸ɺ͞Βʹ domain wall quark Λ༻͍ͨγϛϡϨʔγϣϯʹΑΔίϯ
ϑΥʔϚϧཧ࿦ͷ‫ڀݚ‬΋ਪਐ͠ɺதؒ݁ՌΛɺࠃࡍձٞͰใࠂͨ͠ʢ࿦จ [?]ʣɻ
domain wall quark Ͱ͸ɺ࣭ྔͷνϡʔχϯά͕ෆཁͰ͋ΓɺΧΠϥϧରশੑͷഁΕ/ճ෮ͷ௚઀‫͕ূݕ‬ՄೳͰ͋Δ఺ͰɺWilson quark ͷ‫ࢉܭ‬ΑΓ༏ҐͰ͋
Δɻ‫ࢉܭ‬͸ θϩԹ౓ Nf = 8 Ͱߦ͍ɺWilson quark ʹରͯ͠ߦ͖ͬͯͨલड़
ͷղੳΛߦ͏ͱͱ΋ʹɺσΟϥοΫεϖΫτϧີ౓ͷղੳ͔Βҟৗ࣭ྔ࣍‫ݩ‬Λ‫ੵݟ‬΋ΔࢼΈ΋ߦ͍ͬͯΔɻ(13) ֨ࢠ QCD ʹΑΔόϦΦϯؒ૬‫༻࡞ޓ‬ͷ‫ڀݚ‬ʢHAL QCD Collaborationʣཅࢠ͓Αͼதੑࢠ (֩ࢠ) Λ݁ͼ͚ͭɺ‫֩ࢠݪ‬Λߏ੒͍ͯ͠Δྗ (֩ྗ) ͸ɺ‫ݱ‬৅࿦తʹ͸தؒࢠަ‫ʹ׵‬Αͬͯੜ͡Δͱߟ͑ΒΕ͍ͯΔ͕ɺͦͷ‫ݯى‬ΛΑΓ‫ج‬ຊతͳΫΥʔΫɾάϧʔΦϯͷࣗ༝౓ʹ‫͍ͯͮج‬ཧղ͢Δ͜ͱɺͱΓΘ͚୹‫཭ڑ‬֩ྗʹ͓͚Δੱྗਊͷൃ‫ߏػݱ‬Λཧ࿦తʹಋ͘͜ͱ͸ɺૉཻࢠ‫֩ࢠݪ‬෺ཧʹ࢒͞Εͨେ໰୊ͷ 1 ͭͰ͋Δɻࠜଜɺࠤʑ໦͸ɺ‫౎ژ‬େֶ‫ૅج‬෺ཧֶ‫ॴڀݚ‬੨໦‫ڭ‬तɺཧԽֶ‫ాॳॴڀݚ‬ओ೚‫ڀݚ‬һΒͱ HAL QCD Collaboration Λ݁੒͠ɺ
2 ֩ࢠؒͷ೾ಈؔ਺͔Β֩ࢠؒͷϙςϯγϟϧΛಋ͖ग़͢ͱ͍͏ํ๏ΛԠ༻ͯ͠ɺ༷ʑͳཻࢠؒͷϙςϯγϟϧΛ֨ࢠ QCD ͷ਺஋γϛϡϨʔγϣϯͰ‫ࢉܭ‬͖ͯͨ͠ɻ࿦จ 34 Ͱ͸ɺPACS-CS ʹΑͬͯੜ੒͞Εͨήʔδ഑Ґͷ͏ͪɺ֨ࢠִؒ a = 0.09 fmɺۭؒମੵ L3 = (2.9fm)3 ɺmπ ≈ 700 MeVɺmΩ ≈ 1970
MeV ͷ΋ͷΛ༻͍ͯ 1 S0 νϟωϧͷ ΩΩ ϙςϯγϟϧͷ‫ࢉܭ‬Λߦͬͨɻ࿦จ
35 Ͱ͸ɺCP-PACS/JLQCD ʹΑͬͯੜ੒͞Εͨήʔδ഑ҐΛ༻͍ͯɺۭؒ
ମੵ L3 = (1.93fm)3 ʹ͓͚ΔϑϨʔό SU (3) ରশੑ͕ഁΕͨΫΥʔΫ࣭ྔ(mπ /mK = 0.96, 0.90, 0.86) ͰͷετϨϯδωε S = −2 ηΫλʔͷ݁߹νϟωϧόϦΦϯؒϙςϯγϟϧͷ‫ࢉܭ‬ΛߦͬͨɻҎԼͰ͸ɺ֨ࢠ QCD ʹΑΔ෺ཧ఺ͰͷόϦΦϯؒ૬‫༻࡞ޓ‬ͷܾఆʹؔ࿈ͯ͠ߦΘΕͨ 2015 ೥౓ͷ‫ڀݚ‬੒ՌΛ঺հ͢Δɻ
֨ࢠ QCD ʹΑΔ෺ཧ఺ͰͷόϦΦϯؒ૬‫༻࡞ޓ‬ͷܾఆ
֨ࢠ QCD ʹΑΔ෺ཧ఺ͰͷόϦΦϯؒ૬‫༻࡞ޓ‬ͷܾఆ͸ɺ‫ژ‬଎‫Ͳͳػࢉܭ‬ͷେ‫ن‬໛ͳ‫ݯࢿػࢉܭ‬Λ‫ߦ͕ࢉܭͯ͠༻׆‬ΘΕͨɻ͜ͷ‫ڀݚ‬՝୊ʹ͸ɺετϨϯδωεΛ࣋ͨͳ͍֩ྗϙςϯγϟϧͱɺετϨϯδωεΛ࣋ͬͨϋΠϖϩϯϙ
ςϯγϟϧͷ྆ํ͕‫·ؚ‬ΕΔɻ֩ྗʹ͍ͭͯ͸ɺ͜Ε·Ͱʹ๛෋ͳ࣮‫ݧ‬σʔλ－16－ਤ 14: ମੵ (96a)4 ≈(8.2fm)4 ɺ֨ࢠִؒ a ≈ 0.085fmɺ(mπ , mK ) ≈ (146, 525)MeV ʹରԠ͢Δ΄
΅෺ཧ఺্Ͱ‫͞ࢉܭ‬ΕͨɺΛN − ΛN ର֯੒෼ͷϙςϯγϟϧΛࣔ͢ɻ৭ͷҧ͍͸֨ࢠ্Ͱଌఆ͞Εͨ‫ؒ࣌ڏ‬ͷҧ͍Λ͍ࣔͯ͠Δɻࠨ: 1 S0 νϟωϧʹ͓͚Δத৺ྗϙςϯγϟϧɻதԝ: 3 S1 -3 D1 νϟωϧʹ͓͚Δத৺ྗϙςϯγϟϧɻӈ: 3 S1 -3 D1 νϟωϧʹ͓͚Δςϯιϧྗϙςϯγϟϧɻʹ‫ݱ͍ͯͮج‬৅࿦తʹ͸ਫ਼ີʹௐ΂ΒΕ͍ͯΔͨΊɺ͜ͷ‫ڀݚ‬՝୊Ͱ༻͍Δํ๏ʹΑͬͯɺ͜Ε·Ͱͷ֩ྗϙςϯγϟϧʹର͢Δཧղͱໃ६͠ͳ͍݁Ռ͕
ಘΒΕΔ͜ͱΛ‫͢ূݕ‬Δͱ͍͏ଆ໘͕͋Δɻ͍ͬΆ͏ɺϋΠϖϩϯϙςϯγϟ
ϧʹ͍ͭͯ͸ɺ࣮‫ݧ‬σʔλ͕‫ݶ‬ΒΕ͍ͯΔɺ΋͘͠͸΄ͱΜͲ࣮‫͔ݧ‬Βͷ৘ใ͕ແ͍ͨΊɺ͜ͷ‫ڀݚ‬՝୊ͰಘΒΕΔ݁Ռ͸ɺैདྷͷ‫ݱ‬৅࿦తͳ໛‫ͱܕ‬͸ҟͳΓɺύϥϝʔλϑϦʔͷ༧‫ݴ‬Λ༩͑Δͱ͍͏ॏཁͳ੒Ռ͕‫ظ‬଴͞ΕΔɻैͬͯɺ‫و‬ॏͳ‫ݯࢿػࢉܭ‬ΛͰ͖Δ͚ͩ༗ޮ‫͢༻׆‬ΔͨΊʹɺ2 + 1 ϑϨʔόͷ֨
ࢠ QCD ‫Ͱࢉܭ‬Ҿ͖ग़͢͜ͱͷͰ͖ΔΞΠιεϐϯରশੑΛ࣋ͬͨീॏ߲όϦΦϯؒ૬‫༻࡞ޓ‬ͷ৘ใΛ͢΂ͯ‫ٻ‬ΊΒΕΔΑ͏ʹɺҎԼʹࣔ͢ 52 νϟωϧͷ 4 ఺૬ؔؔ਺ΛҰ౓ͷ‫ࢉܭ‬δϣϒͰಉ࣌ʹ‫͢ࢉܭ‬ΔΑ͏ʹϓϩάϥϜΛ४උ্ͨ͠Ͱ‫ࢉܭ‬Λ։͍࢝ͯ͠Δɻ

⟨pnpn⟩,⟨pΛpΛ⟩,⟨pΛΣ+ n⟩,⟨pΛΣ0 p⟩,

⟨Σ0 ppΛ⟩,⟨Σ0 pΣ+ n⟩,⟨Σ0 pΣ0 p⟩,⟨Σ+ npΛ⟩,⟨Σ+ nΣ+ n⟩,⟨Σ+ nΣ0 p⟩,⟨ΛΛΛΛ⟩,⟨ΛΛpΞ− ⟩,⟨ΛΛnΞ0 ⟩,⟨ΛΛΣ+ Σ− ⟩,⟨ΛΛΣ0 Σ0 ⟩,⟨nΞ0 ΛΛ⟩,⟨nΞ0 pΞ− ⟩,⟨nΞ0 nΞ0 ⟩,⟨nΞ0 Σ+ Σ− ⟩,⟨nΞ0 Σ0 Σ0 ⟩,⟨pΞ− ΛΛ⟩,⟨pΞ− pΞ− ⟩,⟨pΞ− nΞ0 ⟩,⟨pΞ− Σ+ Σ− ⟩,⟨pΞ− Σ0 Σ0 ⟩,⟨pΞ− Σ0 Λ⟩,⟨nΞ0 Σ0 Λ⟩,⟨Σ+ Σ− ΛΛ⟩, ⟨Σ+ Σ− pΞ− ⟩, ⟨Σ+ Σ− nΞ0 ⟩, ⟨Σ+ Σ− Σ+ Σ− ⟩, ⟨Σ+ Σ− Σ0 Σ0 ⟩, ⟨Σ+ Σ− Σ0 Λ⟩,⟨Σ0 Σ0 ΛΛ⟩, ⟨Σ0 Σ0 pΞ− ⟩, ⟨Σ0 Σ0 nΞ0 ⟩, ⟨Σ0 Σ0 Σ+ Σ− ⟩, ⟨Σ0 Σ0 Σ0 Σ0 ⟩,⟨Σ0 ΛpΞ− ⟩,⟨Σ0 ΛnΞ0 ⟩,⟨Σ0 ΛΣ+ Σ− ⟩,⟨Ξ− ΛΞ− Λ⟩,⟨Ξ− ΛΣ− Ξ0 ⟩,⟨Ξ− ΛΣ0 Ξ− ⟩,⟨Σ0 Ξ− Ξ− Λ⟩,⟨Σ0 Ξ− Σ− Ξ0 ⟩,⟨Σ0 Ξ− Σ0 Ξ− ⟩,⟨Σ− Ξ0 Ξ− Λ⟩,⟨Ξ− Ξ0 Ξ− Ξ0 ⟩,⟨Σ− Ξ0 Σ− Ξ0 ⟩,⟨Σ− Ξ0 Σ0 Ξ− ⟩,－17－⟨Σ0 ΛΣ0 Λ⟩,2015 ೥౓தͰ͸ɺ্‫ه‬ീॏ߲ʹՃ͑ͯɺ‫͍ڧ‬૬‫ʹ༻࡞ޓ‬ΑΔ่յνϟωϧͷ
։͔ͳ͍ (ैͬͯ‫ࡏݱ‬ͷํ๏Ͱ҆શʹϙςϯγϟϧΛ‫ٻ‬ΊΒΕΔ) ΩΩ νϟωϧ΋Ճ͑ͨେ‫ن‬໛‫͢͢ࢉܭ‬ΊΒΕͨɻσʔλ͕๲େͰ͋ΔͨΊղੳ΋·ͩਐߦதͰ͋Δ͕ɺ༧උతͳ݁ՌͷҰྫͱͯ͠ɺΛN ͷத৺ྗ‫ͼٴ‬ςϯιϧྗϙςϯγϟϧΛਤ 14 ʹࣔ͢ɻ(14) ֨ࢠ QCD ‫༻ڀݚ‬σʔλάϦου JLDG/ILDG ͷӡ༻JLDG (Japan Lattice Data Grid) ͸ɺࠃ಺ͷ‫ࢉܭ‬ૉཻࢠ෺ཧ‫ڀݚ‬άϧʔϓ͕೔ʑͷ‫ڀݚ‬σʔλΛ؅ཧɾ‫ڞ‬༗͢ΔҝͷσʔλάϦουͰ͋ΔɻओγεςϜ͸ɺࠃ಺ͷओཁͳ֨ࢠ QCD ‫̕఺ڌڀݚ‬Օॴʹઃஔͨ͠ϑΝΠϧαʔόΛࠃཱ৘ใֶ‫͕ॴڀݚ‬ఏ‫͢ڙ‬Δ SINET VPN Ͱ઀ଓ͠ɺάϦουϑΝΠϧγεςϜιϑ
τ΢ΣΞ Gfarm ͰଋͶͨϑΝΠϧγεςϜͰ͋ΔɻͲͷ‫͔఺ڌ‬ΒΞΫηεͯ͠΋ಉҰͷϑΝΠϧγεςϜ͕‫͑ݟ‬ΔͷͰɺʮ͋Δ‫఺ڌ‬ͷεύίϯͰੜ੒ͨ͠
σʔλʢ֨ࢠ QCD ഑ҐͳͲʣΛ JLDG ʹ౤ೖɾ஝ੵ͠ɺผ‫Ͱ఺ڌ‬ಡΈग़ͯ͠ɺͦͷ‫఺ڌ‬ͷεύίϯͰ࠶ղੳʢ෺ཧྔͷ‫ࢉܭ‬ʣΛ͓͜ͳ͏ʯͱ͍ͬͨσʔλ‫ڞ‬༗Λɺ༰қʹ͓͜ͳ͏ࣄ͕Ͱ͖Δɻ·ͨɺαϒγεςϜͱͯ͠ɺHPCI ‫ڞ‬༻ετϨʔδͱͷ࿈‫ܞ‬γεςϜͱ ILDG (International Lattice Data Grid) ͱͷ઀ଓγεςϜΛඋ͍͑ͯΔʢਤ ࢀরʣɻJLDG ͷӡ༻͸ɺ֤‫఺ڌ‬ͷ୅දऀɺ‫ڀݚ‬άϧʔϓͷ୅දऀɺγεςϜ։ൃऀɺ؅ཧӡ༻ࢧԉͷҕୗઌͷ‫ऀۀ‬ͷ୲౰ऀɺΛϝϯόʔͱ͢Δ JLDG νʔϜ͕ߦ͓ͬͯΓɺஜ೾େ͔Β͸ɺ‫ݐ‬෦ɺఱּʢγεςϜ৘ใʣͱࢁ࡚ɺ٢ߐ͕ࢀՃ͍ͯ͠ΔɻJLDG ͸ 2005 ೥ʹ։ൃΛ։࢝͠ɺ2007 ೥͔Βӡ༻͍ͯ͠ΔɻJLDG ͸ɺҰࡢ೥౓·Ͱ͸γεςϜͷվྑ΍৽‫ػ‬ೳͷ࣮૷Λ͓͜ͳͬͯɺͦͷརศੑ͕޲্
͖͕ͯͨ͠ɺࡢ೥౓͔Β͸ɺγεςϜͷ૿‫ڧ‬ɾ҆ఆӡ༻ʹओ‫͕؟‬Ҡ͖͍ͬͯͯ
Δɻ·ͨɺࠃ಺ͷෳ਺ͷେ͖ͳ‫ڀݚ‬άϧʔϓ͕‫ڀݚ‬Πϯϑϥͱͯ͠ JLDG Λ࢖༻͍ͯ͠Δɻ͜ͷࣄ͔ΒɺJLDG ͕࣮༻γεςϜͱͯ͠ɺҰఆͷ‫׬‬੒ͷҬʹୡͨ͠ͱ൑அ͠ɺ͜ͷஈ֊ͰͷγεςϜͱͦͷӡ༻ʹ͍ͭͯͷ‫ه‬࿥ͱࠃ಺֎
΁ͷ޿ใͷ໨తͰɺࠃࡍձٞ CHEP2015 ʹͯ JLDG ͷ૯߹ใࠂΛ͓͜ͳͬͨ
ʢ࿦จ 33ʣɻࠓ೥౓͸ɺҎԼͷγεςϜ૿‫҆ͱڧ‬ఆӡ༻ͷҝͷ‫׆‬ಈΛ͓͜ͳͬͨɻ• ϑΝΠϧαʔόͷ૿‫ڧ‬:લ೥౓ 28 αʔό 5.0PB ͔Β 39 αʔό 7.5PB ΁• ؅ཧ‫৽ߋثػ‬ʢJLDG 2 ݅ɺILDG 2 ݅ʣ
• Gfarm ߋ৽ (4 ճ)• SINET5 ΁ͷҠߦରԠ: Ұ෦‫ Ͱ఺ڌ‬1Gbps ͔Β 10Gbps ΁૿଎• ϑΝΠϧαʔόͷ‫ݸ‬ผো֐ରԠ

ILDG ͸ɺੈք 5 ஍Ҭʹߏங͞Εͨ Lattice QCD ༻ͷσʔλάϦουΛɺLattice
QCD ͷ‫ૅج‬σʔλʢ഑Ґʣͷ‫ڞ‬༗Λ໨తͱͯ͠ɺ૬‫ޓ‬ӡ༻ΛՄೳʹ͢Δ Girdof Grids Ͱ͋ΔɻJLDG ͸ ILDG ͷ೔ຊ஍ҬάϦουͰ͋Δɻ·ͨɺ೔ຊ͔Β－18－

͸ɺILDG ͷ board member ͱͯ͠᤽૿͕ɺMetadata working group memberͱͯ͠ ٢ߐ͕ࢀՃ͍ͯ͠Δɻ·ͨɺ΋͏ͻͱͭͷ Middleware working groupʹ͸ɹఱּʢγεςϜ৘ใʣ͕ϝϯόʔͱͯ͠ࢀՃ͢Δͱͱ΋ʹɺ٢ߐ΋Φϒβʔόͱͯ͠ࢀՃ͠ϢʔβʔαΠυ͔Βͷఏ‫ݴ‬౳Λ͓͜ͳ͍ͬͯΔɻILDG
͸ɺ2007 ೥ͷӡ༻։࢝ґཔɺࡉ͔ͳվྑ͸͋Δ΋ͷͷɺओཁ෦෼͸҆ఆͨ͠ӡ༻Λଓ͚͍ͯΔɻ

ILDG ʹ͸ɺӡ༻։࢝౰ॳ͔Βʮެ։͞Ε͍ͯΔ֨ࢠ QCD ഑ҐΞϯαϯϒϧ
ͷར༻ঢ়‫گ‬Λ೺Ѳ͢Δ࢓૊Έ͕ແ͍ʯࣄ͕໰୊Ͱ͋ͬͨɻ࿦จͷҾ༻ɾඃҾ༻ͷ‫ه‬࿥ͱ͸ผʹɺσʔλͷҾ༻ɾඃҾ༻ؔ܎ͷ‫ه‬࿥Λ஝ੵͰ͖Ε͹ɺͦΕΛ༻͍ͯɺͦͷ഑Ґσʔλͷ༗༻ੑΛଌΔࢿྉͱͳΓ͏Δ͠ɺͻ͍ͯ͸ɺσʔλ‫ڞ‬༗ͷҝͷ ILDG ͷ༗༻ੑΛࣔ͢ࢿྉͱ΋ͳΓ͏Δɻ͜ͷࣄ͸ɺ֨ࢠ QCD ഑Ґσʔλʹ‫ͨͬݶ‬໰୊Ͱ͸ͳ͘ɺଟ͘ͷ‫ڀݚ‬෼໺͕ɺσʔλͷҾ༻ɾඃҾ༻ؔ܎Λ೺Ѳ͢ΔχʔζΛ͍࣋ͬͯΔɻ͜ͷ༷ͳഎ‫ܠ‬ͷԼͰɺֶज़࿦จͷग़൛քͰ޿
͘༻͍ΒΕ͍ͯΔʰDOI(DigitalObjectIdentifier) ొ࿥ʱͷ࢓૊ΈΛ‫ڀݚ‬σʔλʹ΋༻͍ΔࢼΈ͕࢝·͍ͬͯΔɻILDG Ͱ΋ɺʰ֨ࢠ QCD Ξϯαϯϒϧ΁
ͷ DOI ొ࿥ʱΛߦ͍ɺHigh Energy Physics ෼໺ͷ࠷େͷ৘ใγεςϜͰ͋Δ
INSPIRE-HEP Λ༻͍ͯɺΞϯαϯϒϧͷҾ༻ɾඃҾ༻ؔ܎Λ೺ѲͰ͖Δ࢓૊
ΈΛߏங͢ΔఏҊ͕ͳ͞Εɺ2015 ೥ 4 ݄ͷ ILDG workshop Ͱɺ֤஍ҬάϦουͰ‫ݕ‬౼͢Δࣄͱͳͬͨɻ
͜ͷ߹ҙΛड͚ɺ೔ຊͰ͸ɺఱּɺদ‫( ݹ‬KEK)ɺ٢ߐ͕த৺ͱͳͬͯɺDOI
ొ࿥ͷମ੍໘ͷ‫ݕ‬౼ʢDOI ొ࿥‫ͱؔػ‬ͷ‫ڠ‬ٞɺؔ܎‫ͱؔػ‬ͷ‫ڠ‬ٞͱ DOI ొ࿥࣮ࢪମ੍ͱϑϩʔͷ‫ݕ‬౼ʣΛ͓͜ͳ͏ͱͱ΋ʹɺDOI ొ࿥ʹඞཁͳ࣮࡞‫ۀ‬
ʢMetadata ͱ landing page ͷ ILDG ensemble/configuration metadata ͔Βͷ൒ࣗಈੜ੒ʣͷࢼߦʹணखͨ͠ɻ

(15) ֨ࢠ QCD ‫ڞ‬௨ίʔυ։ൃࡢ೥౓ʹҾ͖ଓ͖ɺ֨ࢠ QCD ‫ڞ‬௨ίʔυ Bridge++ ͷ։ൃΛਐΊͨʢ࿦จ
37 , 38ʣɻ֨ࢠ QCD ‫ڞ‬௨ίʔυ Bridge++ ͸ɺQCD Λ‫ؚ‬Ή֨ࢠήʔδཧ࿦

－19－γϛϡϨʔγϣϯͷͨΊͷ൚༻ίʔυηοτͰ͋Δɻ༷ʑͳ֨ࢠ࡞༻΍ΞϧΰϦζϜΛద༻ՄೳͰɺϊʔτ PC ͔Β௒ฒྻ‫Ͱ·ػࢉܭ‬෯޿͍ΞʔΩςΫνϟ
ʹରԠ͍ͯ͠Δɻ2012 ೥ 7 ݄ʹ Bridge++ ver.1.0.0 Λެ։ͯ͠Ҏ߱ɺ‫ܧ‬ଓͯ͠ίʔυͷվળɺ֦ுΛߦ͍ͬͯΔ (http://bridge.kek.jp/Lattice-code/)ɻૉ
ཻࢠཧ࿦άϧʔϓ͔Β͸ɺۚ୩ɺ‫׈‬઒ɺࠜଜɺ୩‫ޱ‬ɺුా͕ࢀՃ͍ͯ͠Δɻຊ೥౓͸ɺҰൠԽϑΣϧϛΦϯͷ௥ՃɺFFT ରԠɺXML ‫ࣜܗ‬ͷಋೖͳͲΛߦͬͨɻ͜ΕΒͷมߋΛ‫ؚ‬Ίͨ Bridge++ ver.1.3.0 ΁ͷϝδϟʔΞοϓσʔτ͕ 2015 ೥ 10 ݄ʹ࣮ࢪ͞Εͨɻͦͷ‫ޙ‬΋ɺίʔυͷࡉ͔͍վఆɺվྑ͕ਐΊΒΕ͍ͯΔɻ࠷৽൛͸ ver.1.3.2 Ͱ͋Δɻͳ͓ɺ‫ڞ‬௨ίʔυΛ࢖༻ͨ͠‫ڀݚ‬࿦จ͕ɺࠓ೥౓৽ͨʹ̕ຊ௥Ճ͞Εͨɻ௨ࢉ̍̏ຊͷ࿦จ͕‫ڞ‬௨ίʔυΛ‫ൃʹݩ‬ද͞Ε͍ͯΔɻʲ̎ʳ ௒‫ݭ‬ཧ࿦ʢੴ‫ ڮ‬Ԇ޾ɺҏෑ ‫ޗ‬࿠ɺࠤ౻ ༐ೋɺໟར ݈࢘ʣ(1) Sine-square deformation ͱ‫ܗڞ‬৔ͷཧ࿦Ұ࣍‫ݩ‬εϐϯ‫͍͓ͯʹܥ‬ɺྡͷεϐϯͱͷ૬‫༻࡞ޓ‬ΛҐஔͷαΠϯؔ਺ͷ 2 ৐ʹൺྫ͢ΔΑ͏ʹͱͬͨ৔߹ɺͦͷ‫ج‬ఈঢ়ଶ͸૬‫͕༻࡞ޓ‬Ґஔʹ‫د‬Βͳ͍৔߹ͱҰக͢Δ͜ͱ͕‫ܡ‬ʢ౦େʣΒͷ‫ʹڀݚ‬ΑͬͯΘ͔͍ͬͯΔɻੴ‫ڮ‬͸ଟాʢཧ‫ݚ‬ʣͱͱ΋ʹɺ͜ͷ‫ݱ‬৅Λ‫ܗڞ‬ରশੑ͕͋Δ৔߹ʹ͍ͭͯௐ΂ͨɻ૬‫༻࡞ޓ‬ΛαΠϯؔ਺ͷ 2 ৐ʹͱͬͨ৔߹ͱఆ਺ͷ৔߹͸ɺ͋Δ‫ܗڞ‬ม‫͍͍ͯͭͼ݁Ͱ׵‬Δ͜ͱΛࣔ͠ɺ͜ͷ‫ܗڞ‬ม‫͔׵‬Β‫ج‬ఈঢ়ଶ౳ͷੑ࣭͕ཧղͰ͖Δ͜ͱΛࣔͨ͠
ʢ࿦จ 39ʣɻ·ͨɺ͜ͷཧ࿦ʹ‫ݱ‬ΕΔԋࢉࢠɾঢ়ଶͷੑ࣭Λௐ΂ͨʢ࿦จ 40ʣɻ(2) ήʔδ-ॏྗ૒ରੑͱՄੵ෼ੑʹ‫߹݁ڧͮ͘ج‬ήʔδཧ࿦ͷ‫ڀݚ‬ॏྗཧ࿦ͱήʔδཧ࿦ͷ૒ରੑʹΑΓɺplanar ‫Ͱݶۃ‬ͷ̐࣍‫ۃݩ‬େ௒ରশήʔδཧ࿦ͷ‫ࢄ߹݁ڧ‬ཚৼ෯͸ɺ൓υδολʔۭ࣌தͷޫత‫ڥ‬քΛ࣋ͭ‫ۃ‬খ‫ۂ‬໘ͷ໘ੵͰ༩͑ΒΕΔɻ͜ͷࢄཚৼ෯͸ޫత‫ܦ‬࿏͔ΒͳΔ΢Οϧιϯϧʔϓͷਅۭ‫ظ‬଴஋ͱ౳ՁͰ͋Δɻ͜Ε·Ͱͷ‫ʹڀݚ‬ΑΓզʑ͸ɺ૒ରੑͷഎ‫ݱʹޙ‬ΕΔՄ
ੵ෼໛‫ܕ‬Λ༻͍ͯ‫ࢄ߹݁ڧ‬ཚৼ෯Λղੳతʹ‫ٻ‬ΊΔํ๏ΛఆࣜԽ͖ͯͨ͠ɻ
ࠤ౻͸ Z. Bajnok, J. Balog, G.Z. Toth (Wigner Research Centre), ҏ౻ʢ౦‫޻ژ‬‫ۀ‬େֶʣͱ‫ʹڞ‬ɺྔࢠՄੵ෼‫ܥ‬Λղੳ͢Δ৽ͨͳख๏Λ։ൃ͠ɺ̎࣍‫ݩ‬తͳӡಈྔΛཻ࣋ͭࢠͷ̍̌఺‫ࢄ߹݁ڧ‬ཚৼ෯Λ༩͑ΔՄੵ෼໛‫͋Ͱܕ‬Δ su(3)2 /u(1)2౳࣭αΠϯΰϧυϯ໛‫ܕ‬ͷ‫ྔ࣭ͳີݫ‬-݁߹ؔ܎ࣜΛಋ͍ͨɻ͜Ε͸ɺෳ਺ͷεέʔϧΛ࣋ͭྔࢠՄੵ෼໛‫ʹܕ‬ର͢ΔॳΊͯͷ݁ՌͰ͋Γɺ౰֘෼໺ͷ̎̌೥དྷͷ໰୊Λղܾ͢Δ΋ͷͰ͋Δɻ·ͨɺ͜ͷ࣭ྔ-݁߹ؔ܎ࣜʹΑΓɺରԠ
͢Δ‫ࢄ߹݁ڧ‬ཚৼ෯ΛղੳతʹධՁ͢ΔզʑͷఆࣜԽ͕‫ͨ݁͠׬‬ʢ࿦จ 41ʣɻ(3) ίώʔϨϯτঢ়ଶΛ༻͍ͨߦྻ‫ز‬Կͷ‫ڀݚ‬௒‫ݭ‬ཧ࿦ͷඇઁಈతఆࣜԽͱͯ͠‫ظ‬଴͞Ε͍ͯΔߦྻ໛‫Ͱܕ‬͸ɺ‫ݭ‬΍ D ϒϨʔϯͱ͍ͬͨ෺ମ͸ɺߦྻ‫ز‬Կͱ‫ݺ‬͹ΕΔ཭ࢄతͳ‫ز‬Կͷ࿮૊ΈʹΑΓ‫ه‬ड़͞Ε

－20－

Δɻ͔͠͠ɺ͜ͷߦྻ‫ز‬Կͷੑ࣭͸͜Ε·Ͱਂ͘ཧղ͞Ε͍ͯͳ͔ͬͨɻҏෑ͸͜ͷ‫ز‬Կͷߏ଄Λཧղ͢Δख๏ͱͯ͠ɺྔࢠྗֶͷίώʔϨϯτঢ়ଶΛ༻͍ͨ৽ͨͳํ๏ΛఏҊͨ͠ʢ࿦จ 42ʣɻ͜ͷํ๏ʹΑΓ཭ࢄతͳߦྻ‫ز‬Կ͔Βɺ‫ྔܭ‬΍‫ݭ͍ͨͬͱ཰ۂ‬΍ D ϒϨʔϯͷඍ෼‫ز‬Կֶతͳ৘ใΛಘΔ͜ͱ͕ग़དྷ
ΔΑ͏ʹͳͬͨɻ·ͨҏෑͱଜ໦͸େֶӃੜͷদຊͱͱ΋ʹɺ͜ͷํ๏Λ༻͍ͯߦྻ‫ز‬Կͷߏ଄Λௐ΂ͨʢ࿦จ 43ʣɻͦͷ݁Ռɺಛఆͷߦྻ‫ز‬Կ͸έʔϥʔߏ଄ͱ‫ݺ‬͹ΕΔඇৗʹྑ͍ੑ࣭ͷߏ଄Λ࣋ͭ͜ͱ͕ࣔ͞Εͨɻ·ͨɺ͜ͷέʔϥʔߏ଄ͱߦྻͷ഑ҐΛ௚઀݁ͼ͚ͭΔؔ܎͕ࣜಘΒΕͨɻ(4) ‫ݭ‬ͷ৔ͷཧ࿦ͷ࣍‫ݩ‬ਖ਼ଇԽͱϧʔϓৼ෯‫ݭ‬ͷཧ࿦͸ࢄཚৼ෯͕ઁಈ࿦Λ༻͍ͯ༗‫͖Ͱࢉܭʹݶ‬Δ͜ͱ͕஌ΒΕ͍ͯΔ
͕ɺൃࢄ͸૬ࡴ͢ΔͷͰ͋Γɺ࠷ॳ͔Βͳ͍Θ͚Ͱ͸ͳ͍ɻैͬͯɺ఺ཻࢠͷ৔ͷཧ࿦ͱಉ༷ʹɺ͏·͍ਖ਼ଇԽͷํ๏Λߟ͑Δ͜ͱ͸ॏཁͰ͋Δɻಛʹ௒‫ݭ‬ͷ৔ͷཧ࿦ʹ͓͍ͯ͸ίϯλΫτλʔϜͷ໰୊ͱ‫ݺ‬͹ΕΔ໰୊͕͋Γɺtree ৼ෯Ͱ͑͞‫ͨ͏·ͯ͠͠ࢄൃ্͚͔ݟ‬Ίɺਖ਼ଇԽΛ༩͑ͳ͚Ε͹ఆٛ͢Δ͜ͱ͕
ग़དྷͳ͍ɻ·ͨɺD-ϒϨʔϯͷӨ‫ڹ‬౳ͷࢄཚৼ෯ͱ͸ҟͳΔྔΛ‫͢ࢉܭ‬Δࡍʹ͸ɺ‫ݭ‬ͷཧ࿦ͷ͏·͍ਖ਼ଇԽͷํ๏Λ༩͑Δ͜ͱ͕ඞཁෆՄܽʹͳΔɻੴ‫ڮ‬͸ଜ্ʢ۴࿏ߴઐʣΒͱͷ͜Ε·Ͱͷ‫Ͱڀݚ‬ɺ࣍‫ݩ‬ਖ਼ଇԽΛ༻͍ͨ‫ʹࢉܭ‬ΑΓɺtree ৼ෯ʹ͍ͭͯ͸ୈҰྔࢠԽͷ‫ͱࢉܭ‬Ұக͢Δ݁ՌΛಘΔ͜ͱ͕Ͱ͖
Δ͜ͱΛ͍ࣔͯ͠Δɻࠓ೥౓͸௒‫ݭ‬ͷ৔߹ʹ͜ͷ݁ՌΛ֦ு͢ΔͨΊɺඇྟք࣍‫ݩ‬ͷ௒‫ݱʹݭ‬ΕΔੈք໘্ͷཧ࿦ͷ૬ؔؔ਺ͷ‫ࢉܭ‬Λߦͬͨʢ࿦จ 44ʣɻ(5) ‫ݭ‬ཧ࿦ʹ͓͚Δඇ‫ز‬Կֶతഎ‫ͱۭ࣌ܠ‬Ӊ஦߲໰୊‫ݭ‬ཧ࿦ͷରশੑͰ͋Δ‫ݭ‬૒ରੑʹΑΓɺϦʔϚϯ‫ز‬Կֶతͳۭ࣌ඳ૾Λ௒͑Δඇ‫ز‬Կֶతͳۭ࣌΋‫ݭ‬ཧ࿦ͷഎ‫ͯ͠ͱۭ࣌ܠ‬ՄೳͱͳΔɻ͜ͷΑ͏ͳഎ‫࣌ܠ‬ۭ (T-fold/monodrofold) ͸య‫ܕ‬తʹ͸ਅۭͷϞδϡϥΠ͕‫ݭ‬εέʔϧͷ৔߹ʹՄೳͱͳΔɻࠤ౻͸ੁ‫ݪ‬ɺ࿨ాʢ໋ཱ‫ؗ‬େֶʣͱ‫ʹڞ‬ɺ‫ܗڞ‬৔ཧ࿦ʹ‫ݭ͖ͮج‬εέʔϧͰ΋༗ޮͳඇ‫ز‬Կֶతഎ‫ۭ࣌ܠ‬ͷղੳΛਐΊͨɻ·ͣɺ‫ܗڞ‬ରশੑΛอͭ‫ܗڞ‬৔ཧ࿦ͷք໘ (‫ܗڞ‬ք໘/conformal interface) Λ༻͍ͯඇ‫ز‬Կֶతഎ‫ۭ࣌ܠ‬தͷ‫ݭ‬ʹର͢Δ৽͍͠λΠϓͷϞδϡϥʔෆมͳ෼഑ؔ਺Λߏ੒ͨ͠ʢ࿦จ 45ʣɻ·ͨɺ͜ͷΑ͏ͳߏ੒Λ֦ு͠ɺT-fold λΠϓͷඇ‫ز‬Կֶతഎ‫ܠ‬தͷ‫ݭ‬ཧ࿦Ͱ͸ɺۭ࣌ͷ௒ରশੑ͕ഁΕ͍ͯΔʹ΋߆Βͣ̍ϧʔϓͰͷӉ஦߲͕ফ͑Δɺ‫ݱ‬৅࿦తʹ‫ڵ‬ຯਂ͍໛‫͕ܕ‬༰қʹߏ੒Ͱ͖Δ͜ͱΛࣔͨ͠ʢ࿦จ 46ʣɻ(6) ήʔδ/ॏྗରԠͷ਺஋త‫ূݕ‬ҏෑ͸‫ژ‬େ‫ݚج‬ͷՖాਖ਼ൣ।‫ڭ‬तɺҵ৓େֶͷඦ෢‫ܚ‬จ।‫ڭ‬तɺ̠̠̚ͷ੢ଜ३।‫ڭ‬तΒͱͱ΋ʹɺήʔδ/ॏྗରԠͷ਺஋త‫ূݕ‬Λߦͬͨʢ࿦จ 47ʣɻҏෑΒ͸௒‫ݭ‬ཧ࿦ͱͷ౳Ձੑ͕༧૝͞ΕΔ 1 ࣍‫ݩ‬ͷήʔδཧ࿦ͷ਺஋‫ࢉܭ‬Λߦ͍ɺ಺෦ΤωϧΪʔ౳ͷ೤ྗֶྔΛ‫ٻ‬ΊɺಘΒΕͨ݁ՌΛ௒‫ݭ‬ཧ࿦ͷ΋ͷͱൺֱͨ͠ɻͦͷ݁Ռɺήʔδ/ॏྗରԠ͕͔֬ʹ੒ཱ͍ͯ͠Δͱ͍͏‫ڌূ͍ڧ‬Λ
ಘΔ͜ͱ͕ग़དྷͨɻ͜ͷ‫Ͱڀݚ‬͸ɺήʔδ‫܈‬ͷϥϯΫ͕ൺֱతେ͖͍৔߹ͱখ

－21－͍͞৔߹ͷ྆ํ͕ௐ΂ΒΕͨɻϥϯΫ͕େ͖͍৔߹ͷ‫ࢉܭ‬͸͢Ͱʹଞͷઌߦ‫ݚ‬‫Ͱڀ‬΋ߦΘΕ͍͕ͯͨɺҏෑΒ͸ͦͷ݁ՌΛ͞Βʹਫ਼ີԽͨ͠ɻҰํɺϥϯΫ͕খ͍͞৔߹ͷઌߦ‫ڀݚ‬͸͜Ε·ͰʹߦΘΕ͓ͯΒͣɺ͜ͷ‫ʹڀݚ‬Αͬͯ͸͡ΊͯରԠ͕‫͞ূݕ‬Εͨɻ(7) ҰൠԽ‫ز‬Կֶͷ‫ڀݚ‬ɹ௒ॏྗཧ࿦ͷ NSNS ෦෼͸ɺۭ࣌ͷ‫ྔܭ‬ɺKalb-Ramond ৔ͱσΟϥτϯ৔͔ΒͳΔɻҰൠԽ‫ز‬Կֶ͸ɺ͜ΕΒͷ৔ʹ‫ز‬ԿֶతཧղΛ༩͑Δɻ͢ͳΘͪɺ઀ଋͱ༨઀ଋ͔ΒͳΔ௚࿨ଋͷ্ʹɺۭ࣌ͷ‫ ͱྔܭ‬Kalb-Ramond ৔ͷ‫ز‬Կֶతͳ‫ه‬ड़Λ࣮‫͍ͯ͠ݱ‬Δɻ‫ݭ‬ཧ࿦Ͱ͸ɺ͜ΕΒͷ৔ͷద౰ͳ഑ҐΛഎ‫͠ͱܠ‬ͯɺͦͷதͰͷ‫ݭ‬ͷӡಈΛߟ࡯͢ΔɻҟͳΔഎ‫ܠ‬ಉ࢜Ͱ‫ݭ‬ͷӡಈ͕ඇࣗ໌ʹ౳ՁʹͳΔؔ܎ͱͯ͠ɺT ૒ରੑ͕஌ΒΕ͍ͯΔɻۭ࣌ͷ‫ ͱྔܭ‬Kalb-Ramond৔Λಉ౳ʹѻ͏ҰൠԽ‫ز‬Կֶ͸ɺ͜ͷ T ૒ରੑΛ‫ؚ‬Ίͯ‫ز‬Կֶతʹ‫ه‬ड़͢Δͱ‫ظ‬଴͞ΕΔɻɹ‫ࣜܗ‬తʹ T ૒ରੑม‫׵‬Λࢪ͢ͱɺ͜Ε·Ͱߟ͑ΒΕͯ͜ͳ͔ͬͨΑ͏ͳ৔ͷ഑Ґ͕ಘΒΕΔɻಛʹ‫ڵ‬ຯਂ͍ͷ͸ɺ‫ط‬ଘͷ‫ز‬ԿֶͰ͸ଊ͖͑Εͳ͍ʮඇ‫ز‬Կֶతʯͳ৔ͷ഑Ґ͕ग़‫͢ݱ‬Δͱ͍͏ٞ࿦Ͱ͋ΔɻҰൠԽ‫ز‬Կֶ͸ T ૒ରੑΛ‫ؚ‬Ίͯഎ‫ܠ‬৔ͷ‫ز‬Կֶత‫ه‬ड़Λ༩͑Δ͜ͱ͔Βɺ͜ΕΛ༻͍ͯඇ‫ز‬Կֶతͳഎ‫ܠ‬Λʮ‫ز‬Կֶతʯʹཧղ͠Α͏ͱ͍͏ٞ࿦͕ͳ͞Ε͍ͯΔɻ
ɹଜ໦͸ҰൠԽ‫ز‬Կֶʹ͓͍ͯ઀ଋͱ༨઀ଋͷ໾ׂΛೖΕସ͑ͨมछΛಋೖ͠ɺඇ‫ز‬Կֶతഎ‫ܠ‬ͷཧղΛ୳‫ͨ͠ٻ‬ɻಛʹҰൠԽ‫ز‬Կֶͷมछʹ‫ͮ͘ج‬ॏྗΛߏங͠ɺඇ‫ز‬Կֶతഎ‫ͱܠ‬ॏྗ৔ͱͷ݁߹Λ໌Β͔ʹͨ͠ʢ࿦จ 48ʣɻ(8) ‫ݭ‬Λϓϩʔϒͱͨ͠ΤΩκνοΫϒϨʔϯͷഎ‫ۭ࣌ܠ‬ͷ‫ڀݚ‬ΤΩκνοΫϒϨʔϯ͸௿࣍‫ۭ࣌ݩ‬ͷ௒‫ݭ‬ཧ࿦ʹొ৔͢ΔಛघͳϒϨʔϯͰ͋Δɻഎ‫ۭ࣌ܠ‬͸Ұൠ࠲ඪม‫Ͱ͚ͩ׵‬͸ଊ͑ΒΕͣɺ௒‫ݭ‬ཧ࿦ͷ૒ରੑͷߏ଄͕‫·ؚ‬ΕΔɻ͜ͷ༷ͳϒϨʔϯ΍എ‫ۭ࣌ܠ‬͸ɺ௒‫ݭ‬ཧ࿦ͷίϯύΫτԽͱ͔ͦ͜ΒಘΒΕΔૉཻࢠ෺ཧΛแ‫ׅ‬తʹཧղ͢ΔͨΊʹॏཁͰ͋ΔɻΤΩκνοΫ
ϒϨʔϯͷҰྫͰ͋Δ 522 ϒϨʔϯ͸ NS5 ϒϨʔϯʹରͯ͠ 2 ճ T ૒ରม‫͢׵‬Δ͜ͱͰొ৔͢Δɻ໦ଜ͸ɺ2013 ೥ʹ 522 ϒϨʔϯഎ‫ۭ࣌ܠ‬Λ 2 ࣍‫ݩ‬௒৔‫ࣜܗ‬Λ༻͍ͨήʔδཧ࿦Λ༻͍ͨఆࣜԽΛ੒ޭ͍ͤͯͨ͞ɻ2 ࣍‫ݩ‬௒৔‫Ͱࣜܗ‬͸ T૒ରม‫ʹ׵‬ରԠ͢Δ Legendre ม‫׵‬Λਖ਼࣮͘͠ߦ͢ΔͨΊʹՄ໿ͳ௒৔Λಋೖ͍͕ͯͨ͠ɺՄ໿Ͱ͋ΔͨΊଟ͘ͷ༨෼ͳ੒෼৔͕ొ৔͢ΔɻͦͷͨΊɺ௒ରশήʔδม‫ʹ׵‬Αͬͯ෺ཧతࣗ༝౓͚͕ͩੜ͖࢒Δਖ਼͍͠ήʔδ‫ݻ‬ఆ৚݅Λൃ‫( ͨ͠ݟ‬࿦จ 49)ɻ͜ͷήʔδ‫ݻ‬ఆ͸ɺ‫ॴہ‬ԽఆཧΛ༻͍ͨ 2 ࣍‫ݩ‬௒ରশήʔδཧ࿦ͷ‫ܦ‬࿏ੵ෼ΛධՁ͢ΔࡍʹॏཁͰ͋Δɻʪ࿦จʫ

1. Takeshi Yamazaki, Ken-ichi Ishikawa, Yoshinobu Kuramashi, Akira Ukawa,
Study of quark mass dependence of binding energy for light nuclei in 2+1
flavor lattice QCD, Phys. Rev. D92 (2015) ref. 014501.

－22－

2. X.-Y. Jin, Y. Kuramashi, N. Nakamura, S. Takeda, and A. Ukawa, Curvatureof the critical line on the plane of quark chemical potential and pseudoscalarmeson mass for three-flavor QCD, Phys. Rev. D92 (2015) ref. 114511.
3. S. Takeda, X.-Y. Jin, Y. Kuramashi, N. Nakamura, and A. Ukawa, Phase
structure of Nf = 3 QCD at finite temperature and density by Wilson-Clover
fermions, Proceeding of Science (LATTICE 2015) 145.
4. N. Nakamura, X.-Y. Jin, Y. Kuramashi, S. Takeda, and A. Ukawa, Towards thecontinuum limit of the critical endline of finite temperature QCD, Proceedingof Science (LATTICE 2015) 160.
5. H. Suno, Y. Nakamura, K.-I. Ishikawa, Y. Kuramashi, Y. Futamura, A. Imakura,and T. Sakurai, Eigenspectrum Calculation of the Non-Hermitian O(a)-Improved
Wilson-Dirac Operator using the Sakurai-Sugiura Method, Proceeding of Science (LATTICE 2015) 026.
6. Hirokazu Kobayashi, Yoshifumi Nakamura, Shinji Takeda, and Yoshinobu Kuramashi, Optimization of Lattice QCD with CG and Multi-Shift CG on Intel
Xeon Phi Coprocessor, Proceeding of Science (LATTICE 2015) 029.
7. PACS Collaboration: K.-I. Ishikawa, N. Ishizuka, Y. Kuramashi, Y. Nakamura, Y. Namekawa, Y. Taniguchi, N. Ukita, T. Yamazaki, T. Yoshié, Massand Axial Current Renormalization in the Schrödinger Functional Scheme for
the RG-Improved Gauge and the Stout Smeared O(a)-Improved Wilson Quark
Actions, Proceeding of Science (LATTICE 2015) 271.
8. PACS Collaboration: K.-I. Ishikawa, N. Ishizuka, Y. Kuramashi, Y. Nakamura, Y. Namekawa, Y. Taniguchi, N. Ukita, T. Yamazaki, T. Yoshié, 2+1
Flavor QCD Simulation on a 964 Lattice, Proceeding of Science (LATTICE
2015) 075.
9. N. Ishizuka, K.-I. Ishikawa, A. Ukawa, T. Yoshie, Calculation of K → ππ
decay amplitudes with improved Wilson fermion action in lattice QCD, Phys.
Rev. D92 (2015) 074503.
10. Ryo Iwami, S. Ejiri, K. Kanaya, Y. Nakagawa, T. Umeda, D. Yamamoto(WHOT-QCD Collaboration), Multipoint reweighting method and beta functions for the calculation of QCD equation of state, PoS (LATTICE 2014)(2015) 222.
11. R. Iwami, S. Ejiri, K. Kanaya, Y. Nakagawa, D. Yamamoto, and T. Umeda,
Multipoint reweighting method and its applications to lattice QCD, Phys.
Rev. D 92, No.9 (2015) ref.094507, pp.1-11.

－23－

12. T. Umeda, S. Ejiri, R. Iwami, K. Kanaya, Towards the QCD equation of stateat the physical point using Wilson fermion, PoS (LATTICE 2015) (2016), tobe published.
13. A. Francis, O. Kaczmarek, M. Laine, T. Neuhaus and H. Ohno, Critical point
and scale setting in SU(3) plasma: An update, Phys. Rev. D 91, no. 9, 096002(2015).
14. H.-T. Ding, S. Mukherjee, H. Ohno, P. Petreczky and H.-P. Schadler, Diagonal
and oﬀ-diagonal quark number susceptibilities at high temperatures, Phys.
Rev. D 92, no. 7, 074043 (2015).
15. A. Francis, O. Kaczmarek, M. Laine, T. Neuhaus and H. Ohno, Nonperturbative estimate of the heavy quark momentum diﬀusion coeﬃcient, Phys. Rev.
D 92, no. 11, 116003 (2015).
16. A. Bazavov, H.-T. Ding, P. Hegde, O. Kaczmarek, F. Karsch, E. Laermann,
Swagato Mukherjee, H. Ohno, P. Petreczky, C. Schmidt, S. Sharma, W. Soeldner, and M. Wagner, Curvature of the freeze-out line in heavy ion collisions,Phys. Rev. D 93, 014512 (2016).
17. H. Ohno, H.-T. Ding, S. Mukherjee, O. Kaczmarek and H.-T. Shu, Charmonia
and bottomonia at finite temperature on large quenched lattice, Proceeding of
Science (Lattice 2015) ref. 175.
18. A. Nakamura, S. Oka, Y. Taniguchi, QCD phase transition at real chemical
potential with canonical approach, Journal of High Energy Physics, 2016(2),
1-19,
19. A. Nakamura, S. Oka, A. Suzuki and Y. Taniguchi, Study of high density
phase transition in lattice QCD with canonical approach, PoS LATTICE 2015(2016) 165.
20. A. Nakamura, S. Oka, A. Suzuki and Y. Taniguchi, Calculation of high-order
cumulants with canonical ensemble method in lattice QCD PoS LATTICE
2015 (2016) 168.
21. R. Fuluda, A. Nakamura, S. Oka, S. Sakai, A. Suzuki and Y. Taniguchi, Beating the sign problem in finite density lattice QCD PoS LATTICE 2015 (2016)
208.
22. Takeshi Yamazaki, Ken-ichi Ishikawa, Yoshinobu Kuramashi, Akira Ukawa,
Study of quark mass dependence of binding energy for light nuclei in 2+1
flavor lattice QCD, Physical Review D92 (2015) no.1, 014501.

－24－

23. Takeshi Yamazaki for PACS Collaboration, Light Nuclei and Nucleon Form
Factors in Nf=2+1 Lattice QCD, Proceedings of Science(LATTICE 2015) 081,
arXiv:1511.09179.
24. Yasumichi Aoki, Tatsumi Aoyama, Ed Bennett, Masafumi Kurachi, Toshihide Maskawa, Kohtaroh Miura, Kei-ichi Nagai, Hiroshi Ohki, Enrico Rinaldi,
Akihiro Shibata, Koichi Yamawaki, Takeshi Yamazaki (LatKMI Collaboration), SU(3) gauge theory with four degenerate fundamental fermions on thelattice, arXiv:1512.00957.
25. Yasumichi Aoki, Tatsumi Aoyama, Ed Bennett, Masafumi Kurachi, Toshihide Maskawa, Kohtaroh Miura, Kei-ichi Nagai, Hiroshi Ohki, Enrico Rinaldi,
Akihiro Shibata, Koichi Yamawaki, Takeshi Yamazaki (LatKMI Collaboration), Walking and conformal dynamics in many-flavor QCD, arXiv:1601.02287.
26. Yasumichi Aoki, Tatsumi Aoyama, Ed Bennett, Masafumi Kurachi, Toshihide Maskawa, Kohtaroh Miura, Kei-ichi Nagai, Hiroshi Ohki, Enrico Rinaldi,
Akihiro Shibata, Koichi Yamawaki, Takeshi Yamazaki (LatKMI Collaboration), Lattice study of the scalar and baryon spectra in many-flavor QCD,
arXiv:1510.07373.
27. Yasumichi Aoki, Tatsumi Aoyama, Ed Bennett, Masafumi Kurachi, Toshihide Maskawa, Kohtaroh Miura, Kei-ichi Nagai, Hiroshi Ohki, Enrico Rinaldi,
Akihiro Shibata, Koichi Yamawaki, Takeshi Yamazaki (LatKMI Collaboration), S-parameter and vector decay constant in QCD with eight fundamental
fermions, arXiv:1602.00796.
28. Yasumichi Aoki, Tatsumi Aoyama, Ed Bennett, Masafumi Kurachi, Toshihide Maskawa, Kohtaroh Miura, Kei-ichi Nagai, Hiroshi Ohki, Enrico Rinaldi,
Akihiro Shibata, Koichi Yamawaki, Takeshi Yamazaki (LatKMI Collaboration), Topological insights in many-flavor QCD on the lattice, arXiv:1510.05863.
29. Yasumichi Aoki, Tatsumi Aoyama, Ed Bennett, Masafumi Kurachi, Toshihide Maskawa, Kohtaroh Miura, Kei-ichi Nagai, Hiroshi Ohki, Enrico Rinaldi,
Akihiro Shibata, Koichi Yamawaki, Takeshi Yamazaki (LatKMI Collaboration), Topological observables in many-flavour QCD, arXiv:1601.04687.
30. K.-I. Ishikawa, Y. Iwasaki, Yu Nakayama, T.Yoshie, IR fixed points in SU (3)gauge Theories, Phys. Lett. B748 (2015) 289-294.
31. J. Noaki, G. Cossu, K-I. Ishikawa, Y. Iwasaki, T. Yoshie, Study of the conformal region of the SU(3) gauge theory with domain-wall fermions, arXiv:1511.06474[hep-lat], in Proceedings of (Lattice 2015) in press.

－25－32. K. -I. Ishikawa, Y. Iwasaki, Yu Nakayama, T. Yoshie, Conformal Properties
in High Temperature QCD, arXiv:1511.03411 [hep-lat].
33. T. Amagasa, S. Aoki, Y. Aoki, T. Aoyama, T. Doi, K. Fukumura, N. Ishii, K.I. Ishikawa, H. Jitsumoto, H. Kamano, Y. Konno, H. Matsufuru, Y. Mikami,
K. Miura, M. Sato, S. Takeda, O. Tatebe, H. Togawa, A. Ukawa, N. Ukita, Y.
Watanabe, T. Yamazaki, T. Yoshie, Sharing lattice QCD data over a widelydistributed file system J. Phys.: Conf. Ser. 664 (2015) 4, 042058 (CHEP2015).
34. M. Yamada, K. Sasaki, S. Aoki, T. Doi, T. Hatsuda, Y. Ikeda, T. Inoue, N.
Ishii, K. Murano and H. Nemura, for HAL QCD Collaboration, ΩΩ interaction
from 2+1 flavor lattice QCD, PTEP 2015, no. 7, 071B01 (2015).
35. K. Sasaki, S. Aoki, T. Doi, T. Hatsuda, Y. Ikeda, T. Inoue, N. Ishii and K. Murano, for HAL QCD Collaboration, Coupled-channel approach to strangenessS =-2 baryon-bayron interactions in lattice QCD, PTEP 2015, no. 11, 113B01(2015).
36. S. Aoki, Hadron Interactions from lattice QCD EPJ Web Conf. 113 (2016)
01009, arXiv:1603.00989[hep-lat].
37. H. Matsufuru, S. Aoki, T. Aoyama, K. Kanaya, S. Motoki, Y. Namekawa, H.
Nemura, Y. Taniguchi, S. Ueda, N. Ukita, OpenCL vs OpenACC: Lessons from
Development of Lattice QCD Simulation Code, Procedia Computer Science
Volume 51 (2015) 1313.
38. S. Motoki, S. Aoki, T. Aoyama, K. Kanaya, H. Matsufuru, Y. Namekawa, H.
Nemura, Y. Taniguchi, S. Ueda, N. Ukita, Lattice QCD code Bridge++ onarithmetic accelerators, Proceeding of Science (Lattice 2015) 040.
39. N. Ishibashi and T. Tada, Infinite circumference limit of conformal field theory,
Journal of Physics A48 (2015) no.31, 315402.
40. N. Ishibashi and T. Tada, Dipolar quantization and the infinite circumference
limit of two-dimensional conformal field theories, arXiv:1602.01190 [hep-th],UTHEP-681.
41. Zoltán Bajnok, János Balog, Katsushi Ito, Yuji Satoh and Gábor Zsolt Tóth,
Exact mass-coupling relation for the homogeneous sine-Gordon model, Phys.
Rev. Lett. 116 (2016) 181601, arXiv:1512.04673 [hep-th].
42. G. Ishiki, Matrix Geometry and Coherent States, Phys. Rev. D 92, no. 4,(2015) ref. 046009.
43. G. Ishiki, T. Matsumoto and H. Muraki, Kähler structure in the commutative
limit of matrix geometry, arXiv:1603.09146 [hep-th], UTHEP-685.

－26－

44. N. Ishibashi and K. Murakami, Worldsheet theory of light-cone gauge noncritical strings on higher genus Riemann surfaces, arXiv:1603.083337 [hep-th],UTHEP-683.
45. Yuji Satoh and Yuji Sugawara, Non-geometric backgrounds based on topological interfaces, JHEP 1507 (2015) 022.
46. Yuji Satoh, Yuji Sugawara and Taiki Wada, Non-supersymmetric asymmetricorbifolds with vanishing cosmological constant, JHEP 1602 (2016) 184.
47. M. Hanada, Y. Hyakutake, G. Ishiki and J. Nishimura, Numerical tests of thegauge/gravity duality conjecture for D0-branes at finite temperature and finite
N, arXiv:1603.00538 [hep-th], UTHEP-682.
48. T. Asakawa, H. Muraki, S Watamura Gravity theory on Poisson manifold with
R-flux, Fortschritte der Physik 63 (2015) 683-704.
49. Tetsuji Kimura, Gauge-fixing Condition on Prepotential of Chiral Multiplet for
Nongeometric Backgrounds, Prog. Theor. Exp. Phys. (2016) no.2, 023B04.

ʪஶॻɾ૯આ౳ʫ

1. Ֆా ਖ਼ൣ, ඦ෢ ‫ܚ‬จ, ҏෑ ‫ޗ‬࿠, ੢ଜ ३, ʮྔࢠϒϥοΫϗʔϧͷϗϩάϥϜ
త‫ه‬ड़ͷ਺஋త‫ূݕ‬ʯ, SienceʮαΠΤϯεࢽʹࡌͬͨ೔ຊਓ‫ऀڀݚ‬ʯ(2015),
p46.
2. ҏෑ ‫ޗ‬࿠, ੢ଜ ३, Ֆా ਖ਼ൣ, ඦ෢ ‫ܚ‬จ, ʮϒϥοΫϗʔϧʹର͢Δϗϩάϥ
ϑΟοΫ‫ݪ‬ཧͷ਺஋త‫ূݕ‬ʯ, ೔ຊ෺ཧֶձࢽ 70 ‫ר‬, 6 ߸ (2015), p436 .

ʪֶҐ࿦จʫ

[म࢜࿦จ]
1. լ਺ ३ฏ
ʮNf = 2 + 1 ֨ࢠ QCD ʹΑΔඍখͳӡಈྔҠߦͰͷ π தؒࢠ‫ܗ‬ঢ়Ҽࢠ‫ࢉܭ‬΁޲͚ͨ‫ڀݚૅج‬ʯ
2. ࡾ࡚ തಓʮߴ֊ඍ෼߲Λ‫ؚ‬Ήॏྗཧ࿦ʹ͓͚ΔҼՌ཯ͷഁΕʯ
3. ਂࢁ ཅฏʮϝϯϒϨϯͷ‫ز‬Կͱߦྻ໛‫ܕ‬ʯʪඇৗ‫ࢣߨۈ‬ɾूதߨٛʫ

－27－

1. ҏෑ‫ޗ‬࿠, ʮ௒‫ݭ‬ཧ࿦ͱߦྻਖ਼ଇԽʯ, Advanced Summer School on Lattice
Gauge Theories, ஜ೾େֶ‫ػࢉܭ‬ηϯλʔ, 2015 ೥ 8 ݄ 26 ೔-28 ೔.
2. ໦ଜ఩࢜ʮඍ෼ੵ෼ IIʯɺ౦‫޻ژ‬ՊେֶίϯϐϡʔλαΠΤϯεֶ෦ɺ2015 ೥
4 ݄–9 ݄.
3. ໦ଜ఩࢜ʮૉཻࢠ΍ۭ࣌ͱ͸?ʯ(Ն‫ظ‬ಛผߨ࠲)ɺઍ୅ాཱ۠‫۝‬ஈத౳‫ڭ‬ҭֶߍɺ2015 ೥ 8 ݄ 20 ೔.

ʪ‫ڀݚ‬੒Ռൃදʢߨԋʣʫ[ࠃࡍձٞ]
1. T. Umeda, S. Ejiri, R. Iwami, K. Kanaya ʮTowards the QCD equation ofstate at the physical point using Wilson fermionʯ,
The XXXIII International Symposium on Lattice Field Theory (Lattice 2015)(Kobe Convention Center, Kobe, Japan, 7.14-18, 2015).
2. E. Itou, H. Suzuki, Y. Taniguchi, T. Umeda ʮ(2+1)-flavor QCD Thermodynamics from the Gradient Flowʯ,
The XXXIII International Symposium on Lattice Field Theory (Lattice 2015)(Kobe Convention Center, Kobe, Japan, 7.14-18, 2015).
3. Y. Taniguchi ʮQCD energy momentum tensor at finite temperature using
gradient flowʯ,
RBRC Workshop on Lattice Gauge Theories 2016 (BNL, NY, USA, 3.9-11,
2016).
4. Yoshinobu Kuramashi, ʮTensor Network Scheme for Lattice Gauge Theoriesʯʢট଴ߨԋʣɼXXVII IUPAP Conference on Computational Physics (CCP2015), (Indian Institute of Technology Guwahati,, Assam, India, December 2-5, 2015).
5. Hiroshi Ohno, ʮCharmonia and bottomonia at finite temperature on large
quenched latticeʯ, The 33rd International Symposium on Lattice Field Theory(Lattice 2015) (Kobe International Conference Center, Kobe, Japan, Jul. 1418, 2015).
6. Hiroshi Ohno,ʮCharmonium and bottomonium spectral functions from lattice
QCD at finite temperatureʯ, The XXV International Conference on Ultrarelativistic Nucleus-Nucleus Collisions (Quark Matter 2015) (Kobe Fashion Mart,
Kobe, Japan, Sept. 27-Oct. 3, 2015).
7. Hiroshi Ohno, ʮCharmonia and bottomonia in hot medium and heavy quark
diﬀusion from lattice QCD at finite temperatureʯ(ট଴ߨԋ), New Progress－28－

in Heavy Ion Collision: What is Hot in the QGP (CCNU, Wuhan, China, Oct.
5-9, 2015).
8. Hiroshi Ohno, ʮCharmonium and bottomonium spectral functions at finite
temperatureʯ(ট଴ߨԋ), RBRC Workshop on Lattice Gauge Theories 2016
(BNL, New York, USA, Mar. 9-11, 2016).
9. ླ໦༡ʮCalculation of high-order cumulants with canonical ensemble method
in lattice QCDʯ, The 33rd International Symposium on Lattice Field Theory(Lattice 2015), ( Kobe International Conference Center, Kobe, Japan, July
14-18, 2015).
10. ླ໦༡ʮStudy of finite density phase transition with Canonical approachʯ,The 13th international eXtreme QCD conference (XQCD 2015), (CCNU, Wuhan,
China, Sep. 21-23, 2015).
11. ླ໦༡ʮCalculation of high-order cumulants with canonical ensemble method
in lattice QCDʯ, The XXV international conference on ultra-relativistic heavyion collisions (Quark Matter 2015), (Kobe Fashion Mart, Kobe, Japan, Sep.
27- Oct. 3, 2015).
12. ླ໦༡ʮCalculation of Hadronic observable with Canonical approach in finite
density lattice QCDʯ, RBRC Workshop on Lattice Gauge Theories 2016,(BNL, NewYork, USA, March 9-11, 2016).
13. ୩‫ޱ‬༟հʮStudy of high density phase transition in lattice QCD with canonical approachʯ, The 33rd International Symposium on Lattice Field Theory(Lattice2015), (Kobe Convention Center, Kobe, Japan, 14 July 2015 - 18 July2015).
14. ୩‫ޱ‬༟հʮStudy of high density phase transition in lattice QCD with canonicalapproachʯ, XXV INTERNATIONAL CONFERENCE ON ULTRA-RELATIVISTIC
NUCLEUS-NUCLEUS COLLISIONS (Quark Matter 2015), (Kobe, Fashion
Mart, Japan, September 27 - October 3, 2015).
15. ୩‫ޱ‬༟հʮStudy of high density lattice QCD with canonical approachʯ, Symposium on ‘Quarks to Universe in Computational Science (QUCS 2015)ʟ
, (NaraKasugano International Forum IRAKA, Nara, Japan, November 4-8, 2015).
16. Takeshi Yamazaki ʮLight nuclei from 2+1 flavor lattice QCDʯ(ট଴ߨԋ),
Lattice Nuclei Nuclear physics and QCD – Bridging the gap – (European
Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT*),
Italy, June 6-10, 2015).
17. Takeshi Yamazaki ʮLight nuclei and nucleon form factors in Nf=2+1 lattice
QCDʯ, The 33rd International Symposium on lattice field theory (Lattice2015) (Kobe International Conference Center, Japan, June 14-18, 2015).

－29－

18. Takeshi Yamazaki ʮLight nuclei and nucleon form factors in Nf=2+1 lattice
QCDʯ(ট଴ߨԋ), The 5th International Workshop on Lattice Hadron Physics(LHPV) (Conference Centre of the Cairns Colonial Club Resort, Australia,
June 20-24, 2015).
19. Takeshi Yamazaki ʮLight nuclei and nucleon form factors in Nf=2+1 lattice QCDʯ(ট଴ߨԋ), Long-term and Nishinomiya-Yukawa Memorial International Workshop on ”Computational Advances in Nuclear and Hadron
Physics” (CANHP2015) (Yukawa Institute of Theoretical Physics (YITP), Kyoto University, Japan, September 21-October 30, 2015).
20. Takeshi Yamazaki ʮLight nuclei and nucleon form factors from lattice QCDʯ,Symposium on Quarks to Universe in Computational Science (QUCS 2015)(Nara Kasugano International Forum IRAKA, Japan, November 4-8, 2015).
21. Takeshi Yamazaki ʮNucleon form factors and light nuclei in Nf=2+1 lattice QCDʯ(ট଴ߨԋ), RBRC Workshop on Lattice Gauge Theories 2016
(Brookhaven National Laboratory, USA, March 9-11, 2016).
22. ٢ߐ ༑র ʮSharing lattice QCD data over a widely distributed file systemʯ
21st International Conference on Computing in High Energy and Nuclear
Physics (CHEP2015) (Okinawa, Japan, April 13 - 17, 2015).
23. ٢ߐ ༑রʮMetadata Working Group Reportʯ23th Workshop of International
Lattice Data Grid (video conference hosted by CSSM, Adelaide, Australia,
April 24, 2015).
24. S. Aoki, ʮHadron Interactions from lattice QCDʯʢট଴ߨԋʣɼ21th International Conference on Few-Body Problems in Physics, (Chicago, USA, May
18-22, 2015).
25. S. Aoki, ʮNuclear forces from lattice QCDʯʢট଴ߨԋʣɼECT* Workshopon ”Lattice Nuclei Nuclear Physics and QCD - Bridging the gap”, (Trento,
Italy, July 6-10, 2015).
26. S. Aoki, ʮComparative studies for baryon interactions with HAL QCD methodand Luscher’s methodʯʢট଴ߨԋʣɼLong-term and Nishinomiya-Yukawa
Memorial International Workshop on ”Computational Advances in Nuclear
and Hadron Physics”, (YITP, Kyoto, Japan, September 21-October 30, 2015).
27. S. Aoki, ʮRecent developments and challenges in lattice QCDʯʢট଴ߨԋʣɼ
International Symposium ”RIKKYO MathPhys 2016”, (Rikkyo University,
Tokyo, Japan, January 9-11, 2016).
28. S. Aoki,ʮNew strategies with HAL QCD potential methodʯʢট଴ߨԋʣɼJointHAL QCD-CalLat mini-workshop on lattice QCD for NP, (LBL, Berkeley,
USA, January 27-29, 2016).

－30－

29. S. Aoki, ʮHadron interactions at heavier quark masses in lattice QCD –Are
deuteron and di-neutron bound ? – ʯʢট଴ߨԋʣɼYITP and IOPP Joint
workshop on Heavy Ion Physics, (CCNU, Wuhan, China, February 20, 2016).
30. H. Nemura, (for HAL QCD Collaboration), ʮAn implementation of hybrid
parallel CUDA code for the hyperonic nuclear forcesʯɼThe 33rd International
Symposium on Lattice Field Theory, (Kobe, Japan, July 14-18, 2015).
31. H. Nemura, (for HAL QCD Collaboration), ʮA fast algorithm for lattice
hyperonic potentialsʯɼThe 12th International Conference on Hypernuclear
and Strange Particle Physics, (Tohoku University, Sendai, Japan, September
7 - 12, 2015).
32. H. Nemura, (for HAL QCD Collaboration), ʮHyperonic lattice QCD potentials and hypernuclear few-body problemsʯɼYIPQS Long-term and NishinomiyaYukawa Memorial International Workshop, Computational Advances in Nuclear and Hadron Physics (CANHP 2015), (YITP, Kyoto, Japan, September
21 - October 30, 2015).
33. H. Nemura, (for HAL QCD Collaboration), ʮAlgorithm, benchmarks, andhyperon potentials with strangeness S = −1 at almost physical pointʯɼSymposium on ‘Quarks to Universe in Computational Science (QUCS 2015)’, (NaraPrefectural New Public Hall, Nara, Japan, November 4 - 8, 2015).
34. K. Sasaki for HAL QCD Coll., ʮFirst results on baryon interactions fromlattice QCD with physical masses (3) –Strangeness S=-2 two-baryon system–ʯɼ
The 33rd International Symposium on Lattice Field Theory(LATTICE2015)(Kobe, Japan, Jul. 14-18, 2015).
35. K. Sasaki for HAL QCD Coll., ʮResults from HALQCD on light nuclei andexotic statesʯɼEMMI workshop on anti-matter, hyper-matter and exotica
production at the LHC (CERN, Geneva, Switzerland, Jul. 20-22, 2015).
36. K. Sasaki for HAL QCD Coll., ʮCoupled channel baryon-baryon interactions on the latticeʯɼThe 12th International Conference on Hypernuclear
and Strange Particle Physics (HYP2015), (Tohoku University, Sendai, Japan,
Sept. 7-12, 2015).
37. K. Sasaki for HAL QCD Coll., ʮLattice QCD studies of baryon-bayon interactions and dibaryon statesʯɼELPH workshop C013 ”Meson Production and
Meson-Baryon Interaction”, (Tohoku University, Sendai, Japan, Sept. 12-14,
2015).
38. K. Sasaki for HAL QCD Coll., ʮPhysical point lattice QCD simulation on
the S = -2 baryon-baryon interactionsʯɼSymposium on Quarks to Universein Computational Science (QUCS 2015), (Nara, Japan, Nov. 4-8, 2015).

－31－

39. Y.Namekawa ʮComparative study of topological charge in lattice QCDʯ,Quarks to Universe in Computational Science (QUCS2015) (Nara, Japan, Nov
4-8, 2015).
40. Nobuyuki Ishibashi, ʮʠ Dimensional regularization of light-cone gauge superstring field theory and multiloop amplitudesʯ(ট଴ߨԋʣ
International Conference on String Field Theory and Related Aspects VII,
SFT2015 (ChengDu, China, May 11-15, 2015).
41. Yuji Satoh ʮAnalytic expansions of strong-coupling amplitudes in N=4 SYMʯ(ট଴ߨԋ),
Amplitudes in Asia 2015 ɹ (National Center for Theoretical Sciences, Taipei,
Taiwan, November 2 - 6 , 2015).
42. Goro Ishiki, ʮMatrix Geometry and Coherent Statesʯʢট଴ߨԋʣ,Workshop on Noncommutative Field Theory and Gravity (Corfu, Greece, Sep.
21-26, 2015).
43. Goro Ishiki, ʮSpherical M5-branes from the plane wave matrix modelʯ,
KEK theory workshop Dec. (KEK, Tsukuba, Japan, Dec. 1-4, 2015).
44. Goro Ishiki, ʮSpherical M5-branes from the plane wave matrix modelʯ,
YITP workshopʮDevelopments in String Theory and Quantum Field Theoryʯ
(YITP, Kyoto, Japan, Nov. 9-13, 2015).
45. Goro Ishiki, ʮMatrix Geometry and Coherent Statesʯ,YITP workshopʮNumerical approaches to the holographic principle, quantum
gravity and cosmologyʯ(YITP, Kyoto, Japan, July 21-24, 2015).
46. Goro Ishiki, ʮMatrix Geometry and Coherent Statesʯ,The 33nd International Symposium on Lattice Field Theory (Lattice 2015)(Kobe, Japan, July 14-18, 2015).
47. Takaki Matsumoto, ʮNew construction method of Matrix ɹ Regularization
using coherent statesʯ,
Geometry in Gauge Theories and String Theory (Korea Institute for Advanced
Study, Seoul, Korea, Sep. 15-18, 2015).
48. Takaki Matsumoto,ʮNew construction method of Matrix Regularization using
coherent statesʯ,YITP workshopʮDevelopments in String Theory and Quantum Field Theoryʯ
(YITP, Kyoto, Japan, Nov. 9-13, 2015).
49. Takaki Matsumoto, ʮKähler Structure in Matrix Geometryʯ,KEK workshop 2015 Dec. (KEK, Tsukuba, Japan, Dec. 1-4, 2015).

－32－

50. Hisayoshi Muraki, ʮGravity on Poisson manifoldʯ
Workshop on Higher structures in string theory and M-theory (Tohoku university, Sendai, Mar. 7-11, 2016).
51. Hisayoshi Muraki, ʮGravity theory on Poisson manifold with R-fluxʯ
KEK workshop 2015 Dec. (KEK, Tsukuba, Dec. 1-4, 2015).
52. Hisayoshi Muraki, ʮGravity theory on Poisson manifold with R-fluxʯ
YITP workshopʮDevelopments in String Theory and Quantum Field Theoryʯ
(Yukawa Institute of Theoretical Physics, Kyoto, Nov. 9-13, 2015).
53. Tetsuji Kimura,ʮExotic five-branesʯ, 2nd String Theory in Greater Tokyo(RIKEN, Saitama, Japan, June 9, 2015).
[ࠃ಺ֶձɺ‫ڀݚ‬ձ]
1. ҏ౻ӻࢠ, ླ໦ത, ୩‫ޱ‬༟հ, കా‫ ࢜و‬ʮάϥσΟΤϯτ ϑϩʔΛ༻͍ͨ
Nf=2+1 QCD ͷ೤ྗֶྔͷଌఆʯ,೔ຊ෺ཧֶձ (େࡕࢢେ, େࡕ, 9.25-28, 2015).
2. ୩‫ޱ‬༟հ, ੴ‫ݟ‬ྋ, കా‫࢜و‬, ߐ৲৴࢘, ۚ୩࿨ࢸ, ๺୔ਖ਼ਗ਼, ླ໦ത, एྛ௚ً
ʮGradient flow Ͱ‫ݟ‬Δ༗‫ݶ‬Թ౓ QCDʯ,೔ຊ෺ཧֶձ ୈ 71 ճ೥࣍େձ (౦๺ֶӃେ, ઋ୆, 3.19-22, 2016).
3. നۜਸ਼थ, ߐ৲৴࢘, ۚ୩࿨ࢸ, ๺୔ਖ਼ਗ਼, ੴ‫ݟ‬ྋ ʮQuenched QCD ͷҰ࣍૬సҠ఺ʹ͓͚Δજ೤ͱѹྗΪϟοϓʯ,೔ຊ෺ཧֶձ ୈ 71 ճ೥࣍େձ (౦๺ֶӃେ, ઋ୆, 3.19-22, 2016).
4. ੴ‫ݟ‬ྋ, ߐ৲৴࢘, ۚ୩࿨ࢸ, େ໺ߒ࢙, കా‫࢜و‬, ٢ా৴հ ʮO(4) εέʔϦϯάΛ༻͍ͨ༗‫ݶ‬Թ౓ɾີ౓ QCD ͷ૬సҠઢʯ,೔ຊ෺ཧֶձ ୈ 71 ճ೥࣍େձ (౦๺ֶӃେ, ઋ୆, 3.19-22, 2016).
5. େ໺ߒ࢙ʮQuarkonia at finite temperatureʯ(ট଴ߨԋ), ‫ڀݚ‬ձʮ༗‫ݶ‬Թ౓ີ౓‫ܥ‬ͷ෺ཧͱ֨ࢠ QCD γϛϡϨʔγϣϯʯ(ஜ೾େֶ‫ࢉܭ‬Պֶ‫ڀݚ‬ηϯλʔ,ɹͭ͘͹, 2015 ೥ 9 ݄ 5 ೔) .
6. େ໺ߒ࢙ʮ༗‫ݶ‬Թ౓֨ࢠ QCD ʹΑΔνϟʔϞχ΢Ϝ‫ͼٴ‬ϘτϞχ΢ϜεϖΫ
τϧؔ਺ͷ‫ڀݚ‬ʯ, ೔ຊ෺ཧֶձ 2015 ೥ळ‫ق‬େձ (େࡕࢢཱେֶਿຊΩϟϯύε, େࡕ, 2015 ೥ 9 ݄ 25 ೔-28 ೔).
7. ୩‫ޱ‬༟հʮQCD phase transition at real chemical potential with canonicalapproach ʯ, JICFUS ηϛφʔ, (‫౎ژ‬େֶ).
8. ୩‫ޱ‬༟հʮΧϊχΧϧ๏Ͱൃ‫ ࢠ֨ͨ͠ݟ‬QCD ͷ༗‫౓ີݶ‬૬సҠ‫ݱ‬৅ͷ‫ڀݚ‬ʯ,೔ຊ෺ཧֶձ 2015 ೥ळ‫ق‬େձ, (2015 ೥ 9 ݄ 25 ೔?2015 ೥ 9 ݄ 28 ೔ େࡕࢢཱେֶʢਿຊΩϟϯύεʣ).

－33－

9. ླ໦ ༡ʮΧϊχΧϧ๏Λ༻͍ͨ༗‫ ࢠ֨౓ີݶ‬QCD ʹ͓͚Δ૬సҠ‫ݱ‬৅ͷ‫ݚ‬‫ڀ‬ʯ, ೔ຊ෺ཧֶձळ‫ق‬େձ, (େࡕࢢཱେֶ, 2015 ೥ 9 ݄ 25 ೔-28 ೔).
10. ླ໦ ༡ʮΧϊχΧϧ๏Λ༻͍ͨ༗‫ ࢠ֨౓ີݶ‬QCD ʹ͓͚Δ૬సҠ‫ݱ‬৅ͷ‫ݚ‬‫ڀ‬ʯ, ‫ऀࡾ֩ࢠݪ‬एखՆͷֶߍ, (ϗςϧ͖ͨͭ, Ѫ஌, 2015 ೥ 8 ݄ 17 ೔-22 ೔).
11. ླ໦ ༡ʮΧϊχΧϧ๏Λ༻͍ͨ༗‫ ࢠ֨౓ີݶ‬QCD ʹ͓͚Δ෺ཧྔͷ‫ͦͱࢉܭ‬ͷମੵґଘੑͷ‫ڀݚ‬ʯ, ୈ 71 ճ೥࣍େձ, (౦๺ֶӃେֶ, 2016 ೥ 3 ݄ 19 ೔-22
೔).
12. ࢁ࡚ ߶, ੴ઒ ݈Ұ, ᤽૿ Յ৳, ࠤʑ໦ উҰ, Ӊ઒ জ for PACS Collaboration,ʮվྑ͞Εͨ΢ΟϧιϯϑΣϧϛΦϯ࡞༻Λ༻͍ͨ 2+1 ϑϨʔόʔ QCD ʹΑΔ֩ࢠ‫ܗ‬ঢ়Ҽࢠͷ‫ڀݚ‬ʯ೔ຊ෺ཧֶձ 2015 ೥ळ‫ق‬େձ (େࡕࢢཱେֶ, େࡕ,2015 ೥ 9 ݄ 25–28 ೔).
13. ࢁ࡚ ߶, ᤽૿ Յ৳, ੴ઒ ݈Ұ, ුా ঘ࠸, ʮ֨ࢠ QCD Λ༻͍ͨ‫ߏ֩ࢠݪ‬଄‫ܭ‬ࢉ΁޲͚ͨ‫ڀݚૅج‬ʯ, HPCI ୈ 2 ճ੒Ռใࠂձ (೔ຊՊֶະདྷ‫ؗ‬, ౦‫ژ‬, 2015೥ 10 ݄ 26 ೔).
14. ࢁ࡚ ߶, ੴ઒ ݈Ұ, ᤽૿ Յ৳, Ӊ઒ জ for PACS Collaboration ʮNf = 2 + 1
֨ࢠ QCD ʹΑΔܰ‫֩ࢠݪ‬ଋറΤωϧΪʔͷ‫ࢉܭ‬ʯ, ೔ຊ෺ཧֶձୈ 71 ճ೥࣍େձ (౦๺ֶӃେֶ, ‫ٶ‬৓, 2016 ೥ 3 ݄ 19–22 ೔).
15. լ਺ ३ฏ ʮNf = 2 + 1 ֨ࢠ QCD ʹΑΔඍখͳӡಈྔҠߦͰͷ π தؒࢠ‫ܗ‬ঢ়Ҽࢠͷ‫ڀݚ‬ʯ೔ຊ෺ཧֶձୈ 71 ճ೥࣍େձʢ౦๺ֶӃେֶɺઋ୆ɺ̎̌̍̒
೥݄̏̍̕೔ʔ̎̎೔ʣ.
16. ٢ߐ ༑র ʮ‫ࢉܭ‬෺ཧֶʹ͓͚ΔσʔλγΣΞϦϯάͷ‫ݱ‬ঢ়ͱ՝୊ʯ(ট଴ߨԋ)σʔλγΣΞϦϯάΛར༻ͨ͠Պֶٕज़ʹؔ͢Δษ‫ڧ‬ձ (จՊল, ౦‫ژ‬ɺ2015೥ 5 ݄ 13 ೔).
17. ٢ߐ ༑র ʮ֨ࢠγϛϡϨʔγϣϯʹΑΔίϯϑΥʔϚϧཧ࿦ͷ‫ڀݚ‬ʯஜ೾େֶ‫ࢉܭ‬Պֶ‫ڀݚ‬ηϯλʔֶࡍ‫ڞ‬ಉར༻੒Ռใࠂձ (ஜ೾େֶɺͭ͘͹ɺ2015 ೥
10 ݄ 20 ೔)
18. ٢ߐ ༑র ʮ‫ࢉܭ‬ૉཻࢠ෺ཧσʔλ؅ཧɾ‫ڞ‬༗‫ج‬൫ JLDGʯHPCI γεςϜར༻‫ڀݚ‬՝୊੒Ռใࠂձ (Պֶະདྷ‫ؗ‬, ౦‫ژ‬ɺ2015 ೥ 10 ݄ 26 ೔).
19. ٢ߐ ༑র ʮHEPnet-J/sc ใࠂʯ2015 ೥౓ HEPnet-J Ϣʔβʔձɺ(޿ౡେֶ,޿ౡɺ2015 ೥ 11 ݄ 24-25 ೔) .
20. ࠜଜӳࠀ, (HAL QCD Collaboration) ɹʮϋΠύʔ֩ͷগ਺ଟମ‫޲ʹࢉܭܥ‬͚ͨ֨ࢠ QCD ʹΑΔϋΠϖϩϯϙςϯγϟϧͷ‫ڀݚ‬ʯ, ೔ຊ෺ཧֶձ ̎̌̍̑೥ळ‫ق‬େձ, (େࡕࢢཱେֶʢਿຊΩϟϯύεʣɺ̎̌̍̑೥݄̎̑̕ʔ̎̔
೔).

－34－

21. ࠜଜӳࠀ, (HAL QCD Collaboration) ɹʮ֨ࢠ QCD ʹΑΔϋΠϖϩϯϙςϯ
γϟϧͱ͍ܰ‫΁֩ࢠݪ‬ͷԠ༻ʯ, ৽ֶज़ྖҬʮ࣮‫؍ͱݧ‬ଌͰղ͖໌͔͢தੑࢠ
੕ͷ֩෺࣭ʯͷୈ̐ճ‫ڀݚ‬ձ, (ভೆࠃࡍଜηϯλʔɺ̎̌̍̑೥݄̍̓̕ʔ̍
̔೔).
22. ࠜଜӳࠀ, (for HAL QCD Collaboration), ɹʮϋΠύʔ֩ͷগ਺ଟମ‫ʹࢉܭܥ‬޲͚ͨ HAL QCD ๏ʹΑΔϋΠϖϩϯϙςϯγϟϧͷ‫ڀݚ‬ʯ, ೔ຊ෺ཧֶձ ୈ̓̍ճ೥࣍େձ, (౦๺ֶӃେֶઘΩϟϯύεɺ̎̌̍̒೥݄̏̍̕ʔ̎̎೔).
23. K. Sasaki for HAL QCD Coll., ʮCoupled channel approach to two-baryon
interactions from QCDʯɼετϨϯδωεɾϋυϩϯ߹ಉ‫ڀݚ‬ձɼ(KEK ౦ւΩϟϯύε, ̎̌̍̑೥݄̔̏ʔ̓೔).
24. ࠤʑ໦݈ࢤ for HAL QCD Coll. ʮ෺ཧ఺֨ࢠ QCD ʹΑΔόϦΦϯؒ૬‫࡞ޓ‬
༻ –S=-2 ηΫλ–ʯɼ೔ຊ෺ཧֶձɹ̎̌̍̑೥ळ‫ق‬େձ ʢେࡕࢢཱେ , ̎̌̍̑೥݄̎̑̕ʔ̎̔೔).
25. ࠤʑ໦݈ࢤ for HAL QCD Coll., ʮ෺ཧ఺֨ࢠ QCD ʹΑΔόϦΦϯؒ૬‫࡞ޓ‬༻ [2] – S=-2 ηΫλʔ –ʯɼ೔ຊ෺ཧֶձɹୈ̓̍ճ೥࣍େձ (౦๺ֶӃେֶɹઘΩϟϯύε , ̎̌̍̒೥݄̏̍̕ʔ̎̎೔).
26. K.Sasaki for HAL QCD Coll., ʮDibaryon searches from lattice QCDʯɼૉཻࢠɾ‫֩ࢠݪ‬ɾӉ஦ʮ‫͔ژ‬Βϙετ‫͚ͯ޲ʹژ‬ʯγϯϙδ΢Ϝ (ϫϯςϥείϞ
ϯϗʔϧɺ౦‫౎ژ‬ઍ୅ా۠ਆా , ̎̌̍̒೥݄̏̏̌ʔ̏̍೔).
27. ੴ‫ڮ‬ɹԆ޾ɺʮDimensional regularization of light-cone gauge superstring field
theory and multiloop amplitudesʯ,೔ຊ෺ཧֶձ 2015 ೥ळ‫ق‬େձ (େࡕࢢཱେֶ, େࡕ, 2015 ೥ 9 ݄ 25 ೔-28 ೔).
28. Yuji Satoh ʮWorld-sheet conformal interfaces and their applicationsʯ(ট଴ߨԋ),‫ݭ‬ͷ৔ͷཧ࿦ 16 (ஜ೾େֶ౦‫ژ‬Ωϟϯύε, ౦‫ژ‬, 2016 ೥ 2 ݄ 22 - 23 ೔).
29. ҏ౻ࠀ࢘, ࠤ౻༐ೋ, Chris Locke, ଋߚඇ, ʮT-Q relation for modified aﬃne
B2 Toda field equationʯ,೔ຊ෺ཧֶձୈ 71 ճ೥࣍େձ (౦๺ֶӃେֶ, ઋ୆ 2016 ೥ 3 ݄ 19 - 22 ೔).
30. Zoltan Bajnok, Janos Balog, ҏ౻ࠀ࢘, ࠤ౻༐ೋ, Gabor Zsolt Toth, ʮExactmass-coupling relation of simplest multi-scale quantum integrable modelʯ,೔ຊ෺ཧֶձୈ 71 ճ೥࣍େձ (౦๺ֶӃେֶ, ઋ୆ 2016 ೥ 3 ݄ 19 - 22 ೔).
31. ࠤ౻༐ೋ, ੁ‫ݪ‬༞ೋ, ࿨ాେथ, ʮNon-susy asymmetric orbifolds with vanishingcosmological constantʯ,೔ຊ෺ཧֶձୈ 71 ճ೥࣍େձ (౦๺ֶӃେֶ, ઋ୆ 2016 ೥ 3 ݄ 19 - 22 ೔).

－35－

32. ҏෑ ‫ޗ‬࿠, ʮNumerical simulation for superstring theoryʯʢট଴ߨԋʣ,ʙεύίϯʮ‫ژ‬ʯ͕ͻΒ͘Պֶͱࣾձʙୈ 2 ճʮ‫ژ‬ʯΛத֩ͱ͢Δ HPCI γεςϜར༻‫ڀݚ‬՝୊ ੒Ռใࠂձ, (೔ຊՊֶະདྷ‫ؗ‬, ౦‫ژ‬, 2015 ೥ 10 ݄ 26 ೔).
33. ҏෑ ‫ޗ‬࿠, দຊ ߴ‫ڵ‬, ਂࢁ ཅฏ, ౡా ӳ඙, ʮίώʔϨϯτঢ়ଶʹΑΔߦྻਖ਼ଇԽͷ৽͍͠ߏ੒๏ʯ,೔ຊ෺ཧֶձ 2015 ೥ळ‫ق‬େձ (େࡕࢢཱେֶ, େࡕ, 2015 ೥ 9 ݄ 25 ೔-28 ೔).
34. ҏෑ ‫ޗ‬࿠, দຊ ߴ‫ڵ‬, ଜ໦ ‫ٱ‬঵, ʮKähler Structure in Matrix Geometryʯ,೔ຊ෺ཧֶձ ୈ 71 ճ೥࣍େձ (౦๺ֶӃେֶ, ઋ୆, 2016 ೥ 3 ݄ 19 ೔-22 ೔).
35. ҏෑ ‫ޗ‬࿠, দຊ ߴ‫ڵ‬, ଜ໦ ‫ٱ‬঵ɼʮΏΒ͍ͩඇՄ‫ٿ׵‬໘্ͷέʔϥʔߏ଄ʹ͍ͭͯʯɼ೔ຊ෺ཧֶձ ୈ 71 ճ೥࣍େձ (౦๺ֶӃେֶ, ઋ୆, 2016 ೥ 3 ݄ 19 ೔-22 ೔).
36. ઙ໺ ါຏ, ҏෑ ‫ޗ‬࿠, ౡ࡚ ৴ೋ, ࣉౢ ༃࣏ɼ
ʮSpherical fivebranes from theplane wave matrix modelʯɼ೔ຊ෺ཧֶձ ୈ 71 ճ೥࣍େձ (౦๺ֶӃେֶ, ઋ୆, 2016 ೥ 3 ݄ 19 ೔-22 ೔).
37. ҏෑ ‫ޗ‬࿠, ʮNumerical simulation for superstring theoryʯʢϙελʔൃදʣ,ʙεύίϯʮ‫ژ‬ʯ͕ͻΒ͘Պֶͱࣾձʙୈ 2 ճʮ‫ژ‬ʯΛத֩ͱ͢Δ HPCI γεςϜར༻‫ڀݚ‬՝୊ ੒Ռใࠂձ, (೔ຊՊֶະདྷ‫ؗ‬, ౦‫ژ‬, 2015 ೥ 10 ݄ 26 ೔).
38. ઙ઒ ࢚඙, ଜ໦ ‫ٱ‬঵, ໖ଜ ఩, ʮA study of construction of gravity theory
based on generalized geometryʯ,೔ຊ෺ཧֶձ̎̌̍̑೥ळ‫ق‬େձ೔ຊ෺ཧֶձ 2015 ೥ळ‫ق‬େձ (େࡕࢢཱେ
ֶ, େࡕ, 2015 ೥ 9 ݄ 25 ೔-28 ೔).
39. ଜ໦ ‫ٱ‬঵ʮA study of construction of gravity theory based on generalized
geometryʯʮ཭ࢄతख๏ʹΑΔ৔ͱۭ࣌ͷμΠφϛΫεʯ‫ڀݚ‬ձʢԬࢁӴੜձ‫ؗ‬ɺԬࢁɺ2015 ೥ 9 ݄ 14-18 ೔ʣ.

ʪड৆ʫ

1. ̝̥̘̞༏ल੒Ռ৆ड৆, ՝୊൪߸ hp140067 (୅ද: Ֆాਖ਼ൣ, ҏෑ‫ޗ‬࿠), 2015೥ 10 ݄ 26 ೔.

ʪࠃࡍձٞɾ‫ڀݚ‬ձͷ࣮ࢪʫ

1. ୈ 33 ճ֨ࢠ্ͷ৔ͷཧ࿦ࠃࡍձٞ૊৫ҕһձओ࠵ʢ૊৫ҕһ௕ɿ᤽૿Յ৳ʣ,The XXXIII International Symposium on Lattice Field Theory (Lattice 2015),
2015 ೥ 7 ݄ 14-18 ೔, ਆ‫ࡍࠃށ‬ձٞ৔, ਆ‫ށ‬.

－36－

2. ஜ೾େֶ‫ࢉܭ‬Պֶ‫ڀݚ‬ηϯλʔ/ཧ‫ ݚ‬BNL ‫ڀݚ‬ηϯλʔ‫࠵ڞ‬,
RBRC Workshop on Lattice Gauge Theories 2016,2016 ೥ 3 ݄ 9-11 ೔, BNL, NY.
3. ஜ೾େֶ‫ࢉܭ‬Պֶ‫ڀݚ‬ηϯλʔ/‫ૅجࢉܭ‬Պֶ࿈‫( ఺ڌܞ‬JICFuS) ओ࠵, ‫ڀݚ‬ձʮ༗‫ݶ‬Թ౓ີ౓‫ܥ‬ͷ෺ཧͱ֨ࢠ̦̘̙γϛϡϨʔγϣϯʯ2015 ೥ 9 ݄ 5 ೔,ஜ೾େֶ‫ࢉܭ‬Պֶ‫ڀݚ‬ηϯλʔ, ͭ͘͹.
4. ஜ೾େֶ‫ࢉܭ‬Պֶ‫ڀݚ‬ηϯλʔ/ཧ‫ ݚ‬BNL ‫ڀݚ‬ηϯλʔ ‫࠵ڞ‬, RBRC Workshop on Lattice Gauge Theories 2016 2016 ೥ 3 ݄ 9 ೔-11 ೔, Brookhaven National Laboratory, New York, USA.
5. ओ࠵: ஜ೾େֶ‫ࢉܭ‬Պֶ‫ڀݚ‬ηϯλʔ, ‫ૅجࢉܭ‬Պֶ࿈܎‫( ఺ڌ‬JICFuS) ༗‫ݶ‬Թ౓ີ౓̦̘̙ͷ਺஋త‫͚͓ʹڀݚ‬Δ࠷ۙͷൃల 2015 ೥ 9 ݄ 5 ೔, ஜ೾େֶ‫ܭ‬ࢉՊֶ‫ڀݚ‬ηϯλʔ, ͭ͘͹.
ੈ࿩ਓɿ੨໦อಓʢ໊‫ݹ‬԰େʣ, ුాঘ࠸ʢஜ೾େʣ, കా‫࢜و‬ʢ޿ౡେʣ, ߐ৲৴࢘ʢ৽ׁେʣ, େ໺ߒ࢙ʢஜ೾େʣ, ۚࣇོࢤʢ̠̠̚ʣ, ෢ాਅ࣎ʢۚ୔
େʣ, ‫׈‬઒༟հʢஜ೾େʣ, ࢁ࡚߶ʢஜ೾େʣ
6. Advanced Summer School on Lattice Gauge Theories 2015 ೥ 8 ݄ 26-28 ೔, ஜ೾େֶ‫ࢉܭ‬Պֶ‫ڀݚ‬ηϯλʔ, ͭ͘͹.
ੈ࿩ਓɿᜊ౻՚ʢ࿈བྷ੹೚ऀʣ, ੴ௩੒ਓ, େ໺ߒ࢙, ۚ୩࿨ࢸ, ᤽૿Յ৳, ୩‫ޱ‬༟հ, ࢁ࡚߶, ٢ߐ༑র7. YIPQS Long-term and Nishinomiya-Yukawa Memorial International Workshop, Computational Advances in Nuclear and Hadron Physics (CANHP 2015),̎̌̍̑೥݄̎̍̕೔ʔ݄̍̌̏̌೔ɺ‫౎ژ‬େֶ‫ૅج‬෺ཧֶ‫ॴڀݚ‬ɺ‫౎ژ‬.
8. ஜ೾େֶ‫ࢉܭ‬Պֶ‫ڀݚ‬ηϯλʔɺ‫ૅجࢉܭ‬Պֶ࿈‫ڀݚ࠵ڞ఺ڌܞ‬ձʮ༗‫ݶ‬Թ౓ີ౓‫ܥ‬ͷ෺ཧͱ֨ࢠ̦̘̙γϛϡϨʔγϣϯʯ2015 ೥ 9 ݄ 5 ೔, ஜ೾େֶ‫ࢉܭ‬Պֶ‫ڀݚ‬ηϯλʔ, ͭ͘͹.
9. ʮ‫ݭ‬ͷ৔ͷཧ࿦̍̒ʯɺ2016 ೥ 2 ݄ 22 ೔-23 ೔ɺஜ೾େֶ౦‫ژ‬Ωϟϯύεจ‫ژ‬ߍࣷɺ౦‫ژ‬.
ੈ࿩ਓɿ‫؛‬ຊޭʢ৽ׁେʣɺҏෑ‫ޗ‬࿠ɺࠤ౻༐ೋɺੴ‫ڮ‬Ԇ޾
10. ‫ڀݚݚج‬ձʮNumerical approaches to the holographic principle, quantum
gravity and cosmologyʯ, 2015 ೥ 7 ݄ 21 ೔-24 ೔, ‫౎ژ‬େֶ‫ૅج‬෺ཧֶ‫ڀݚ‬ॴ, ‫౎ژ‬.

ʪࠃ಺֎ͷ‫ڞ‬ಉ૊৫΁ͷࢀՃ͓Αͼ‫ݦ‬ஶͳֶձͷҕһ‫׆‬ಈʫ

1. ‫ૅجࢉܭ‬Պֶ࿈‫఺ڌܞ‬
http://www.jicfus.jp/jp/－37－

2. High Performance Computing Infrastructure (HPCI) ઓུϓϩάϥϜ
http://www.jicfus.jp/field5/jp/
3. ཧԽֶ‫ࢉܭॴڀݚ‬Պֶ‫( ߏػڀݚ‬AICS)
http://www.aics.riken.jp/
4. International Lattice Data Grid (ILDG)
http://ildg.sasr.edu.au/Plone
5. Japan Lattice Data Grid (JLDG)
http://www.jldg.org/jldg/, http://ws.jldg.org/QCDArchive/index.jsp
6. ੴ‫ڮ‬Ԇ޾, ೔ຊֶज़ৼ‫ڵ‬ձֶज़γεςϜ‫ڀݚ‬ηϯλʔઐ໳ҕһ
7. ੴ‫ڮ‬Ԇ޾, PTEP ฤूҕһ
8. ࠤ౻༐ೋ, Ԥभͷֶࡍ‫ڭڀݚ‬ҭωοτϫʔΫʮGauge Theory as an Integrable
System (GATIS)ʯ (http://gatis.desy.eu/) ͷάϩʔόϧωοτϫʔΫ΁ͷࢀՃ
9. ࠤ౻༐ೋ, Hungarian Academy of Sciences (HAS) ͱͷೋࠃؒަྲྀࣄ‫ۀ‬ʢ‫ڞ‬ಉ‫ڀݚ‬ʣʮήʔδཧ࿦/ॏྗཧ࿦૒ରੑʹ͓͚ΔՄੵ෼ੑͱ‫߹݁ڧ‬ήʔδཧ࿦μΠφϛΫεʯ୅ද

－38－