Direct Photons
andElectronsDirect Photons
Direct photons come from initial hot dense matter•Compton scattering of quarks and gluons: q(q)gÆgq(q)•Annihilation of quarks: qqÆgg
•Information on Thermo-dynamical state of medium•Initial temperature, Degree of freedom, etc.

Decayed photons from hadronic sources

Invariant Yield

Other sources of photons?

Pb+Pb ÷sNN=17.3GeV
WA98 Collaboration
at CERN

pT [GeV/c]Phys. Rev. Lett. 85, 3595 (2000)

Analysis (÷sNN=130GeV Au+Au)• Generate gammas from hadronsourcesCount– Take observed p0 pT spectra– h, h¢, r: mT scaling of power-law fit to
p0 is applied and estimatedCalculated gammapT[GeV/c]– Generate Flat rapidity of –0.5<y<0.5– Generate pT measured or estimated– Decay hadrons into gammas• Inclusive photon spectraCount– Efficiency and contamination
estimated by comparing real dataand simulation• Systematic Error: Showing 1s level– p0 fitting error of 25-35% + table
listedMeasured gamma

Energy[GeV]Comparison of Cluster Energy Distributions (I)Counts/100MeV• 60-80% Central Events• Comparison between
measured andcalculated energy
spectra• Systematic errorbans(Cyan)
Measured inclusive
photons are consistent
with contributions fromknown hadronicsources!

Comparison of measured and calculated

Ratio of measured and calculatedpT[GeV/c]

Ratio

÷sNN=130GeV Au+Au

pT[GeV/c]

Comparison of Cluster Energy Distributions (II)Measured inclusive photons
are yet not inconsistent with
contributions from known
hadronic sources withincurrent systematic errors

Counts/100MeV• 0-10% Central Events• Systematic error bands(Cyan)

Comparison of measured and calculated

Ratio of measured and calculatedpT[GeV/c]

Ratio

÷sNN=130GeV Au+Au

pT[GeV/c]

Photon Result -÷sNN=200GeV

Au+Au• Plotted are ratios ofphotons to p0• Denominator:– Photons calculated
from hadronicsources• Numerator:– Inclusive photons
measured

Measured inclusive photons
are yet not inconsistent withincurrent systematic errors..

Single electron and Charm
Two Au nuclei
collidetime

Formation of
Hot & Dense matter

Hadronization

Hadron gas

Freeze Out

Initial gluon density
gluon shadowing?
Thermal productionof charm
Energy loss of charm

Charm cross section
Charm suppression?
Charm enhancement?
Charm pt distribution

Charm is a very good probe of
initial stage of heavy ion
collisions.
Open charm measurement isimportant to understand J/Yproduction
Charm production at RHIC canbe studied from its decay tosingle electrons

Charm measurement
K+nl

Direct method:
Reconstruction of D-meson(e.g. D0‡Kp).
Very challenging without measurement of
displaced vertex

c
K-

D

0

p+

l

-

D

0

c
Indirect method:
Measure leptons from semileptonic decay of charm.
This method is used by
PHENIX at RHIC

Single electron in RUN-1(130GeV)•••

Inclusive electron spectra are measured at y=0
The background from p0 Dalitz, photon conversions, etc are
estimated and subtracted.
Observe excess over background in pt>0.8 GeV/c
PRL 88, 192303

Background-subtracted single
electron spectra••

Background subtracted
electron spectra are comparedwith the charm decay
contribution.
Charm decay contribution is
calculated as
EdNe/dp3 = TAAEds/dp3– TAA: nuclear overlap integral– Eds/dp3: electron spectrum
from charm decay calculatedusing PYTHIA•

From the single electron yieldin pt>0.8 GeV/c, charm crosssection per binary collision is
obtained as
scc = 380±60±200 mb

PRL 88, 192303

Comparison with other experiments
•

•

•
•

PRL 88, 192303

PHENIX single electron
cross section is comparedwith the ISR data
Charm cross section
derived from the electron
data is compared with
fixed target charm data
Solid curves:
PYTHIA
Shaded band:
NLO pQCDRUN2 single electron result••

The yield of non-photonic electron at 200 GeV is higher than 130 GeV
The increase is consistent with PYTHIA charm calculation(scc(130GeV)=330 mb ‡ scc(200GeV)=650 mb)
PRL 88, 192303
nucl-ex/0209016

Centrality Dependence

In all 4 centralities, the data are consistent with Ncoll scaled
charm decay contribution calculated by PYTHIA. nucl-ex/0209016

Observations• PHENIX single electron data are consistent with binary scaling within current statistical andEnhancement of Open Charm Yield

systematic errors.
• Both errors will be much reduced in final RUN-2 result• NA50 has inferred a factor of ~3 charm enhancement at lower energy. We do not see thislarge effect at RHIC.
• PHENIX observes a factor of ~3-5 suppression in high pT p0 relative to binary scaling. We
do not see this large effect in the single electrons.
• Initial state high pt suppression is excluded?
• smaller energy loss for heavy quark ? (dead cone effect)
NA50 - Eur. Phys. Jour. C14, 443 (2000).

Binary Scaling

PHENIX Preliminary

N partJ/y Suppression

time

J/Y measurement
Two Au nuclei
collideInitial ccbar production

Formation of
Hot & Dense matter

J/Y can not form due toDebye Screening in QGP

Hadronization

Hadron gas

Statistical formation of
J/Y from ccbar pairJ/Y suppression

J/Y enhancementat RHIC?!

J/Y suppression, predicted by Matsui and Satz andobserved by NA50 at SPS, is considered as one of thestrongest evidence of QGP formation.
If J/Y suppression is due to QGP formation, muchstronger suppression is expected at RHIC.

Freeze Out

New theory of J/Y formation predicts J/Y enhancementat RHIC energy by statistical formation of J/Y athadronizatoin

Do we observe J/Y suppression or enhancementat RHIC?

ベクトル中間子（Vector Meson）• スピン = 1、パリティ = -1：光子と同じ量子数• クォーク・反クォーク -- ポジトロニウムと似た系• 重いクォーク
→ 古典的qCharmoniumのパラメーターセット

VC =

4pr
Vlinear = kr
p 2 a eff
H=
+ kr
2m
r
q2 Ê 4 ˆa eff =
Á = as ˜
4p Ë 3 ¯

Confinedaeff = 0.52, k = 0.926 GeV/fm, mc = 1.84 GeV
aeff = 0.30, k = 1.18 GeV/fm, mc = 1.65 GeV

q2 =

4 2
g
3

重い vector mesons
J/y
Y’

Y

composition cccc

bb

Mass (GeV) 3.10
G (keV)
87

3.69
277

9.46
53

Gee (keV)

5.26

2.14

1.32

r (fm)

0.29

0.56

0.13

QGP中での Charmonium
閉じ込めポテンシャルが消滅
Debye screening → 湯川型の ポテンシャル

q - r / lDe
4prlD : Debye screening length

V (r ) =m = l-D1 : Debye screening massp 2 a eff - r / l
H=
e
2m
r

D

dE (r )r Ê
r ˆ -r / l
1
= 0Æ
=
ÁÁ1+
˜˜e
dr
lD Ë lD ¯
a eff ml D

p 2 = 1/ r 2
E (r ) =a eff - r / l
1
e
2mr 2
r

D

D

f (x ) = x (1+ x )e - x : f (x )|max = 0.840 at x = 1.62

1/(aeff m lD) > 0.84 では束縛状態が存在しない
rBohr = 1 / aeff m (lD = ∞：クーロンポテンシャルでのBohr半径)1.19 rBohr > lD

lD (PQCD ) =1
T1
Ê NC N f ˆ 2
ÁÁ
˜˜ g
+
6 ¯
Ë 3

=

2 1
3 gT

( N c = 3, N f = 3)

= 0.36 fm at T = 200 MeV : g 2 = 4pa eff , a eff = 0.52

lD (Lattice - QCD )~ 0.5lD (PQCD );rBohr =

1

a eff m~ 0.4 fm : m = 1840 / 2 MeV

2a effm
TX == 0.291 a eff (GeV)
0.840 9p

charm: aeff = 0.30 → Tx = 143 MeV
aeff = 0.52 → Tx = 209 MeV
bottom: Tx = (4.73/1.84) x 143 = 368 MeV••

J/yは100~200MeV程度で溶Жする
Y’ はJ/yよりも低い温度で溶Жする（半径が大）••Y の溶Ж温度はఫ常に‫ژ‬いr, w, f（‫ޑ‬量が小さい）はQGPでは存在し得ない

J/yの最初の測定
CERN-SPS NA38 (NA50)
muon 対の測定
200 AGeV O, S + A
J/y vs ET
ET ：横放出エネルギー＝中心衝突の度合い
強い J/y Y’ suppressionが大きな ET で観測された
J/y と連続スペクトルの収量比はエネルギー密度 e の増加とともに減少
e = E / V ~ (dET /dy)/ (pr02A2/3t0)

p + A、A + A衝突での‫ޑ‬量依存性
Fermi-Lab E772 実験
ターゲット‫ޑ‬量数 (A) 依存性： Aa•••

Drell-Yan (DY)
J/y, Y’U

a=1
a = 0.92
a = 0.96

p+A, A + A で同一のスケーリング• p + A 衝突で QGP が生成されている？
ありそうも無い• ハドロンとの衝突・反応が原因？

J/y suppression の“ハドロン”描像• ハドロンとの衝突によって、こわれる
J/y + h → D + D + X• 幾何学的な‫ב‬算
BsJ/yAB/AB = 4.1 exp[-r0 sabs (LA + LB)] mb
r0 = 0.14 fm-3
sabs = 5.2 mb
LA + LB : 良い scaling パラメーター- 実効的なパス੹（幾何平均）

J/y suppression は核子のみによる?
stotJ/y-N = 2.2 (0.7) mb(J.J. Aubert et al., Nucl. Phys. B213 (1983) 1)

squasi-elasticJ/y-N = 0.79 (0.12) mb(R.L. Anderson, SLAC-Pub 1741 (1976))

sabsJ/y-N = 1.4 mb

ABY’ 収量の変な振る舞い
Y’ と J/y の振る舞い• p + A ではよく似ている• S + A, Pb + Pb では、 J/yに比べてY’ 収量は大きく
suppress される

Y’ - J/y ratioPb + Pb 衝突での J/y Suppression
強い suppression• p+A、S+Aで見られた幾何学的な系統性から大きくずれる

J/y - Drell-Yan ratio

Co-mover モデルに基づく‫ב‬算：S+U
Pb+Pb
syco = 3.2 mb
if corss section scales with (radius)2
sy’co = 3.8 syco
scco = 2.4 syco

Solid line: syN = 4.8 mb,
syco = 3.2 mb,
nco =0.8/fm3
dashed line: syN = 4.8 mb
dot-dashed line: syN = 7.3 mb

同じパラメーターセットで同時にフィットすることは不可能

Solid line: syco = 3.2 mb,
sy’co = 25 mb,
nco =0.8/fm3
dashed line: sy’co = 3.8 syco
nco =0.5/fm3
a parameter set with feeding to J/yfrom c and y’ included二つのパズルをЖく• y’ の S+U での振る舞い• J/y の Pb + Pb での振る舞い
ひとつのЖ釈• y’ は比ѕ的低い温度で溶Жする– S+Uで既に溶Ж• J/y はPb + Pbで溶Ж：→

Pb+Pbで温度が上がる

RHICでは• より‫ژ‬い温度状態が期待される• SPSではできなかった U の測定が可能→

よりはっきりした結論pp‡J/Y at 200 GeV
pp ‡ e+e- X (|y|<0.35)

pp ‡ m+m- X (1.2<y<2.2)• pp‡J/Y is measured both in ee and in mm

nucl-ex/0210013

J/Y Bds/dy in p+p(200GeV)

B ⋅ s ( pp Æ J /y + X ) = 226 ± 36( stat ) ± 79( sys) nb

s ( pp Æ J / y + X ) = 3.8 ± 0.6( stat ) ± 1.3( sys) mb
nucl-ex/0210013

Comparison with lower energy
PHENIX preliminarys ( pp Æ J / y + X ) = 3.8 ± 0.6( stat ) ± 1.3( sys) mb

Color evapolation model prediction is consistent with
PHENIX data at s1/2=200 GeV CEM predictions (Phys.Lett.B390:323-328,1997)

J/y Æ e+e- in Gold-Gold
From 26 M min. bias
Au+Au collision @ 200 GeV(1/2 – 1/3 of all data)• NJ/y in 3 centrality bins.
n 0-20%:5.9 ± 2.4(stat) ± 0.7(sys)n 20-40%:
4.5 ± 2.1(stat) ± 0.5(sys)n 40-90%:3.5 ± 1.9 (stat)± 0.5(sys)•nucl-ex/0210013

J/y B-dN/dy per binary collisionnucl-ex/0210013

Model Comparisons (1)(1) J/y scale with the number of binary collisions(2) J/y follow normal nuclear absorption with sJ-N=7.1 mb(3) J/y follow same pattern as NA50 (J/y / DY(mb))1
Due to low statistics, our data are compatible all of these models.
nucl-ex/0209015

1

NA50 Phys. Lett. B521, 195 (2001)

Model comparion(2)J/Y re-generation models
Theory curve from R. L Thews, PRC63,054905

•
•

•

•

At RHIC, about 10 ccbar pairs
produced in central event.
They can recombine to form J/Y.
Those models that assume formation of
J/Y inside of QGP predict enhanced
production of J/Y in Au+Au.
PHENIX data does not favor a large
enhancement.
In QGP suppression model, very strong
J/Y suppression at RHIC is expected.
PHENIX data does not favor a verystrong suppression.
Models of statistical generation of J/Y
at hadronization stage predict that J/Yyield in central Au+Au is about half ofthat of pp.
A much larger statistics is required totest those models. (‡RUN4)

J/Y regeneration

PHENIX data
QGP suppression

L. Grandchamp and R. Rapp, hep-ph/0209141

カイラル対称性• カイラル対称性とは• 実験研究QCD真空の性‫ޑ‬
QCD真空は完全反誘ૣ性e (k ) ~ 1 k2
~ 2
mL

C
ln k 2 / L2()

(k 2 Æ •)(k 2 Æ 0)

D = eE
外場Eをかけても内ಊ場D=0
真空凝縮

fp2 mp2
qq 0 = = (-225 ± 25 MeV) 32mq

a s a mnGmn Ga= (350 ± 30 MeV) 4p0

rrQuark-antiquarkPotentialConfinedDeconfined真空凝縮
QCD真空は、あたかも物性（多体系）の特別な状態• 強磁性体：ハミルトニアン H = -gSsi・sｊ は回転対称性を持つが、基底状態では対称性が破れている。臨界温度TCで復活。
• ੶伝導体：Cooper pair の凝縮 <y↑y↓> ≠ 0で、Lagrangian L の対
称性が破れる。‫ژ‬温、‫ژ‬磁場で復活。
LBCSは、y Æ eiqy に対して不変

pair のオペレーターy ↑y Ø： y ↑y Ø Æ y ↑ e 2iqy Ø
L の持つ対称性を持たない operator = order parameterorder parameter の真空期待値：真空の対称性の判定基準• QCD真空：qq の pairing による凝縮、‫ژ‬温、‫ژ‬密度で回復。
カイラル対称性が破れている。
LQCDは、y Æ eig 5qy に対して不変
pair のオペレーターy y： y y Æ y e 2ig 5qy
order parameterカイラル対称性の Order Parameter

ハドロンの‫ޑ‬量

QCD真空の対称性の破れにより動的に形成‫ژ‬温、‫ژ‬密度→真空状態が変化→ハドロンの性‫ޑ‬に影՝

「カイラル対称性の回復」研究の方
法
ハドロンの媒‫ޑ‬効果– ‫ژ‬温、‫ژ‬バリオン密度状態の物‫ޑ‬中に置かれたハ
ドロンの性‫ޑ‬の変化をੴべる

注目：low-mass ベクターメソン r0 w f– ‫ޑ‬量がカイラル対称性のオーダーパラメータに比例 m µ qq
– レプトン対崩壊• 分岐比は小さい• メディアの影՝小「カイラル対称性回復」の実験的研
究原子核中での媒‫ޑ‬効果• KEKĚPS：f → e+e-、K+K• （旧）INSĚES： r → p+ p• Spring-8： f r → e+e• GSI： r → e+e‫ژ‬温状態での媒‫ޑ‬効果• CERN-SPS CERES実験：r w → e+e• RHIC PHENIX– f → e+e-、K+K– r w → e+e-

KEK-田無分室
ૣ子シンクロトロン

g線（‫ژ‬エネルギー光子）
g + A -> r中間子 + Xr中間子 -> p+ + p-

TAGX測定装置• 原子核 = ‫ژ‬いバリオン密度• 原子核内でr中間子を生成

原子核の外で生成された場合

p+ + p- の不変‫ޑ‬量

原子核の内ಊで生成された場合

p+ + p- の不変‫ޑ‬量KEK-PSでの実験• p+A 反応における生成ૣ子対の測定• 軽いターゲットと重いターゲットで、不変‫ޑ‬量分布に顕著な差

CERN-SPS CERES 実験
ひとつの説明：r メソンのカイラル対称性復活
r0 → e+e- 収量が重イオン衝突で増加
短い寿命（~1.3 fm）→ ‫ژ‬温状態で熱平衡
r 0 ´ p +p -()

N r 0 Æ e + e - µ Dt (系の持続時間)

ベクターメソンの収量• ‫ژ‬温熱平衡状態 → 持続時間 DT の後に
freeze-out• ベクターメソン V– 寿命 = t、 e+e- 分岐比 = Ｂ– 熱平衡: 個数ＮV 一定（崩壊分は直ちに補われる）
• BN
BNV
V
nV Æe e ~ Ú
dt + Ú
e -(t - DT ) / t dt
0
DT
t
t
DT
Ê DT ˆ
=BNV + BNV = BNV Á1 +
˜
t
t ¯
Ë

(

+ -

)

DT

t >> DT →n ~ BNVt << DT →n ~ BNV DT/t

RHIC-PHENIX 実験での‫ב‬画
f → e+e-、K+Kr w → e+e-

f がダブルピークĆ

ＱＧＰ相 → ハドロン相
自由度がミスマッチ
エントロピー密度が十分下がるまで
系はほぼ一定温度で膨張を続ける