ハドロンの収量比と化学平衡

Chemistry of Hadrons
2ri = gsisg i 3 Ê mi ˆÊ mi ˆ Qi SiT Á ˜ K 2 Á ˜l q l s22p
ËT ¯ËT ¯Ê mQ ˆ˜˜,l q = expÁÁ
Ë T ¯

Ê ms ˆl s = expÁ ˜ËT ¯

g i : spin - isospin freedom

Fitting parameters
T : Chemical freezeout temperatur e
m q : u, d chemical potential

mi : particle mass

m q : strangenes s chemical potential

Qi : 1 for u d, - 1 for u d
S i : 1 for s, - 1 for sg s : strangenes s saturation factor反෩子／෩子• 反෩子の収量が異常に多い• 反෩子/෩子~0.6

反෩子/෩子粒子・反粒子バランスが1にսいBig Bang にսい状態が実現

RHIC
Au+Au

E866
Au+Au

SPS
Pb+Pb

s1/2 [GeV]‫ژ‬い運動量領域でパイオンを凌Г
新しい対生成機構？
軽い粒子生成の抑制機構？

粒子／反粒子の Chemistry
反粒子・粒子比• Strangeness chemical potential ms ~ 0 を仮定• 反෩子／෩子比 → その他の反バリオン／バリオン比
クォーク fugacity（ତ散度）: zｑ = exp(2mｑ/T)

CAL.
p / p (uud ) = (z q )

-3

EXP.
0.6(0.06)

L / L (uds ) = (z q )0.72(0.05)

0.73(0.03)

X / X(uss ) = (z q )0.84(0.03)

0.82(0.08)

0.84(0.03)

0.88(0.05)-2-1

K - / K + (us ) = (z q )-1• 単純な‫ב‬算と良く合う

Multiplicity dependence of ratios
L/L Preliminaryratio

X+/X- Preliminary

Only statistic errors are shown
Systematic errors
p/p : 10%L/L and X+/X- : under evaluation

p/p submitted to PRL
pT 0.6-0.8 GeV/c|y|<0.3

Peripheral Æ Central(nch/nmax)• 中心衝突で反粒子/粒子の比が下がる傾向– 反粒子の吸収？

Particle ratio
M. Kaneta and N. Xu,
J. Phys. G27 (2001) 589

Tch : Chemical freeze-out temperature
mq : light-quark chemical potential
ms : strangeness chemical potential
gs : strangeness saturation factor

Qi : 1 for u and d, -1 for u and dsi : 1 for s, -1 for s
gi : spin-isospin freedom
mi : particle mass
K2 : the second-order modified
Bessel function

Simple chemical
freeze-out model
remarkably wellagrees with data.

STAR PreliminaryCentral
130 GeV Au+Au

Chemical Equilibrium
Particle ratio ‡Chemical equilibration at high temperature (at QGP?)Strangeness Production in QGP Phase8pa2S Ê 2M 2 ˆ• q q annihilati on : s(q q )=
Á1+˜w (s )27s Ës ¯• two gluon collision :k1k2

˘
2pa2S ÈÊ 4M 2 M 4 ˆ
7s + 31M-1()()
s(gg ) =1++tanhwswsÁ˜˙3s ÍÎËss2 ¯8s˚
1/ 22s = (k1 + k2 )

Ê 4M 2 ˆw (s ) = Á1˜s ¯Ë• as ~ 0.6• M(strange quark) = 150 MeV⋅ s(q q )~ s(gg )~ 0.1mb at s ª 0.4 ~ 1GeV• meson & hyperonscoalescence with u, d quarks
in the hadronization stage

k1k2

dN
8 •=
Ú sdss(gg )[ÚÚ dk1dk2Q(4k1k2 - s )fg (k1)fg (k2 )]dtdx3 p 4 4M
9 •+ 4 Ú4M sdss(q q )ÚÚ dk1dk2Q(4k1k2 - s )fq (k1)fq (k2 )4p

R=22[]

8 : 9/4 = 256 : 64 = 82 x 22 : 32 x 22 x 2 ==> Gluon interaction dominates
Ng Ne Nq Ns
R~Nf

7 251 T˘
3 -2M / T ÈaMTe
1++KS
ÍÎ 14 M˙˚
3p22È˘Êˆ()dnsns t= R Í1- ÁÁ˜˜ ˙dtÍÎ Ë ns (• )¯ ˙˚ns (0) = 0ns (t ) = ns (• )tanh(t / t ) ; t =ns (• )Rns(t) saturation(= chemical equilibrium) :achieved within 6 fm (2x 10-23 sec)
for T > 160 MeV

Strange Particles in Hot Hadron Gas
elaborate calculation:
P. Koch, B. Mueller, J. Rafelski,: Phys. Rep. 142 (1986) 167(p, K; N, L, S, X, W and antiparticles)• strangeness production: pN → KYs ~ 0.1 mb or less: sharply rise with temperature• strangenss exchange: KN → pY
s ~ 0.2 - 0.5 mb: temperature indenpendent• baryon annihilation: NN → np
s ~ 100 mb at low T; fall with temperature• Long equilibration time, compared to QGP case
• (Anti-)baryons takes longer than Kaonssmall cross section for strangeness production
small cross section for baryon pair production

Results in case of Full Evolution•Kaon yield is not different much• large difference for anti-particles; L, X, W

QGP scenario
Hadron scenario

volume (3D) expansion

longitudinal expansionHBTPhysics motivation
Au

Duration timeAu
Fireball
QGP phase

Source size
Mixed phase

Hadron phase

Observation

Some models predict that the source size
will become bigger and duration time
become longer via QGP phase
PHENIX and STAR results show thatsource radii don’t increase and noduration time at sqrt(sNN)=130GeV

STAR

Phys. Rev. Lett. 88 192302

PHENIX

Bertsch-Pratt source radii()

C1expRqRqRq≡+l---2222222sidesideoutoutlonglong

In LCMS frame
Detector

The duration time
RR/Dt=-b22TOTSyDetector

Au
Beam axisxsource

Rlong (RL)z
Beam axis

Ausource

Rout (RTO)
Rside (RTS)Data statistics from PHENIX Run2
• About 50M minimum bias event.
– Z-vertex < 30 cm– pT>0.2GeV/c• Charged pi, K PID by EMCal– 1.5s within pi mass,(and 2.0s away from K mass)– 1.5s within K mass,(and 2.5s away from p, pi mass)pi+ pairpi- pairK+ pair
K- pair

Run2 data
164M
157M
1.2M
1.1M

Run1 data
4.2M
4.6M
0.023M
0.029M

Corrections & systematic errors• Pair cuts
– Tracking inefficiency cut– Ghost track cut– Cluster sharing cut• Coulomb correction– The Coulomb effect is correctedby full coulomb correction with
momentum smearing.
Sytematic errors (%)
Cluster share cut
Tracking inefficiency cut
Ghost track cut
Coulomb
Total (%)

lambda
11.7
5.9
2.8
3.1
13.9

Rside
4.9
2.6
0.8
2.4
6.4

Rout
5.7
6.4
3.4
3.7
10.1

Rlong Rout/Rside
4.4
1.1
2.5
2.4
1.3
4.2
2.2
2.9
6
5.7

3-D correlation result of charged pions
PHENIX PRELIMINARY

200 GeV Au+Au、Top 30% Centrality, 0.2<kT<2.0GeV/c,<kT>=0.46GeV/c_ = 0.397 ± 0.015
Rside = 4.40 ± 0.12
Rout = 3.73 ± 0.12 [fm]Rlong = 4.82 ± 0.15

_ = 0.434 ± 0.018
Rside = 4.58 ± 0.14
Rout = 3.88 ± 0.14 [fm]Rlong = 5.24 ± 0.18

kT dependence of source radii

Centrality is in top 30%

Comparison with hydrodynamic model
Centrality is in top 30%
Recent hydrodynamic calculation
by U.Heinz and P. F. Kolb
(hep-ph/0204061)
Hydro w/o FS• Standard initialization and freeze out
which reproduce single particle spectra.
Hydro at ecrit• Assuming freeze out directly at thehadronization point. (edec = ecrit)kT dependence of Rlong indicates theearly freeze-out?

kT dependence of Rout/Rside

The duration time
RR/Dt=-b

22TOTSCentrality dependence ofsource 0.2<kT<2.0GeV/c,
radii<kT>=0.46GeV/c
Fit withp0+p1*Npart^1/3Rlong increases
rapidly with theNpart than Rout.

Centrality dependence of Rout/Rside

0.2<kT<2.0GeV/c ,<kT>=0.46GeV/c

3-D correlation results of charged kaons

200 GeV Au+Au、Top 30% Centrality, 0.2<kT<2.0GeV/c,<kT>=0.76GeV/c_ = 0.815 ± 0.181
Rside = 4.18 ± 0.54
Rout = 3.72 ± 0.69 [fm]Rlong = 4.27 ± 0.65

_ = 0.785 ± 0.181
Rside = 3.65 ± 0.43
Rout = 3.23 ± 0.47 [fm]Rlong = 4.48 ± 0.68

Comparison of kaon to pion
In the most 30% central

Elliptic Anisotropy

Early thermalization ?
- Strong elliptic flow v2-Reactionpl
aneReaction planeb : Impact parameter

Spatial anisotropy
Momentum anisotropy

dN/df = N [ 1 + S 2vncos(nf) ]f : azimuthal angle for measured particles
from a reaction planevn : anisotropy parameter

Centrality Dependence of Elliptic
Flow
midrapidity : |h| < 1.0

V2

Hydrodynamic model
Preliminary

SPSAGS

relative centrality
surprise: （１）フローがఫ常に強い（２）model の予想とcomparableflow and non-flow contributions

STARReaction plane determination in PHENIX
h = -3.5 vs h = +3.5
(directed : n=1)|h|=3.5 vs |h| < 0.35
(elliptic : n=2)

F2(|h| = 3.5)

F2 (h = -3.5)

F1(h = -3.5)

F2 (h = +3.5)

F2 (|h| < 0.35)

DF = F1A - F1B

DF = F2A - F2B

DF = F2A - F2B

A: (h = -3.5)
B: (h = +3.5)

A: (h = -3.5)
B: (h = +3.5)

charged multiplicity<cos(2 DF)>F1 (h = +3.5)<cos(2 DF)><cos(DF)>h = -3.5 vs h = +3.5
(elliptic : n=2)

A: (|h| = 3.5)
B: (|h| < 0.35)

v2 measurement at PHENIX
v2

v2 measured at (|h|<0.35) with
3 different reaction planes at (|h|=3~4)--- statistical error--- +systematic error

Au+Au atsqrt(sNN)=200GeV
v2(|h|<0.35)
vs centrality
charged particles
0.2 < pT < 10 GeV/cr.p. h = -4~-3
r.p. h = 3~4
r.p. |h| = 3~4
PHENIX Preliminary<sin(2(f-F))>

centrality (%)

Elliptic Anisotropy のエネルギー依存性
ఫ常に強い
ఫ対称性

v2 scaling

Charged particle anisotropy 0<pT<4.5 GeV/c• Minimum bias data
• Only statistical errors• Systematic error 10% - 20% for pt = 2 – 4.5 GeV/c

pT dependence of flow
Hydro+GLV: M. Gyulassy,
I. Vitev and X.N. Wang,
nucl-th/00012092• flow starts to bend over at ~2 GeV/c• matches well with models that incorporate jet quenchingv2 saturates or drops at high pT?
STARPreliminary

NA45pT (GeV/c)

Comparison with a Hydrodynamical Model
Hydrodynamical calculations: Huovinen, Kolb and Heinz

v2 of identified hadrons
v2hydro model including the1st orderphase transition with Tf=120MeV (*)

pion
kaon
protonAu+Au at sqrt(sNN)=200GeV
min. bias r.p. |h|=3~4v2(*) P.Huovinen, P.F.Kolb, U.W.Heinz,P.V.Ruuskanen and S.A.Voloshin,Phys. Lett. B503, 58 (2001)

Negatives

Positives

h-,pi-,K-,pbar

h+,pi+,K+,p

PHENIX Preliminary

PHENIX PreliminarypT (GeV/c)pT (GeV/c)

reversed v2 at pT > 2GeV/c
Preliminary
STAR

Preliminary

Lambdas
K0

Preliminary

Preliminary
STAR

Antiprotons
K- + pi-

Protons
K+ + pi+pt

Protons
Pions+kaons

HBT puzzle
Why duration time t=sqrt(Rout2-Rside2)/bof the freeze-out is so short?
R sideAkitomo Enokizono @ QM02

Centrality is in top 30%

Hydro w/o Free Streaming• Standard initialization and freeze out
which reproduce single particle spectra.
Hydro at ecrit• Assuming freeze out directly at thehadronization point. (edec = ecrit)kT dependence of Rlong indicates theearly freeze-out?

R out

R longAny initial conditions in hydro.
can not solve the small Rside.
Recent hydrodynamic calculation by
U.Heinz and P. F. Kolb
(hep-ph/0204061)

kT: average momentum of two particles