Tamás Csörgő

The final state of Au + Au @ RHIC

Tamás Csörgő

(MTA KFKI RMKI, Budapest, Hungary)

indication for quark deconfinement

•Buda-Lund hydro model, fitted to•spectra and HBT•PHENIX and STAR run-1 data•h+p @ CERN SPS•Pb+Pb @ CERN SPS •outlook: BRAHMS and PHOBOS data•outlook: preliminary run-2 data

T. Cs. & A. Ster, nucl-th/0207016

<- Allegory of Hung. Acad. Sci: „From darkness, the light”, painting by P. Endel

Tamás Csörgő

Buda-Lund hydro model

Separation of the Core and the Halo Core: hydrodynamic evolution Halo: decay products of long-lived resonances

i) Analytic expressions for all the observablesii) Maximal flexibility compatible with i) iii) 3d expansion, local thermal equilibrium, symmetryiv) Goes back to known hydro solutions in nonrel limit

(implies density inhomogeneity !)

Principles for Buda-Lund hydro

Tamás Csörgő

Buda-Lund hydro model (2)

Invariant single particle spectrum:

Invariant Buda-Lund correlation function: oscillating prefactor!

Non-invariant Bertsch-Pratt parameterization:

Non-Gaussian BL form -> Gaussian BP approximation:

Tamás Csörgő

Invariant Buda-Lund q = k1 - k2 decomposition

Invariant decomposition of relative momentum:

Invariant Buda-Lund correlation function: Shape analysis (e.g. Edgeworth expansion) is possible,

when using the invariant BL rel. Momentum components.Not only Gaussian shapes!

Temporal,longitudinal

and transverse, resp.

Tamás Csörgő

In Search of the QGP. Naïve expectations

QGP has more degrees of freedom than pion gas, hence it has higher entrophy density

Entropy should be conservedduring fireball evolution

Hence: Look in hadronic phasefor signs of: Large spatial size, Long lifetime,

Long duration of particle emission

Tamás Csörgő

222222

*1),,( llssoo RqRqRqlso eqqqC

px

qopyqsDecomposition of the pair relative momentum

measured in the LCMS frame; (k1+ k2)z=0,

(T. Cs., S. Pratt, KFKI -1991-28/A, p. 75)

Pratt-Bertsch Parameterization

Tamás Csörgő

HBT signature of QGP: 2 Expectations

“Naïve” picture (no space-momentum correlations):

– Rout2=Rside

2+(pair)2

One step further (direction?):– Hydro calculation of Rischke &

Gyulassy expects Rout/Rside ~ 2->4 @ kt = 350 MeV.

– Looking for a “soft spot”

Story at CERN SPS almost completely repeats itself!!

Buda-Lund prediction: Rout ~ Rside is possible @ large mt (cooling)!

Rout

Rside

T. Cs, B. Lörstad, PRC 54 (1996) 1390,NPA 590 (1995) 465c

Tamás Csörgő

Rout/Rside Ratios at 200 GeV

<- Buda-Lund prediction

Note also: Rside /RL -> const (<=1)

as mt >> T0 is another a BL prediction

T. Cs. & B. Lorstad, PRC54 (1996) 1390NPA 590 (1995) 465

reflects symmetry of the flow !

Tamás Csörgő

BL Hydro fits to NA44 Pb+Pb data

BL-H source parameters

T0 145 3 MeV<ut> 0.57 0.12RG 6.9 1.1 fm

0 6.1 0.9 fm/c 0.1 2.2 fm/c 2.4 1.6<T/T>r 0.08 0.08<T/T>t 0.87 0.722/NDF 63/71 = 0.89

A. Ster, T. Cs, B. Lörstad, hep-ph/9907338

Final dataAbsolute normalization,

Boltzmann approx., ~ 1, 0 = 0 approx.

Tamás Csörgő

BL Hydro fits to NA49 Pb+Pb data

BL-H source parameters

T0 134 3 MeV<ut> 0.61 0.05RG 7.3 0.3 fm

0 6.1 0.2 fm/c 2.8 0.4 fm/c 2.1 0.2<T/T>r 0.07 0.02<T/T>t 0.16 0.052/NDF 163/98 = 1.66

A. Ster, T. Cs, B. Lörstad, hep-ph/9907338

Final dataAbsolute normalization,

Boltzmann approx., ~ 1, 0 = 0 approx.

Tamás Csörgő

Fits to preliminary STAR data (HEP2001)

0,0 0,1 0,2 0,3 0,4 0,5

100

101

102

103

5% central

K- 6% centralp 6% central

1/(

2m

t) d

2 n/(

dm

tdy

)

mt - m (GeV)

0,0 0,5 1,00

2

4

6

8

1012% central

Rlo

ng (

fm)

mt (GeV)

0,0 0,5 1,00

2

4

6

8

10

Ro

ut (

fm)

mt (GeV)

0,0 0,5 1,00

2

4

6

8

10

Rsi

de (

fm)

mt (GeV)

BL-H source parameters

T0 144 5 MeV<ut> 0.86 0.1RG 8.0 0.5 fm

0 8.9 0.5 fm/c 0.5 1.0 fm/c 1.0 0.1<T/T>r 0.09 0.01<T/T>t 1.6 0.4

0

0 fixed

0K 46 11 MeV

0p 300 18 MeV

2/NDF 32/54 = 0.59

A. Ster, T. Cs. Hep-ph/0112064

Tamás Csörgő

Fits to preliminary PHENIX data (HEP2001)

0,0 0,5 1,00

2

4

6

8

1015% central

Rlo

ng (

fm)

mt (GeV)

0,0 0,5 1,00

2

4

6

8

10

Ro

ut (

fm)

mt (GeV)

0,0 0,5 1,00

2

4

6

8

10

Rsi

de (

fm)

mt (GeV)

0,0 0,5 1,0 1,5 2,0 2,510-3

10-2

10-1

100

101

102

103

5% central

K- min.biasp 5% central

1/(2

mt)

d2 n

/(d

mtd

y)

mt - m (GeV)

BL-H source parameters

T0 139 5 MeV<ut> 0.68 0.3RG 6.6 0.3 fm

0 7.9 0.3 fm/c 0.6 1.2 fm/c 1.5 0.1<T/T>r 0.04 0.01<T/T>t 0.86 0.09

0

0 Fixed

0K -

0p 376 38 MeV

2/NDF 46/58 = 0.79

A. Ster, T. Cs. Hep-ph/0112064

Tamás Csörgő

Fits to year-1 final PHENIX and STAR data8

BL-H sourceparameters

Fit I. Fit II.

T0 [MeV] 174 12 140 fixed<ut> 1.03 0.14 0.98 0.14RG [fm] 9.3 1.0 9.2 1.0

0 [fm/c] 6.7 0.3 7.6 0.2 [fm/c] 0.2 2.8 0.1 1.4 2.5 fixed 2.5 fixed<T/T>r 0.46 0.16 0.17 0.06<T/T>t 3.0 0.9 1.0 0.2

0 [MeV] 0 fixed 0 fixed

0K [MeV] 50 16 76 9

0p [MeV] 391 35 422 12

2/NDF 84/69=1.22 100/70=1.43CL 11.3% 1.1%

Final dataAbsolute normalization,

Boltzmann approx., ~ 1, 0

= 0 approx.

Tamás Csörgő

First comparision of RHIC and SPS results

BL-H sourceparameters

Au+AuRHIC

Pb+Pb<SPS>

h+pSPS

T0 [MeV] 140 fixed 139 6 140 3<ut> 0.98 0.14 0.55 0.06 0.20 0.07RG [fm] 9.2 1.0 7.1 0.2 0.88 0.13

0 [fm/c] 7.6 0.2 5.9 0.6 1.4 0.1 [fm/c] 0.1 1.4 1.6 1.5 1.3 0.3 2.5 fixed 2.1 0.4 1.36 0.02<T/T>r 0.17 0.06 0.06 0.05 0.71 0.14<T/T>t 1.0 0.2 0.59 0.38 -

0 [MeV] 0 fixed - -

0K [MeV] 76 9 - -

0p [MeV] 422 12 - -

But what about the CL of the fit to the RHIC data?

See nucl-th/0207016 for details!

Tamás Csörgő

Comparing RHIC Au+Au to SPS results

BL-H sourceparameters

Au+AuRHIC

Pb+Pb<SPS>

h+pSPS

T0 [MeV] 202 13 139 6 140 3<ut> 111...000888 000...111777 000...555555 000...000666 000...222000 000...000777RG [fm] 999...888 111...222 777...111 000...222 000...888888 000...111333

0 [fm/c] 666...111 000...333 555...999 000...666 111...444 000...111 [fm/c] 0.1 1.5 1.6 1.5 1.3 0.3 2.5 fixed 2.1 0.4 1.36 0.02<T/T>r 0.84 0.24 0.06 0.05 0.71 0.14<T/T>t 1.3 0.4 0.59 0.38 -

0 [MeV] 75 19

0K [MeV] 107 14

0p [MeV] 305 41

2/NDF 74/68 = 1.09CL 28.9 %

A 4.5 effect, T0 ~ Tc = 170 MeVIndication for quarks &

hard EOSFurther checkings!

Tamás Csörgő

Summary:

The analysis of the 1st year final data of single-particle momentum distributions and Bose-Einstein correlation function radii of the RHIC experiments PHENIX and STAR show:

fastest transverse flow (~3d Hubble flow)

short mean decoupling time ( ~ 6 fm/c)

short duration of particle emission (~<1 fm/c)

a hot center of the core with T>~ Tc = 170 MeV

and the central temperature is 4.5 higher than in h+p and Pb + Pb reactions at CERN SPS experiments.

Further testings are needed (new data from BRAHMS, PHENIX, CERES and NA49 are helpful, both p+p and A+A)

Thanks to A. Ster, S. Panitkin and the HBT gang...