Two-particle correlations in 158 A GeV collisions

NUCLEAR PHYSICS

ELSEVIER

A

Nuclear Physics A661 (1999) 427c-430c www.elsevier.nl/Iocate/npc

T w o - P a r t i c l e Correlations in 158 A G e V Collisions S£ndor VSrSs for the WA98 Colaboration M.M. Aggarwal, 1 A. Agnihotri, 2 Z. Ahammed, 3 A.L.S. Angelis, 4 V. Antonenko, 5 V. Arefiev, 6 V. Astakhov, 6 V. Avdeitchikov, 6 T.C. Awes, 7 P.V.K.S. Baba, s S.K. Badyal, 8 A. Baldine, 6 L. Barabach, 6 C. Barlag, 9 S. Bathe, 9 B. Batiounia, 6 T. Bernier, 1° K.B. Bhalla, 2 V.S. Bhatia, I C. Blume, 9 E.-M. Bohne, 9 Z.K. BSr5cz, 9 D. Bucher, 9 A. Buijs, 12 H. Biisching, 9 L. Carlen, 13 V. Chalyshev, 6 S. Chattopadhyay, 3 R. Cherbatchev, 5 T. Chujo, 14 A. Claussen, 9 A.C. Dos, 3 M.P. Decowski, is H. Delagrange, 1° V. Djordjadze, 6 P. Donni, 4 I. Doubovik, 5 S. Dutt, s M.R. D u t t a Majumdar, 3 K. El Chenawi, 13 S. Eliseev, 15 K. Enosawa, TM P. Foka, 4 S. Fokin, 5 V. Frolov, s M.S. Ganti, 3 S. Garpman, is O. Gavrishchuk, s F.J.M. Geurts, 12 T.K. Ghosh, 16 R. Glasow, 9 S. K.Gupta, 2 B. Guskov, s H./~.Gustafsson, 13 H. H.Gutbrod, 1° R. Higuchi, 14 I. Hrivnacova, 15 M. Ippolitov, 5 H. Kalechofsky, 4 R. K a m e r m a n s , 12 K.-H. Kampert, 9 K. Karadjev, 5 K. Karpio, 17 S. Kato, 14 S. Kees, 9 H. Kim, 7 B. W. Kolb, 11 I. Kosarev, 6 I. Koutcheryaev, 5 T. Kriimpel, 9 A. Kugler, 15 P. Kulinich, is M. Kurata, 14 K. Kurita, 14 N. Kuzmin, 6 I. Langbein, H A. Lebedev, 5 Y.Y. Lee, 11 H. L5hner, 16 L. Luquin, 1° D.P. Mahapatra, 19 V. Manko, 5 M. Martin, 4 G. Martinez, m A. Maximov, 6 R. Mehdiyev, 6 G. Mgebrichvili, 5 Y. Miake, 14 D. Mikhalev, 6 Md.F. Mir, 8 G.C. Mishra, 19 Y. Miyamoto, 14 D. Morrison, 2° D. S. Mukhopadhyay, 3 V. Myalkovski, a H. Naef, a B. K. Nandi, 19 S. K. Nayak, 1° T. K. Nayak, 3 S. Neumaier, 11 A. Nianine, 5 V. Nikitine, 6 S. Nikolaev, s P. Nilsson, 13 S. Nishimura, la P. Nomokonov, 6 J. Nystrand, 13 F.E. Obenshain, 2° A. Oskarsson, 13 I. Otterlund, 13 M. Pachr, 15 A. Parfenov, 6 S. Pavliouk, 6 T. Peitzmann, 9 V. Petracek, 15 F. Plasil, 7 W. Pinganaud, 1° M.L. Purschke, 11 B. Raeven, 12 J. Rak, is R. Raniwala, 2 S. Raniwala, 2 V.S. Ramamurthy, 19 N.K. Rao, s F. Retiere, 1° K. Reygers, 9 G. Roland, is L. Rosselet, 4 I. Roufanov, 6 C. Roy, 1° J.M. Rubio, a H. Sako, 14 S.S. Sambyal, s R. Santo, 9 S. Sato, 14 H. Schlagheck, 9 H.-R. Schmidt, 11 Y. Schutz, m G. Shabratova, 6 T.H. Shah, s I. Sibiriak, 5 T. Siemiarczuk, 17 D. Silvermyr, 13 B.C. Sinha, 3 N. Slavine, 6 K. SSderstrSm, 13 N. Solomey, 4 S.P. S0rensen, 7,2° P. Stankus, 7 (3. Stefanek, 17 P. Steinberg, is E. Stenlund, 13 D. Stiiken, 9 M. Sumbera, 15 T. Svensson, 13 M.D. Trivedi, 3 A. Tsvetkov, 5 L. Tykarski, 17 J. Urbahn, H E.C.v.d. Pijll, 12 N.v. Eijndhoven, 12 G.J.v. Nieuwenhuizen, is A. Vinogradov, 5 Y.P. Viyogi, 3 A. Vodopianov, 6 S. VSrSs, 4 B. Wystouch, is K. Yagi, 14 Y. Yokota, 14 G.R. Young, 7

I University of Panjab, Chandigarh 160014, India 2 University of Rajasthan, Jaipur 302004, Rajasthan, India 3 Variable Energy Cyclotron Centre, Calcutta 700 064, India 4 University of Geneva, CH-121I Geneva 4,Switzerland 5 RRC "Kurchatov Institute", RU-123182 Moscow, Russia s Joint Institute for Nuclear Research, RU-141980 Dubna, Russia 7 Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6372, USA s University of Jammu, Jammu 180001, India 9 University of Miinster, D-48149 Miinster, Germany lo SUBATECH, Ecole des Mines, Nantes, France 11 Gesellschaft fiir Schwerionenforschung (GSI), D-64220 Darmstadt, Germany 12 Universiteit Utrecht/NIKHEF, NL-3508 TA Utrecht, The Netherlands 13 University of Lund, SE-221 O0 Lund, Sweden 14 University of Tsukuba, Ibaraki 305, Japan 15 Nuclear Physics Institute, CZ-250 68 Rez, Czech Rep. 16 KVI, University of Groningen, NL-9747 AA Groningen, The Netherlands 17 Institute for Nuclear Studies, 00-681 Warsaw, Poland 18 MIT Cambridge, MA 02139, USA 19 Institute of Physics, 751-005 Bhubaneswar, India 20 University of Tennessee, Knoxville, Tennessee 37966, USA

1. I N T R O D U C T I O N The

only

structure particle between ing

the

contribution

for HBT

way

particle

to

obtain

emitting

(Hanbury-Brown-Twiss

sources

duction

known

of the

momenta

of the

of the spectra

by

various

correlation

particles

experimental

created

(HBT))

of the

as predicted

indirect source

correlations and

the

hydrodynamical resonances strength

A at

decay

small

KT

emission

[2,3].

on

heavy-ion

[1]. I n p a r t i c u l a r

space-time models

that

information

in relativistic

the

space-time

collisions a strong

point

Calculations

is two-

correlation

indicate

expand-

suggest

that

after

freezeout

is mainly

and

distortion

of the

seen

Gaussian

the

as a reshape

[4,5].

2. THE RESULTS The WA98 experiment at the CERN SPS was specifically designed to perform high statistics, simultaneous measurements of photons and charged particles produced in P b + P b 0 3 7 5 - 9 4 7 4 / 9 9 / $ s e e f r o n t m a t t e r © 1999 E l s e v i e r S c i e n c e B.V. PII S0375-9474(99)00489-3

All r i g h t s r e s e r v e d .

428c

M.M. Aggarwal et al./Nuclear Physics A661 (1999) 427c-430c

collisions. A description of the experimental apparatus can be found in [6]. The data presented here were taken in 1995 using the pt tracking arm and correspond to about the 10% most central part of the total cross-section. Severe quality cuts were applied on the tracks at the expense of statistics resulting in a final sample of 4.2 10 s identified ~r- tracks. The 7r- acceptance ranges from y = 2.1 to 3.1 with an average at 2.70 (Fig. 1). All measured correlation functions are corrected for the Coulomb effect in an iterative way using a code supplied by Scott Pratt [7]. 2.1. T h e s h a p e o f t h e s p e c t r u m A Gaussian fit to the 1-dimensional correlator plotted as a function of qi~v gives P ~ . -- 6.s3 + 0.10 fm and A = 0.307 + 0.008. However, the Gaussian ansatz is not optimal since the result depends significantly on the lower bound of the fit interval [6]. a similar effect is observed when plotting the correlator for the qa = ~/q~ + q~ + q~ variable in the longitudinally comoving system (LCMS). It can be seen (by comparing the x2/d.o.f.) that an exponential ansatz (dashed curve) fits the data better, in particular in the tail of the distribution (40 _< q+~, < 80 MeV) (Fig. 3). This effect is independent of the severity of the track selection, and is therefore not due to spurious tracks. As a consequence, the extracted Gaussian source parameters may depend on the acceptance of a given experiment, depending whether they are more or less sensitive to the tail. Such a non-Gaussian behaviour is expected by some models including resonance decays [5].

+

1

~

o~ 1.4

to =

Preliminary

o.. 1

1° z

te

1,3

"•

1+~.,exp[-2q~ct,I

1+Xexpl-q~RLI

R.--6.67 ± 0,13 fm

R~=6.83 ± 0.10 fm

~,= 0.718 ± 0,023

~= 0.307 ± 0.008

o et

*% 4.++ +**

1.1 Z lO .i 1 ..... o.z Y

Figure 1. ~ r - acceptance in the 1st tracking arm.

,i, ........ ,,,.. o.4 o.e o.a I

1.2

14

+.e

1.8

0.02

MT'M 0 [GeV/cl

Figure 2. Single particle spectrum for ~r-.

Figure 3. correlator.

0.04

O.Oe

o.oe o.1 q i . , [GeV/c]

One dimensional

In the remainder of this paper, the Gaussian fit will be used in order to allow comparison with other experiments. 2.2. T h e r e s o l u t i o n c o r r e c t i o n a n d KT d e p e n d e n c e To correct for the finite momentum resolution, the formula C~(q, K) used to fit the data was replaced by C~C(q, K) = f f f r(q, q')C2(q', K)dq' which is the convolution of I a--~(q--q C2(q, K) with the resolution function r(q, q') = (2~),q2jvj1/2 ,) r V -, ( q - q ) ' The diag~ 1 onal elements of the covariance matrix V are equal to the square of the resolution of the different q variables and are estimated separately as a function of KT. The non-diagonal

M.M. Aggarwal et al. /Nuclear Physics A661 (1999) 427c-430c

429c

elements are neglected. As an example, the resolution corrected fit to the q~nv spectrum gives P~nv = 7.30 ± 0.12 fm and A = 0.328 ± 0.009. For the multi-dimensional analysis, two different parameterizations have been used in the LCMS : the Bertsch-Pratt fit including the cross-term Rol : C2(q, K ) = 1 + /~e-q2sR2(g)-q2°R2°(K)-q2R~(K)-2q°qtR2°l(K),and the Yano-Koonin-Podgoretski~ fit : C2(q, K ) =

1+,~e-q~R~(K)-(q~-q])R~I(K)-(q'U(K))2(R]+R~I).The parameters for both fits are given in table 1 for all KT. Figures 4 and 5 give their KT dependence. The strong decrease of the longitudinal radius compared to the side radii suggests a larger longitudinal than lateral expansion. Hydrodynamical models predict a dependence of the form Rl =

Table 1 3-dimensional analysis

TO~o/MT,

which yields a freezeout time To - 8 fm/c for freezeout temperature To ~- 150 MeV/c. The duration of emission Ro is compatible with zero.

~ 3

fit in LCMS fm

Rt

fm

fm

Ro

= =

6.54±0.11

6.60±0.16

0.01±0.69

fm

Rt

=

7.50±0.18

fm

Rll

=

7.51±a18

fm

A

0.350±0.010

A v~

= =

0.325±0.009

R2t

= =

x~/d.o.f.

=

x2/d.o.f.

=

-1.0±1.3

fm 2

1.06

8

~

o

8

v

''=1'''1' 0.2 0.4

0

4 3 2 1 0

-0.2

R~ i n f u n c t i o n

. , I , . , I . . . ] •

0.2

0.4

0.6

K r [ GeV/c]

0.4

0.6

K. r [ G e V / c ]

of K T

r

=i i , . , i . . . i . 0.2 0.4 0.6

• , . I , , • [ , . . [ ,

0.2

0.6

0.5 0.45 0.4 0.35 0.3 025 0.2 0.15 0.1 0.05 o

0 -0.1

Kor [ G e V / c ]

7 0 5 4 3 2 1 o

of K T

> - 0.3

*

4 3 2 1

~

1.02

0.1

5 5

lO 9

0.03=E0.05

v I in f u n c t i o n

R t in f u n c t i o n of K lO

~7

E

fit

6.41±0.13

lO ~

Yano-Koonin-Podgoretskil

= =

R o i n f u n c t i o n of K T

R s in f u n c t i o n of K T

lO

Standard

Ro

Rs

~. i n f u n c t i o n of K T

R~I in f u n c t i o n of K T

5

Figure 4. KT dependence of the HBT radii in the Bertsch-Pratt parameterization. The cross-term R2t is compatible with 0 for all KT (with rather large error bars), and it is not shown here.

K T [ GeV/c] k in f u n c t i o n

~1o 0.45 0.4 0.35 0.3 ,~ 0.25 0.5 0.2 0.15 0.1 0.05 0

~5

K T [ GeVlc]

, , I , , , I , , . I , 0.2 0.4 0.6

K T [ GeWcl

O-4~.+

' ' I . . , I , , . I • 0.2 0.4 0.6

-0.3

÷

5 4 3 2 1

0

0.2

0.4

0.6

K. r [ G e V / c ]

of K T

+ 11.11

0

0.2

, , • I • • , I , 0.4 0.6 K T [ GeV/c]

Figure 5. KT dependence of the HBT radii in the Yano-Koonin-Podgoretski~parameterization. The/:to and vt parameters are compatible with 0 for all KT.

The KT dependence of Rt = R/V/1 + (MT/T)r/} determines an allowed region in the T vs ~/f plane. A fit to the single-particle spectrum (Fig. 2) using a hydrodynamical model including all resonances up to 2 GeV [4] gives an additional constraint, and the

430c

M.M. Aggarwal et al./Nuclear Physics A661 (1999) 427c-430c

common region of the T - ~ / plane lies at rather low t e m p e r a t u r e (around 100 MeV or slightly below) and high flow ( U / a r o u n d 0.5). Comparison with other experiments is only possible with NA49 whose acceptance partly overlaps with ours [9], and the agreement is found to be good. 3. H B T C O R R E L A T I O N S

IN NON-CENTRAL

COLLISIONS

A unique capability of the WA98 experiment is the determination of the reaction plane event-by-event at target rapidity using the Plastic Ball detector [10]. This study was done with ~+ mesons using the 2 nd tracking arm of the experiment. Events with impact p a r a m e t e r in the range 5-11 fm were selected. Due to limited statistics, a 2-dimensional situation was considered, by fitting the correlator plotted as a function of qt for a slice 0.0 < ql -< 0.02 GeV/c. In order to avoid geometrical acceptance effects, the events were selected as "in-plane" if their event-plane lay within +45 ° in azimuth with respect to the horizontal plane (near which the detector was located), and "out-of-plane" otherwise. W i t h i n the error bars no significant difference was seen between in-plane and out-of-plane values for the extracted H B T parameters. 4. C O N C L U S I O N The analysis of the 1995 d a t a with identified ~ - yields HBT radii of about 7 fm for 158 A GeV P b + P b collisions. The 1-dimensional correlators are better fitted by an exponential t h a n by a Gaussian, which might be due to resonance decay effects. The cross-term Rot is found to be compatible with 0 for the B e r t s c h - P r a t t parameterization in the LCMS and the same is true for vl in the Yano-Koonin-PodgoretskiY fit, suggesting a boost invariant expansion. The results in b o t h parameterizations are consistent within error bars. A clear dependence of the invariant radius parameters on KT is observed and the short duration of emission does not favour a long-lived intermediate phase. A preliminary study of HBT correlations as a function of event-plane in non-central collisions shows no significant difference between in-plane and out-of-plane parameters. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8.

D. Boal, C. K. Gelbke, and B. Jennings, Rev. Mod. Phys. 62 (1990) 553. T. CsSrg5 and B. Lcrstad, Phys. Rev. C 54 (1996) 1396. U.A. Wiedemann, P. Scotto, and U. Heinz, Phys. Rev. C 53 (1996) 918 U.A. Wiedemann and U. Heinz, Phys. Rev. C 56 (1997) 3265. J. Bolz, U. Ornik, M. Pliimer, B. R. Schlei, and R. M. Weiner, Phys. Rev. D 47 (1993) 3860. L. Rosselet for the WA98 Collaboration, Nucl. Phys. A610 (1996) 256c. S. Pratt, T. CsSrgS, and J. Zim£nyi, Phys. Rev. C 42 (1990) 2646. J.M. Rubio et al., Nucl. Instr. and Meth. A367 (1995) 358.; A. L. S. Angelis et al., Nucl. Phys. A566 (1994) 605c.; M. Iiicki et al., Nucl. Instr. and Meth. A310 (1991) 98. 9. H. Appelsh~.user et al. (NA49 Collaboration), Eur. Phys. J. C 2 (1998) 661. 10. S. Nishimura for the WA98 Collaboration and references therein, these proceedings. H. Schlagheck for the WA98 Collaboration and references therein, these proceedings.