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and
Berkeley, California
Springer Science+Business Media, LLC
L i b r a r y of Congress C a t a l o g l n g - i n - P u b l I c a t t o n Data
Advances In nuclear dynamics 4 / ed i ted by Wolfgang Bauer and Hans -Georg R i t t e r .
p. cm. "Proceedings of the 14th Winter Workshop on Nuclear Dynamics, held
January 31-February 7 , 1998, in Snowbird, U t a h " — T . p . verso. Includes b i b l i o g r a p h i c a l re ferences and index.
1 . C o l l i s i o n s (Nuclear physics)—Congresses. 2 . Nuclear f ragmenta t lon- -Congresses . 3 . Heavy ion co11 is ions- -Congresses . I . Bauer, W. (Wol fgang) , 1959- . I I . R i t t e r , Hans-Georg. I I I . Winter Workshop on Nuclear Dynamics (14th : 1998 . Snowbird, Utah) IV . T i t l e : Advances in nuclear dynamics four . QC794.6.C6A374 1998 5 3 9 . 7 ' 5 7 — d c 2 1 98-40689
CIP
Proceedings of the 14th Winter Workshop on Nuclear Dynamics, held January 31 - February 7, 1998, in Snowbird, Utah
ISBN 978-1-4757-9091-7 ISBN 978-1-4757-9089-4 (eBook) DOI 10.1007/978-1-4757-9089-4
© Springer Science+Business Media New York 1998 Originally published by Plenum Press, New York in 1998
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PREFACE
These are the proceedings of the 141h Winter \Vorkshop on Nuclear Dynamics, the latest of a serif'S of workshops that was started in 1~)78. This series has grown into a tradition. bringing together experimental and theoretical expertise from all areas of the study of nudear dynamics.
Following tllf' tradition of the Workshop the program covered a broad range of topics aerof'S a large energy range. At the low energy end llluitifragmentation and its relationship to the nuclear liquid to gas phase transition was disclIssf'd in grf'at df'­ tail. New pxpf'rimental data, refined analysis techniques, and new theoretical effort have lead to considerable progress. In the AGS energy range we see the emergence of systematic data that contribute to our understanding of the reaction dynamics. The workshop also showf'd that at CERN energies Itadronic data become much more precise and complet.e and a renewed emphasis on basic hadronic processes and hadronic struc­ ture as a precondition to understand the initial conditions and a basis for systematic comparisons.
Wolfgang Bauer Michigan State Univcr'sity
Hans-Georg Ritter Lawrence Berkeley National Laboratory
v
PREVIOUS WORKSHOPS
The following table contains a list of the dates and locations of the previous Winter Workshops on Nuclear Dynamics as well as the members of the organizing committees. The chairpersons of the conferences are underlined.
1. Granlibakken, California, 17-21 March 1980 W. D. Myers, J. Randrup, G. D. Westfall
2. Granlibakken, California, 22-26 April 1982 W. D. Myers, J. J. Griffin. J. R. Huizenga, J. R. Nix, F. Plasil, V. E. Viola
3. Copper Mountain, Colorado, 5-9 March 1984 W. D. Myers, C. K. Gelbke, J. J. Griffin, J. R. Huizenga, J. R. Nix, F. Plasil, V. E. Viola
4. Copper Mountain, Colorado, 24-28 February 1986 .1. J. Griffin, J. R. Huizenga, J. R. Nix, F. Plasil, J. Randrup, V. E. Viola
5. Sun Valley, Idaho, 22-26 February 1988 .J. R. Huizenga, .1. I. Kapusta, J. R. Nix, J. Randrup, V. E. Viola, G. D. Westfall
6. Jackson Hole, Wyoming, 17-24 February 1990 B. B. Back, J. R. Huizenga, J. I. Kapusta, J. R. Nix, J. Randrup, V. E. Viola,
G. D. Westfall
7. Key West, Florida, 26 January-2 February 1991 13. B. Back, W. Bauer, .1. R. Huizenga, J. I. Kapusta, J. R. Nix, J. Randrup
8 . .Jackson Hole, Wyoming, 18-25 January 1992 B. B. Back, W. Bauer, J. R. Huizenga, J. I. Kapusta, J. R. Nix, J. Randrup
9. Key West, Florida, 30 .January-6 February 1993 B. B. Back, W. Bauer, .J. Harris, J. I. Kapusta, A. Mignerey, .J. R. Nix, G. D. Westfall
10. Snowbird, Utah, 16 22 January 1994 B. B. Back, W. Bauer, .J. Harris, A. Mignerey, .J. R. Nix, G. D. Westfall
vii
11. Key WeRt. Florida, 11-18 February 1995 W. Bauer, J. Harris, A. Mignerey. S. Steadman. G. D. Westfall
12. Snowbird. Utah, 3-10 February 1996 W. Bauer. J. Harris, A. Mignerey, S. Steadman. G. D. Westfall
13. Marathon, Florida. 18 February 1997 W. Bauer, J. HarriR. A. Mignerey. H. G. Ritter. E. Shuryak. S. Stpadman. G. D. Westfall
14. Snowbird. Utah, 31 January 7 February 1998 W. Bauer. J. Harris, A. Migncrcy. H. C. Ritter. E. Shuryak. C. D. Wpstfall
viii
CONTENTS
1. Experimental evidence of "in medio" effects in heavy-ion collisions at intermediate energies .................................................. 1
A. Badala, R. Barbera, A. Bonasera, M. Gulino, A. Palmeri, G. S. Pappalardo, F. Riggi, A. C. Russo, G. Russo, and R. Turrisi
2. Hadrochemical vs. microscopic analysis of particle production and freeze-out in ultra-relativistic collisions ................................ 13
S. A. Bass, S. Soff. M. Belkacem, M. Brandstetter, M. Bleicher, L. Gerland, J. Konopka, L. Neise, C. Spieles, H. Weber, H. Stocker, and W. Greiner
3. Di-leptons at CERN ........................................................ 25
Wolfgang Bauer, Kevin Haglin, and Joelle Murray
4. Multifragmentation at intermediate energy: dynamics or statistics? ......... 33
Luc Beaulieu, Larry Phair, Luciano G. Moretto, and Gordon J. Wozniak
5. Survival probabilities of disoriented chiral domains in relativistic heavy ion collisions ................................................... 43
Rene Bellwied, Sean Gavin, and Tom Humanic
6. Low Pt particle spectra and strange let search from Au + Au collisions: Final results from BNL-AGS experiment E878 ......................... 55
Michael J. Bennett
A. Bonasera, M. Bruno, and M. D'Agostino
8. Fragment production in a finite size lattice gas model ....................... 69
Philippe Chomaz and Francesca Gulminelli
9. H dibaryon search in p-A collisions at the AGS ............................. 79
Anthony D. Frawley
ix
x
10. A dynamical effective model of ultrarelativistic heavy ion collisions .......... 89
P.-B. Gossiaux and P. Danielewicz
11. The Coulomb Dissociation of 8 B and the 7 Be(p.,)8 B Reaction ............ 101
Moshe Gai
12. Sharp (e+ e-) pairs: Alternative paths to escape the heavy ion impasse ..... 107
James J. Griffin
13. Studying the spin structure of the proton using the Solclloidal Tracker At RHIC ............................................................ 117
Timothy J. Hallman
John W. Harris
15. Novel approach to sampling ultrarelativistic heavy ion collisions in tltn VENUS model ...................................................... 137
Michael Hladik, Hajo Drescher, Scrgej Ostapchenko, and Klaus Werner
16. Neutron production from the 40Ca + H reaction at Elab = 357 and 565A MeV .......................................................... 145
A. Insolia, C. Tuve. S. Albergo. D. Boemi, Z. Caccia, C. X. Clwn, S. Costa, H. J. Crawford, M. Cronqvist, J. Engeiage, P. Ferrando, L. Greiner, T. G. Guzik, F. C. Jones, C. N. Knott, P. J. Lindstrom, J. W. Mitchell, R. Potenza. G. V. Russo, A. Souton\. O. TestanL A. Tricomi, C. E. Tull, C .. J. Waddington, W. R. Webber, J. P. Wefe!' and X. Zhang
17. Recent results from NA49 ............ 155
Peter Jacobs, Milton Toy, Glenn Cooper, and Art Poskanzer
18. Thermal dilepton signal and dileptolls from correlated open charlll and bottom decays in ultrarelativistic heavy-ion collisions ................. 163
B. Kampfer, K. Gallmeister, and O. P. Pavlenko
19. Dynamic and statistical effects in light-ion-induced multifragmcntation ..... 173
K. Kwiatkowski, W.-c. Hsi, G. Wang, A. Botvina, D. S. Bracken, H. Breuer, E. Cornell, W. A. Friedman, F. Gimcno-Nogues, D. S. Ginger, S. Gushue, R. Huang, R. G. Kortding, W. G. Lynch. K. B. Morley, E. C. Pollacco, E. Ramakrishnan, L. P. Remsberg, E. Renshaw Foxford, D. Rowland, M. B. Tsang, V. E. Viola, H. Xi, C. Volant, and S. J. Yennello
20. The E895 7[- correlation analysis
M. A. Lisa
a status report ........................ 183
21. Statistical models of heavy ion collisions and their parallels ................ 193
Aram Z. Mekjian
22. The macroscopic liquid-drop collisions project: a progress report ........... 203
A. Menchaca-Rocha and A. Martinez-Davalos
23. Peripheral reaction mechanisms in intermediate energy heavy-ion reactions 209
D. E. Russ, A. C. Mignerey, E. J. Garcia-Solis, H. Madani, J. Y Shea, P. J. Stanskas, O. Bjarki, E. E. Gualtieri, S. A. Hannuschke, R. Pak, N. T. B. Stone, A. M. VanderMolen, G. D. Westfall, and J. Yee
24. What invariant one-particle multiplicity distributions and two-particle correlations are telling us about relativistic heavy-ion collisions ...... 215
J. Rayford Nix, Daniel Strottman, Hubert W. van Heeke, Bernd R. Schlei, John P. Sullivan, and Michael J. Murray
25. E917 at the AGS: high density baryon matter ............................. 223
Robert Pak
Sergei Y. Panitkin
Hans-Werner Pfaff
28. Neutral pion production in nucleus-nucleus collisions at 158 and 200 GeV /nucleon ........................................... 247
F. Plasil
29. Dynamics of the multifragmentation of the remnant produced in 1 A GeV Au + C collisions .......................................... 255
N. T. Porile, S. Albergo, F. Bieser, F. P. Brady, Z. Caccia, D. A. Cebra, A. D. Chacon, J. L. Chance, Y. Choi, S. Costa, J. B. Elliott, M. L. Gilkes, J. A. Hauger, A. S. Hirsch, E. L. Hjort, A. Insolia, M. Justice, D. Keane, J. C. Kintner, V. Lindenstruth, M. A. Lisa, H. S. Matis, M. McMahan, C. McParland, W. F. J. Miiller, D. L. Olson, M. D. Partlan, R. Potenza, G. Rai, J. Rasmussen, H. G. Ritter, J. Romanski, J. L. Romero, G. V. Russo, H. Sann, R. P. Scharenberg, A. Scott, Y. Shao, B. K. Srivastava, T. J. M. Symons, M. Tincknell, C. Tuve, S. Wang, P. Warren, H. H. Wieman, T. Wienold, and K. Wolf
30. Hadron interactions ... hadron sizes ....................................... 267
Bogdan Povh
Scott Pratt
xi
32. Syst.em size and isospin effects in central heavy-ion collisions at SIS energies ......................................................... 285
Fouad Rami
33. Search for strange quark matt.er at the AGS ............................... 295
Claude A. Pruneau
.10rgen Randrup
35. Recent test results and status of the HADES detector at GSI .............. 311
James Ritman
36. Fast particle emission in inelastic channels of heavy-ion collisions ........... 319
.1. A. Scarpaci. D. BeaumeL Y. Blumenfeld. Ph. Chomaz. N. Frascaria . .l . .longman. D. Lacroix. H. Lament. 1. Lhenry. V. Pasealou-Rozier. P. Roussel-Chomaz . .1. C. Royuette. T. Suomijiirvi. A. van der Woude
37. A detailed comparison of exclusive 1 GeV A Au on C data with the statistical multifragmentatioll model (SMM) ......................... 329
R. P. Scharenberg. S. Albergo. F Bieser. F. P. Brady. Z. Caccia. D. A. Cebra. A. D. Chacon . .1. L. Chance. Y. Choi. S. Costa . .1. B. Elliott. M. L. Gilkes . .1. A. Hauger. A. S. Hirsch, E. L. Hjort. A. Insolia. M. Justice . .1. C. Kintner. V. Lindenstmth. M. A. Lisa. H. S. Matis. M. McMahan. C. McParland. W. F . .1. Muller. D. L. Olson. M. D. Partlan, N. T. Porile, R. Potmza. G. Rai. .1. Rasmussen. H. G. Ritter. .1. Romanski . .1. L. Romero. G. V. Russo. H. Sann. A. Scott. Y. Shao. 13. K. Srivastava. T . .T. M. Symons. M. Tincknell. C. Tuve. S. Wang. P. Warren. H. H. Wipman. and K. Wolf
38. Event-by-event analysis of NA49 emtral Pb Ph data ...................... 341
Thomas A. Trainor
W. Trautmann
40. Baryon junction stopping at the SPS and RHIC via HI.1ING/B ............ 361
S. E. Vance. M. Gyulassy. and X. N. Wang
41. Anti-lambda/anti-proton ratios at the AGS ................................ 369
G. J. Wang, R. 13ellwied, C. Pruneau, and G. Welke
42. The isospin dependence of nuclear reactions at intermediate energies ....... 379
Gary D. Westfall
EXPERIMENTAL EVIDENCE OF "IN MEDIO" EFFECTS IN HEAVY-ION COLLISIONS AT INTERMEDIATE ENERGIES
A. Badala.,! R. Barbera/,2 A. Bonasera,3 M. Gulino/,2 A. Palmeri/ G. S. Pappalardo,! F. Riggi,!,2 A. C. Russo,! G. Russo,1,2 and R. Turrisi!,2
lIstituto N azionale di Fisica N ucleare, Sezione di Catania Corso Ita.lia, 57, I 95129 Catania, Italy
2Dipartimento di Fisica dell'Universita di Catania Corso Italia, .S 7, I 9,S 129 Catania, Italy
3Istituto 01azionale eli Fisica Nucleare, Laboratorio Nazionale del Sud Via S. Sofia, 44, I 9512:3 Catania, Italy
INTRODUCTION
Heavy-ioll collisions at hombardillg cnergies ranging from about 100 Me V /nucleoll up to a few GeV /llllcleon represcnt a unique tool to study the excitation of non­ lluckonic degrees of freedolll like haryonic resonances in excited nuclear matter far frorn ground-state conditions, i.e. outside the usual domain of existing nuclear struc­ ture information. Indeed, in ,1 reccnt paper! we have demonstrated the existence of the dCl11enlar)! indil'fict process :Y iY --+ N.6. --+ N N 7r0 in 36 Ar+27 Al collisions at. around 100 :vIcV / Ilucleon and we have deduced from experimental data the relative cross section. Notwithstanding.6. --+ N7r is by far the most favoured decay channel (B.R.,,-, 100% 2), it is 1I0t however the best-suited one to study the signals of excitation and propagation of .6.( I :t~2)-resonancc in nuclear matter because of the high distortion introduced by 111<' filial-state interactions of pions with the surrounding medium. In this context. the ('kc1romagnetic decc1.v .6. --+ N; would be, on the contrary, much more appropriate due 10 the almost complete absencE' of interaction of photons with nuclear matter. The free branching ratio of that decay channel is, however, only 6· 10-3 2, and the successful realization of an experimcnt aimed to the detection of ;'s coming from .6. decay has to reckon with the existence of several serious drawbacks: i) in order not to have COll­
tamination from othcr nlf'chanisll1s (such as statistical photon emission and/or giant­ resom1llce de-C'xcitation) a lower energy cnt-off of at least 25-30 MeV must be imposed 011 the data and this strongly reduces the yields, ii) it is well known that high-energy photons are mostly emitted in the elementary direct process N N --+ N N; so that one' has to identify a reasonable ensemble of conditions on the available observables apt to disentangle the l1!dinct mechanism from the direct one, iii) in order to reduce as much as possible the strong background clUE' to photons coming from 7r
0 decays, the bombard­ ing energy should not be much larger than 100 MeV/nucleon and, at the same time,
1
it should not be much smaller than that value because of the consequent reduction of the phase space available for the excitation of the ~ resonance.
In spite of this quite discouraging framework, several theoretical studies 3, 4, 5 based both on statistical 3 and microscopic 4, 5 calculations, have drawn the conclusion that ,,('s coming from ~ electromagnetic decay should be easily observable as they are re­ sponsible of the presence of a bump (or, more simply, of a change in the slope) in the photon energy spectrum above E"( = 100 MeV in heavy-ion collisions at bombarding energies between 35 and 200 MeV/nucleon. Since then, several experiments either ex­ pressly dedicated 6 or not 7,8,9 to this issue have measured with a great accuracy the inclusive energy spectrum of hard-photons emitted in heavy-ion collisions at intermedi­ ate energies and no deviation from an exponentially decreasing trend has been observed up to K, ~ 300 MeV.
In this contribution we report on the first study of the excitation of the ~(1232)­ resonance and its electromagnetic decay performed analysing the data of a truly exclu­ sive experiment, where high-energy photons emitted in the reactions induced by a 9.5 MeV/nucleon 36Ar beam on a 27Al target (the same reaction studied in Ref. 1) have been detected in coincidence with protons by a large-area and high-granularity multi­ detector. For the first time it has been possible to get an estimate of the branching ratio a(~ ~ N"()/a(~ ~ N7r) in nuclear matter and a comparison with its free value. This has a great significance since it implicitly allows a quantitative investigation on tlw weights of two very important processes such as pion reabsorption (7r N N ~ N N) and rescattering (7r N ~ ~ ~ N,,() which can sensibly affect the in medio branching ratio with respect to the free one.
Further results on this issue have been recently published 10.
EXPERIMENTAL SETUP
The used experimental setup basically consisted of the BaF 2 ball of the MEDEA multi-detector. In the experiment described here it was made up by 144 trapezoidal scintillation modules of bariulll fluoride (20 cm thick) placed at 22 em from the target point and arranged illto six rings ill order \.0 cover the whole azimuthal angular dynamics between () = 400 and () = 140 0 with respect to the beam direction. A very detailed description of this multi-detector can be found in Ref. 11. Ref. 10 contains also a description of the methods used for particle identification as well as the results of the detector response and efficiency ca.!culations.
RESULTS
As stated before, all experimental studies conducted so far 6, 7, 8, 9 have a char­ acter strictly inclusive. This crucial point deserves a deeper reflection. It is by now well known that high-energy photons are mostly created in single and incoher­ ent nucleon-nucleon collisions NN~NN"(. This direct and very rapid contribution to the production cross-section largel~' overwhelms any other channel like the indirect one NN~N~ ~NN"( which we are interested in here. Furthermore, one also has to take into account that when ~ 's are created inside nuclear matter during the collision they almost exclusively decay into a nucleon and a pion inducing a very large background with respect to the signal one wants to observe. Thus, it should not be so surprising if experimental inclusive energy spectra, which also suffer of an unavoidably finite energy resolution, do not show any signa.! in tl1P region where it is theoretically expected to
2
be. The situation is not hopeless, however. In fact, if a b. resonance is excited in a nucleon-nucleon collision and Own it transforms in a photon and a proton, the final four-momenta of these two particles must be somehow affected by the fact that they come from the decay of a resonant state. Then, a study of kinematical and geometrical correlations between high-energy photons and protons emitted in the same event could ptovide valuable information about any eventual excitation of non-nucleonic degrees of freedom in nuclear matter at these energies.
In the analysis of exclusive (r - p) events we imposed the condition that only one high-energy photon was detected in the event. This cut allows, from one side, to eliminate all two-photon events which have a large probability to come from 11"0 decay (the detector efficiency of the detection of both photons coming from 11"0 decay is about twice that of the detection of only one photon) and, on the other side, to reduce the average proton multiplicity in photon events to Vp = 1.91 ± 0.03. The question of the value of the proton multiplicity has been already addressed in Ref. 1,10.
The first correlation distribution we analyzed was the (r - p) invariant-mass dis­ tribution. For those events where a high-energy photon is detected in coincidence with at least one proton, the (r - p) invariant mass distribution has been calculated using the formula:
mint. = Jm~ + 2EpE"((l - (3p cos B,.cd (1)
with an obvious meaning of the symbols. In order to get safe of any possible stray angular correlation, proton detection angles (which enter into the calculation of Brei) have also been randomized within the angular range covered by the fired detector.
In order to extract a true correlation signal above any combinatorial background level, the same dist.ribution has also been calculated for a sample of so-called mixed events which has been generated in accordance with the prescriptions of Ref. 12, i.e. taking the photon from one event and the proton from another randomly-chosen event. In order to minimize the statistical error in the mixed-event invariant-mass distribution, the total number of mixed events is 150 times larger than that of real events. The difference spectrum between the real- and mixed-event invariant mass distributions lIorInalized each ot.her to the same integral is shown in the panel (a) of Fig. 1. It is worth emphasizing that both in real and mixed distributions the detector efficiency f( Bred, as a function of the photon-proton relative angle, has been properly taken into account and that t.he used bin of 20 Me V has been chosen equal to the maximum invariant mass resolution (O'-value) possible in this experiment (see Ref. 10).
The distribution plotted in the panel (a) of Fig. 1 shows a correlation around mint' = 1000 Me V (even if points have large error bars) and a smaller but clearer "negative-positive" signal above minv = 1060 MeV (indicated by the arrow in the panel). In order to quantitatively estimate the significance of these two signals with the respect to the null distribution (i.e. no signal at all) we separately applied the x2-test to the point.s below and above minv = 1060 MeV. The results of the test are x2/ndflmmv<1060Md' = 1.15 and x2/n({flrnmv>1060MeV = 98.12 indicating that the first signal is statistically much smaller than how it appears looking at the figure while the second one is absolutely real. The physical interpretation of the first one is quite easy: it is related to those photons emitted in incoherent nucleon-nucleon collisions and it is present here only because of the combination of the proton rest mass with the average values of proton and photon energies above their thresholds (mp + Ep + E"( '" 1000 MeV). The second signal is, on the contrary, quite unexpected and its interpretation is not obvious at first sight. It is, however, placed in the same range of invariant masses where we observed the signal due to the hadronic decay of the b.-resonance (see Fig. 1, upper panel, of Ref. 1). In order to further investigate on its origin, we then conditioned
3
4
------ >= (f)
c :::J 0 900 1000 1100 1200 1300
D L (,,-p) invariant moss (MeV) 0
u (c) OJ -100 200 - >- '"' (f)
c 100 ::J
L
-300 >= E,< 1 00 MeV -300 -
I I I
900 1000 1100 1200 1300 900 1000 1100 1200 1300
(,,-p) invariant moss (MeV) (,,-p) invariant moss (MeV)
Figure 1. Panel (a): difference sp"ctrum bctwE'cn normalized real- and mlJ'ed-cvent b - p) invariant-mass distributions. Panel (b): the same as in panel (a) for E, > 100 MeV. Panel (c): the same as in panel (a.) for E, < 100 MeV. Tn all panels data are corrected for the relative-angle efficiency (see text).
tlH' invariant-mass difference spectrum plotted in panel (a) with two separate regions of the photon energy spectrum. Results are reported in panels (b) and (c) of Fig. 1. Panel (b) refers to those photons with an energy larger than 100 MeV (we shall call them "high-energy" photons or HE-photons), while panel (c) refers to those photons hayiug an energy lying between :30 and 100 MeV (we shall call them "low-energy" photons. or LE-photons). The energy threshold of 100 MeV has been chosen looking at the results of the theoretical calculations performed in Ref. 3,4,5 where the authors claim that photons coming from the electromagnetic decay of the ~-resonance should have an energy greater than 100 Me V in this bombarding energy regime.
For HE-photons the correlation around 1000 MeV remains alive while it almost completely disappears for LE-photons. This supports the picture that the correlation \)f'tween photons and protonR coming from single nucleon-nucleon collisions should be the more pronounced the sma.ller is the available phase-space for the proton in the elementary collision (similar conclusions have been reached by the authors of Ref. 13
reducing the available phase-space for the photon emitted in the elementary nucleon­ nucleon collision).
Concerning the most important signal around 1100 MeV, it is still present almost entirely in the case of HE-photons while it vanishes in the case of LE-photons.
Before to draw any conclusion about the origin of photons and protons producing the signal observed around minv '" 1100 MeV, one has to show, however, that no experimental bias can invalidate the results shown in Fig. 1. Some considerations to exclude other possible explanations different from the ~-resonance excitation have \)('('11 already discussed in Ref. 1 and the reader is then addressed to that paper for more details. Here we only want to report about the investigation on the possible bias due to particle misidentification. We have extracted from experimental data the difference spectra between the real- and miud-event invariant-mass distributions relative to both (f" - p) and (f - a) events. where I'" are those photons coming from 7r 0 decay. These spectra are plotted in the panel (a) and (b) of Fig. 2, respectively. No signal above the statistical errors is observed. The same ,\ 2-test discussed above has been applied to the points of the distributions plotted in panel (a) and (b). The results are y2/ndf = 3.77 for panel-( a) distribution and \,2 /1l(~f = 1.:32 for panel-(b) distribution.
As it has been shown in Ref. 1, the excitation of the ~ resonance in nuclear matter can be investigated looking not only at the momentum-energy correlations (as done so far) but also at the geometrical ones. Photons and protons coming from ~ decay should indeed evidence definite correlations in their relative angle distribution. Starting from the measured (f - ]J) invariant mass, it is easy to calculate a ~ velocity distribution which is peaked at small values, about 0.2-0.25 c. This should allow us to expect a preferential back-lo-back angular correlation even in the laboratory frame between the photon and the proton. In the panel (a) of Fig. 3 is plotted the ratio:
Rr/m = (dN/dBrel)realevents (dN / dBrei )mixedevents
(2)
bE'tweE'n the normalized h - p) real- and mixed-event relative-angle distributions. It is worth noting that a bin larger than the experimental resolution of Brei (see above) has been used and that thE' relative anglE' efficiency has been taken into account.
The distribution is strongly peaked at small relative angles, where the contribution of photons coming from incoherent nucleon-nucleon collisions is mostly expected, but it also shows a signal at much larger relative angles (indicated by the arrow in the panel). In order to disentangle the contribution of direct photons from that due to indirect ones, we conditioned the invariant-mass difference spectrum plotted in panel (a) of Fig. 1
5
6
o f :J
.D 0 ¢ 0 0 0 0 0 0 0 0 0 '- 0
'-../ -100 u Q)
(y"-p) invariant mass (MeV)
r---. (J)
+-' 100 f-c
? t ? ? ¢ Q 0 0 0 0 0 0 0 0 0
::J
>= -300 -
3700 3750 3800 3850 3900 3950 4000 4050 4100
(y-ex) invariant mass (MeV)
Figure 2. Panel (a): difference spect,rum between normalized real- and lIl1J;ed-event ('rn - p)
invariant-mass distributions (see test for the meaning of "Y"). Panel (b): the same as in panel (a) for (")' - a) events. In all panels data are corrected for the relative-angle efficiency (see text).
(0) 1.4 r-
1.2 r- signal
eas19",,<0.6
C :J
..0 L
(-y-p) invariant moss (MeV)
-50 t- t1 QJ 0 27AI(16Ar,-yp) >= -15 t-
-200 t:- eas19, .. >0.6
-250 -.l I I
(-y-p) invariant mass (MeV)
Figure 3. Panel (a): Ratio between real- and mixed-event yields as a function of the cosine of the correlation angle. Panel (b): difference spectrum between normalized real- and mixed-event (,- p) invariant-mass distributions for cos Orel < 0.6. Panel (c): the same as in panel (b) far cos Orel > 0.6. In all panels data are corrected for the relative-angle efficiency (see text).
7
with two separate regions of the (,- p) rdative angle distribution. Results are reported in panels (b) and (c) of Fig. 3. Pand (b) refers to those photon-proton pairs for which ('os B,r! < 0.6 (we shall call them "large-angle" pairs or LA-pa.irs), while panel (c) refers to those photon-proton pairs having C08 Brei > 0.6 (we shall call them "small-angle" pairs, or SA-pairs). In tl1f' ('ase of LA-pa.irs the signal around mill!' = 11 00 MeV is still present, while in the ('ase of SA-pairs it ('ompietdy disappears.
All experimental evicienn's des(')'ibed so far indi('ate that we are really observing the excitation of the [-,. j'('sonan('e in nucif'ar matter and its subsequcnt eledromagnetic decay. Then the energy of the photon and that of tl1f' proton ('an not be barely inde­ pendent one from each otlwr (sinn' both particles ('0111<" frolll the decay of a resonant state) and a corrdatioll signa.! should be visihle in the (Ep - F')) planc. In fa.ct. if two particles (let us call them 1 and 2) come fmlll the binary decay of (l resonant state their energies must define a locus in the plalle (E1 - E2)' This locu:-; is thc straight line E1 + E2 = canst if the parent state is (alillost) at rest ill the lahoratory reference frame. As it has been already said ahove. the [-,. velocity distribution is peak(~d at small values so that one should observe a correlation all around tlw locus Ep + E-i = con.st independently of the photon energy and photon-proton relative angle. Ac!.ually, the real situation is not so simple due to the presence of the huge ba('kground coming from nn('Qrrelated photons and protons ami a comparative analysis of real- andmi;red-event distributions is mandatory.
Panel (a) of Fig. 4 shows the ratio between the real and mLred event bi-dimensional distrilmtions of the photon energy vs. the proton kinetic energy. Indeed. a clear ('orrelation signal emerges all around the lo('us Ep + E" = con.si, which is drawn in the figure as a straight lille. The existence of the correlation sign(ll and its constant presence over all the photon and proton energy ranges are cOllfirmed by the shapes of the projections of the distribution plotted ill pallel (a) on all axis perpendicular to the axis Ep + E, = canst and on the axis Ep + K, = cOllsf itself. which aTC reported in panel (b) and (c) of Fig. 'L respec1.ivclv.
This signal is not due to any experimental bias and i1 is cha.raderistic of (, - p) events as it is demonstrated ill Fig. :) w \inC' the experi Illental real-even t h - J!) invariant-mass distribution (upper pand) is compared with the hIT - p) one (lower panel) where no signal is observable. In both pa.nels continuous line; are relative to the corresponding mind-event distributions normalized atnl m " = 970 MeV.
The coupling of the results on the electromagnetic decay of the [-,. reSOnanCf\ reported in this paper. with those relative to the hadronic dc('ay of the [-,. resonance, perfolTlled in Ref. 1, offers the unique' possibility to evaillate the in 17)niio branching ratio B.R.=: CT6.--tl\h/CT6.--tNIT' ~Ioreov('r, ('ompa.ring il with the f1'£'( value e<[ual to 6.10-3 , 011e
can have a global quantitative estimation of the pion re-absorption and re-scattering effects inside excited nuclear matter. The measured cross section of the indirect channel lV;V -t N [-,. -t N 1'1 I has been evaluated here using the fonnula:
O"~,
0" !J.--tN~, = rd- N 6.-+I'h ..i\...y
where 0",) is the tota.! photon produC'tion ('l'OSS section, N" is the total number of high­ energy photons detected, and N !J.--tS" is the totalnumher of high-energy photoIls coming from the indirect channel. This lal1n qlla.1l1.i1y has been evaluated normalizing the real- anel the mind-event h - I)) illvariant-Illass distributiolls (wlii('h is a very good approximation of the ('ombinatorial hackground) in tilt' region 1I?im. < I 000 MeV (where no correlation is observed) and then cakulati ng the integral of the difference spectrum in the interva.! 177inv = I 0.'iO-11.50 ME'V. The fi lIal result is CT 6.--tN" = (1.6± 1.2)/l.h which,
8
300
250
150
I I I -200 -100 0 100 200
-E,sin4So+E,cOS4So (MeV)
Figure 4. Panel (a): bi-dimensional distribution of the photon energy vs. the proton kinetic energy. The solid line indicates the locus of the points for which E,+Ep=const. Panel (b): projection of the dist.ribution plotted in panel (a) on an axis perpendicular to the axis E,+Ep=const. Panel (c): projection of the distribution plotted in panel (a) on the axis E,+Ep=const.
9
10 2 C ::J
(-y-p) invarian mass (MeV)
(')'" - p) invariant moss (MeV)
Figure 5. Panel (a): experilllental h - p) invariant-mass distribution relative (,0 real events. Panel Ib): experimental (;" - ]I) ill\'ariant-llla~s distribut.ion relative to real events (sec test for the meauing of ,"). In both panels continuous lines are relative to the corresponding 1Jll.red-event distributions. Dashed line in panel (a) is drawn to guide the eye.
10
togetllf'r with the value reported in Ref. 1 for (JA-+N" , gives B.R.=(7.6 ± 5.9) . 10-2 .
Taking into account the fact that in this experiment photons and neutral pions have been dptected in differpnt angular ranges, this value of the branching ratio, although affected by a rather large error bar, is compatible with that of 3.3 . 10-2 foreseen in Ref. 4.
SUMMARY AND CONCLUSIONS
The study of kinematical (invariant mass) and geometrical observables has al­ lowed to claim the first clear and direct. observation of the elementary indirect pro­ cess N N --+ N 6" --+ N N r whose revealability was predicted several years ago by theoretical calculations but never proved in any of the inclusive experiments realized so far. Together with those reported in Ref. 1 about the elementary indirect process NN --+ N 6" --+ N N7fo (for the same system at the same bombarding energy), the results presented here represent the up-to-date most complete information about the excitation and decay of the 6,,(12:32)-resonance in nuclear matter at around 100 MeV/nucleon.
The first estimation of the in medio branching ratio (J A-+N, / (J A-+N" has been also performed and the result is in agreement with the prediction of a microscopic theoretical calculation.
REFERENCES
1. A. Badala, R. Barbera, A. Bonasera, A. Palmeri, G. S. Pappalardo, F. Riggi, A. C. Russo, G. Russo, and R. Turrisi, Phys. Rev. C 54:R2138 (1996).
2. M. Aguilar-Benitez et al., Phys. Rf'V. D 50:1173 (1994). ~l. M. Prakash, P. Braun-Munzinger, .J. Stachel. and N. Alamanos, Phys. Rev. C 37:1959 (1988). 4. W. Bauer and G. F. Bertsch, Phys. Lett. B 22~1:16 (1989). 5. A. Bonasera, G. F. Burgio, F. Glliminelli, and H. H. Wolter, Nuovo Cimento A 103:309 (1990). 6. .1. Clayton, .J. StevE'l1son, W. Bellenson. D. Krofchek. D . .1. Morrissey, T. K. Murakitmi, and .1.
S. Winfield, Phys. Rev. C 42:1009 (1990). 7. .1. Stevenson et al., Phys. Rev. Lett. 57:555 (1986). 8. M. Kwato Njock, M. Maurel, E. Monnand, H. Nifenecker, P. Perrin, .1. A. Pinston, F. Schussler,
and Y. Schutz, Nuc/. Phys. A 48\1:368 (1988). 9. A. Schubert et al., Phys. Rev. Lett. 72:1608 (1994). 10. A. Badala, R. Barbera, A. Bonasera, M. Gulino, A. Palmeri, G. S. Pappalardo, F. Riggi, A. C.
Russo, G. Russo, and R. Turrisi, Phys. Rev. C 57:166 (1998). 11. E. Migneco et al.. Nuc/. Instrum. Methods Phys. Res., Sect. A 314:31 (1992). 12. D. Drijard, H. G. Fischer, and T. Nakada, Nucl. Instrum. Methods Phys. Res., Sect. A 225:367
(1984). 1:1. P. Sapienza et al.. Phys. Rev. Lett. 73:1769 (1994).
11
HADROCHEMICAL VS. MICROSCOPIC ANALYSIS OF PARTICLE PRODUCTION AND FREEZE-OUT IN ULTRARELATIVISTIC HEAVY ION COLLISIONS
S. A. Bass,!> S. SOff,2 M. Belkacem,2 M. Brandstetter,2 M. Bleicher,2 L. Gerland,2, J. Konopka,2 1. Neise,2 C. Spieles,2 H. Weber,2 H. Stocker,2 and W. Greiner2
1 Department of Physics, Duke University Durham, N.C. 27708-0305, USA
2 Institut fiir Theoretische Physik der J.W. Goethe Univ. Frankfurt Robert-Mayer-Str. 10, D-60054 Frankfurt am Main, Germany
INTRODUCTION
The investigation of hot and dense nuclear matter in ultra-relativistic heavy-ion collisions in general 1, 2, 3, and the search for a deconfinement phase transition from hadronic to quark matter in particular 4, 5, 6, 7, is one of the currently fastest moving research fields of nuclear physics. Hadron abundances and ratios have been suggested as possible signatures for exotic states and phase transitions in dense nuclear matter. In addition they have been applied to study the degree of chemical equilibration in a relativistic heavy-ion reaction. Bulk properties like temperatures, entropies and chemi­ cal potentials of highly excited hadronic matter have been extracted assuming thermal and chemical equilibrium 8,9,10, 11, 12, 13, 14.
The present work confronts the conclusions of a series of publications which have attempted to fit the available AGS 15 and SPS 16 data on hadron yields and ratios. The latter have been done either in the framework of a hadronizing QGP droplet 14,18 or of a hadron gas in thermal and chemical equilibrium 13 - even for elementary proton­ proton interactions 11. It has been shown that the thermodynamic parameters T and MB imply that these systems have been either very close to or even above the critical T, MB line for QGP formation 13,14.
Here, in contrast, the microscopic Ultra-relativistic Quantum Molecular Dynamics transport model (UrQMD) 19 is used to calculate hadron ratios without thermalization assumptions and to perform an analysis of the freeze-out dynamics leading to the hadronic final state.
'Feodor Lynen Fellow of the Alexander v. Humboldt Foundation
13
Table 1. Baryons and baryon-resonances included into the UrQMD model. Through baryon-antibaryon symmetry the respective antibaryon states are included as well.
N938 L'l1232 All16 I:1l92 3 1315 fl1672
N 1440 L'l1600 A1405 I:1385 3 1530
N 1520 L'l1620 A1520 I:1660 3 1690
N 1535 L'll700 A1600 I:1670 3 1820
N 1650 L'l1900 A1670 I:1750 3 1950
N 1675 L'l1905 A1690 I: l775 3 2030
N 1680 L'l1910 A1800 I:1915
N l700 L'l1920 A18lO I:1940
Nl7lO L'l1930 A1820 I:2030
N l720 L'l1950 A1830
The UrQMD Model
The UrQMD model 19 is based on analogous principles as (Relativistic) Quantum Molecular Dynamics 20, 21, 22, 23, 24. Hadrons are represented by Gaussians in phase space. The nucleons are initialized in spheres of radius R = 1.12A1/ 3 fm. Momenta are chosen according to a non-interacting Fermi-gas ansatz. Hadrons arc then propagated according to Hamilton's equation of motion.
The microscopic evolution of the hadrochemistry in heavy-ion reactions requires the solution of a set of hundreds of coupled (Boltzmann-type) integro-differential equa­ tions. This means that all (known) hadrons need to be included into the model as realistically as possible. The collision term of the UrQMD model treats 55 different isospin (T) degenerate baryon (B) species (including nucleon-, delta- and hyperon- res­ onances with masses up to 2.25 GeV) and 32 different T-degenerate meson (M) species, including (strange) meson resonances as well as the corresponding anti-particles, i.e. full particle/antiparticle symmetry is included. The number of implemented baryons therefore defines the number of antibaryons in the model and the alltibaryon-antibaryon interaction is defined via the baryon-baryon interaction cross sections. Isospin is ex­ plicitly treated (although the SU(2) multiplets are assumed to be degenerate in mass). The baryons and baryon-resonances which can be populated in UrQMD are listed in table 1, the respective mesons in table 2. The states listed can either be produced in string decays, s-channel collisions or resonance decays. For excitations with masses> 2 GeV (B) and 1.5 GeV (M) a string model is used. All (anti-)particle states can be produced - in accordance with the conservation laws - both, in the string decays as well as in s-channel collisions or in resonance decays.
Tabulated or parameterized experimental cross sections are used when available. Resonance absorption and scattering is handled via the principle of detailed balance. If no experimental information is available, the cross section is either calculated via an OBE model or via a modified additive quark model, which takes basic phase space properties into account. The baryon-anti baryon annihilation cross section is parameter-
14
Table 2. Mesons and meson-resonances, sorted with respect to spin and parity, included into the UrQMD model.
0-+ 1-- 0++ 1++ 1+- 2++ (1--)* (1--)**
11" P ao al b1 a2 P1450 P1700
K K* K* 0 K* 1 Kl K* 2 Ki410 Ki680
rJ w fo It hI h W1420 W1662
rJ' <P fa f~ h' 1 f~ <P1680 <P1900
ized as the proton-antiproton annihilation cross section and then rescaled to equivalent relative momenta in the incoming channel. For a detailed overview of the elementary cross sections and string excitation scheme included in the UrQMD model, see ref. 19.
The UrQMD model allows for systematic studies of heavy-ion collisions over a wide range of energies in a unique way: the basic concepts and the physics input used in the calculation are the same for all energies. A relativistic cascade is applicable over the entire range of energies from 100 MeV/nucleon up to 200 GeV /nucleon (a molecular dynamics scheme using a hard Skyrme interaction is used between 100 MeV/nucleon and 4 GeV /nucleon). However, UrQMD can also perform infinite matter calculations by evolving the initial state in a box with periodic boundary conditions. Thus, the equilibrium limit of the UrQMD transport model may be investigated in a unique fashion (see the following section).
Equilibrium Properties - Infinite Matter Limit
Equilibrium properties of the microscopic transport model are of utmost theoretical interest, since they define the actual equation of state, which is hidden in particle properties, potential interaction, cross sections etc .. Fig. 1 shows the result of a UrQMD simulation of infinite matter, i.e. hadronic matter in a box with periodic boundary conditions, after the system has reached equilibrium. The l.h.s. depicts energy spectra for nucleons, deltas and pions after obtaining thermal equilibrium. The temperature of approximately 95 MeV and the obtained delta to nuCleon ratio are consistent with the theoretical expectation for a hadron gas. This can be seen on the r.h.s. which displays the delta to nucleon ratio for box-calculations with different initial conditions. The gray shaded area shows the delta to nucleon ratio calculated from the law of mass action in a Boltzmann approximation, taking fluctuations in the delta mass into account. The microscopic equilibration process is due to elastic and inelastic binary collisions, resonance excitation and decay, and - at high energy densities - even string formation and fragmentation.
Having established that UrQMD in its infinite matter mode evolves into a state of thermal and chemical equilibrium we now may proceed to probe the resulting equation of state. Figure 2 shows the energy density as a function of temperature for UrQMD (cascade mode), a Hagedorn gas with a limiting temperature of 165 MeV and an ideal hadron gas containing the same degrees of freedom (i.e. hadrons) as UrQMD. In order to obtain this EoS in UrQMD, nuclear matter has been initialized at ground state density and varying energy densities. The temperatures have been extracted (after evolving the system for several hundred fm/c in order to establish equilibrium) from Boltzmann-fits to energy spectra of different hadron species. For low energy densities a steep rise with temperature is visible, which is in agreement with the ideal hadron gas model. For higher energy densities, however, UrQMD exhibits a limiting temperature
15
0.5 1.0 1.5 2.0 40 60 80 100 140 120
Etot (GeV) T (MeV)
Figure 1. UrQMD infinite matter calculation. Energy spectra for nucleons, deltas and pions are shown on the left and the delta to nucleon ratio vs. temperature is shown on the right. The calculation yields thermal and chemical equilibrium with the particle ratios agreeing well with the obtained temperatures.
of T = 135 ± 5 MeV, in a similar fashion as a Hagedorn gas. Note that the comparison to the Hagedorn EoS must remain a qualitative one, since the Hagedorn EoS depicted in figure 2 has been obtained with ME = O,ILs = O. The deviation of UrQMD from an ideal hadron gas for high energy densities is understandable since in UrQMD string degrees offreedom act as an infinite reservoir of "heavy resonances" (analogously to the exponential mass spectrum in a Hagedorn gas) whereas the ideal hadron gas calculation only contains the hadronic degrees of freedom listed in tables 1 and 2. In the region of temperature saturation, the hadron ratios in UrQMD may not anymore be consistent with the limiting temperature obtained from energy spectra. A detailed investigation of the equilibrium properties of UrQMD can be found in reference 25.
Ratios and Abundances in Heavy-Ion Collisions
Let us now make a comparison between a compilation of experimental measure­ ments 17 of hadron production in elementary proton-proton collisions with yields as calculated by the UrQMD model in figure 3. This is an important issue since the pre­ dictive power of the transport model for nucleus-nucleus collisions can only be estimated correctly when its performance on elementary hadron production is known.
Note the overall good agreement (compatible to thermal model fits 17 yielding a temperature of 170 Me V) which spans three orders of magnitude. ¢-production is underestimated by a factor of 2. A + ~o (as well as the A + to) production is over­ estimated. Problems in the strangeness sector are common to most string models and indicate that strangeness production is not yet fully understood on the elementary level 26. These deviations in the elementary channel have to be considered when comparing with heavy-ion experiments.
Unlike simple non-expanding fireball models , UrQMD describes also the momen­ tum distributions (e.g. the dN/dy, dN/dxF and dN/dpt distributions) for all hadron species under consideration. A detailed description and a com parison to available hadron-hadron data can be found in ref. 19.
How do hadron ratios in elementary nucleon-nucleon interactions compare to those stemming from the final state of a nucleus-nucleus reaction? Do isospin and secondary
16
1.0
UrQMD
T (GeV)
Figure 2. UrQMD Equation of State (diamonds). Also plotted is a hadron gas EoS, using the same degrees of freedom as UrQMD (full line), and a Hagedorn EoS with a limiting temperature of 165 Me V (dotted line).
interactions playa major role or is the hadronic makeup of the system fixed after the first primordial highly energetic nucleon-nucleon collisions? Since even the particle abundances in elementary proton-proton reactions may be described in a "thermal" model 17 one could speculate that the hadronic final state of a nucleus-nucleus collision should not differ considerably from the primordial "thermal" composition. The upper frame of figure 4 shows hadron ratios calculated by the UrQMD model for the S+Au system at CERN/SPS energies around mid-rapidity Ylab = 3 ± 0.5 (full circles). The ratios are compared to those stemming from a proton-proton calculation (open squares) and from a nucleon-nucleon calculation, i.e. with the correct isospin weighting (open triangles) for the primordial S+Au system, which is obtained by weighting a cocktail of pp, pn and nn events in the following way: N N(S+Au) = 0.188·pp+0.55·pn+0.27·nn.
The correct isospin treatment is of utmost importance, as it has a large influence on the primordial hadron ratios: Due to isospin conservation the pip and A/(p - p) ratios are enhanced by '" 30% and", 40%, respectively; it is easier to produce neutral or negatively charged particles in a nn or pn collision than in a pp interaction.
Rescattering effects, which are visible when comparing the nucleon-nucleon calcu­ lation (open triangles) with the full S+Au calculation (full circles), have even a larger influence on the hadron ratios than isospin: Changes in the ratios due to rescattering are easily on the order of 20%-50%. Ratios involving anti baryons even change by factors of 3 - 5, due to their high hadronic annihilation cross section. Most prominent examples are the ratios of '3/2 (factor 5 suppression), PiP (factor 3 suppression), AI A (factor 2 suppression), 2- IA (factor 2 enhancement) and KUA (factor 3 enhancement).
The lower frame of figure 4 compares the UrQMD hadron ratios with experimental measurements 16. We use a data compilation which has been published in ref. 13. The open circles represent the measurements whereas the full circles show the respective UrQMD calculation for S+Au at 200 GeV Inucleon and impact parameters between 0 and 1.5 fm. For each ratio the respective acceptance cuts, as listed in 13, have been
17
multiplicity (UrQMD)
Figure 3. UrQMD hadron yields in elementary proton-proton reactions at JS = 27 GeV compared to data. The overall agreement spanning three orders of magnitude is good - the most prominent deviations from the experiment occur for the <p-meson and for (anti-) A + ~o
applied. The size of the statistical error-bars of the UrQMD model does not exceed the size of the plot-symbols. The crosses denote a fit with a dynamical hadronization scheme, where thermodynamic equilibrium between a quark blob and the hadron layer is imposed 14. A good overall agreement between the data and the UrQMD model is observed, of similar quality as that of the hadronization model. Large differences between UrQMD and experiment, however , are visible in the ¢/(p + w) , KU A and 0,/2 ratios. Those discrepancies can be traced back to the elementary UrQMD input. A comparison with figure 3 shows e.g. the underestimation of the elementary c,b-yield in proton-proton reactions by a factor of 2.
A thermal and chemical equilibrium model can be even used to fit the hadron ratios of the UrQMD calculation displayed in the upper frame of figure 4. The parameters of the thermal model fit to the microscopic calculation in the Ylab = 3 ± 0.5 region (a detailed discussion of the rapidity dependence of the ratios is given below) yields a temperature of T = 145 MeV and a baryo-chemical potential of MB = 165 MeV. However, the assumption of global thermal and chemical equilibrium is not justified: Both, the discovery of directed collective flow of baryons and anti-flow of mesons in Pb+Pb reactions at 160 GeV / nucleon energies27, 28 as well as transport model analysis, which show distinctly different freeze-out times and radii for different hadron species (see the following section as well as refs. 29,30), indicate that the yields and ratios result from a complex non-equilibrium time evolution of the hadronic system. A thermal model fit to a non-equilibrium transport model (and to the data!) may therefore not seem meaningful.
The large difference in the Ko/A ratio (as calculated by UrQMD) visible between figure 4a) and figure 4b) exemplifies the strong dependence of the hadron ratios on the experimental acceptances: While the experimental acceptance in rapidity is similar to the cut employed in figure 4a), the additional cut in Pt, which has been performed in
18
2 r-~~~~~-----------.------~ 102 0 d •••
)C nGn-eq . model (Incl . reedinsl't 5/A'"~'5. '.= 0. A._ IOO. B =235 M.V b)
• UrQMD 5+ Au (wi.h exp. <uti)
hadron ratios
Figure 4. Top: UrQMD calculation of hadron ratios in S+Au collisions at mid-rapidity (full circles). The ratios are compared to a proton-proton calculation (open squares) and a nucleon-nucleon calculation (correct isospin weighting) (open triangles). Bottom: Comparison between the UrQMD model (full circles) and data (open circles) for the system S+Au(W,Pb) at 200 GeV Inucleon. Also shown is a fit by a microscopic hadronization model (crosses). Both non-equilibrium models agree well with the data. Discrepancies are visible for the ,pI (p + w), KVA and 0./3 ratios.
figure 4b), changes the ratio by one order of magnitude. The rapidity dependence of individual hadron ratios ~ is shown in Figure 5: The
pl1f+, 'TJ11fo, K+ I K-, pip, Alp and KU A ratios are plotted as a function of Ylab for the system S+Au (upper frame) and as a function of Yc.m. for the system Pb+Pb (lower frame). A strong dependence of the ratios Ri on the rapidity is visible - some ratios, especially those involving (anti-) baryons, change by orders of magnitude when going from target rapidity to mid-rapidity. The y-dependence in the S+Au case is enhanced by the strong mass asymmetry between projectile and target which leads to strong absorption of mesons and anti baryons in the heavy target. The observed shapes of Ri (y) are distinctly different from a fireball ansatz, incorporating additional longitudinal flow: There, the ratios would also be symmetric with respect to the rapidity of the central source. A broad plateau would only be visible for ratios of particles with similar masses. When fitting a thermal model to data, one must take this rapidity dependence into account and correct for different experimental acceptances.
Figure 6 shows the UrQMD prediction for the heavy system Pb+Pb. The ra­ tios around mid-rapidity (full circles) are again compared to those stemming from an isospin-weighted nucleon-nucleon calculation (open triangles). For this heavy system, rescattering effects are even larger than in the S+Au case: Due to the large number of baryons around mid-rapidity, antibaryon annihilation at mid-rapidity occurs more
19
.... ... .. .... . l' •
.. " •• I ••• ,: ..... :""" ••..••• ! . . . ,
10" L--o--.....L-~---3----L--..::..:....---'
10' •
Pb+Pb. 160 GeV /nucleon t t t t t t ••••••••••••••
•• 111.1111, .-., 11 J .,~
d'" i f
I ! i • pl.· · ~/"
• K+/K' .. pbar/p
YCM
Figure 5. Rapidity dependence of hadron ratios in the UrQMD model for the system S+Au(W,Pb) (top) and Pb+Pb (bottom) at CERN/SPS energies_ The ratios vary by orders of magnitude, yielding different T and J-LB values for different rapidity intervals,
often and therefore ratios involving anti baryons may be suppressed stronger than in the S+Au case, Most prominent examples are (again) the SIS (factor 20 suppression), pip (factor 8 suppression) and the KVA (factor 3 enhancement) ratios,
Details in the treatment of the baryon-antibaryon annihilation cross section may have a large influence on the final yield of antiprotons and antihyperons: If the proton­ antiproton annihilation cross section as a function of Vs is used for all baryon-antibaryon annihilations, instead of rescaling the cross section to equivalent relative momenta, the S yield in central Pb+Pb reactions at 160 GcV Inucleon would be enhanced by a factor of 3. The p and Y yields would then be enhanced by 50% and 25%, respectively.
A systematic study of different baryon to antibaryon ratios as functions of sys­ tem size, impact parameter, transverse momentum and azimuthal angle may help to gain further insight into the antihyperon-nuc!eon and antihyperon-hyperon annihilation cross section.
Analysis of Freeze-out
One possible way of tackling the issue whether the final hadronic yields in a heavy­ ion reaction stem from an equilibrated fireball or from a complex non-equilibrium time
20
5 .-----------------~~~~~_r~--.__r~__,
D. UrQMD NN(Pb+Pb) I Pb+Pb, 160 GeV /nucleon 2
2
hadron ratio Rj
Figure 6. UrQMD prediction for hadron ratios in Pb+Pb collisions at mid-rapidity (full circles). The ratios are compared to a superposition of pp, pn and nn reactions with the isospin weight of the Pb+Pb system (open triangles), i.e. a first collision approach. Especially in the sector of anti-baryons the ratios change by at least one order of magnitude due to the large anti-baryon annihilation cross section.
evolution of the hadronic system is to investigate the question if all hadron species exhibit a uniform freeze-out behavior - or if each species has its own complicated space-time dependent freeze-out profile.
As a first step we investigate the origin of pions - the most abundant meson species -- in central Pb+Pb collisions at 160 GeV /nucleon. Figure 7 displays the respective sources from which negatively charged pions freeze-out. Only inelastic processes have been taken into account. Approximately 80% of the pions stem from resonance decays, only about 20% originate from direct production via string fragmentation. Elastic meson-meson or meson-baryon scattering adds a background of 20% to those numbers, i.e. 20% of all pions scatter elastically after their last inelastic interaction before freeze­ out. The decay contribution is dominanted by the p, wand k* meson-resonances and the b.1232 baryon-resonance. However, more than 25% of the decay-pions originate from a multitude of different meson- and baryon-resonance states, some of which are shown on the l.h.s. of figure 7; e. g. the two contributions marked p* stem from the P1435 and the P1700, respectively.
The analysis of the pion sources is of great importance for the understanding of the reaction dynamics and for the interpretation of HBT correlation analysis results. The 20% contribution of pions originating from string fragmentation is clearly non-thermal, since string excitation is only prevalent in the most violent, early reaction stages.
Let us now turn to freeze-out distributions for individual hadron species: Figure 8 shows the freeze-out time distribution for pions, kaons, antikaons and hyperons at mid­ rapidity in central Pb+Pb reactions at 160 GeV /nucleon. The distributions have been normalized in order to compare the shapes and not the absolute values. In contrast to the situation at 2 GeV /nucleon, where each meson species exhibits distinctly different
21
o total decay string
200
150
100
50
p w
- 7r sources
Figure 7. Pion sources in central Pb+Pb collisions at CERN energies: 80% of the final pions stem from resonance decays and 20% from direct production via string fragmentation. Decay-pions predominantly are emitted from the p and w mesons and the ~1232 resonance.
freeze-out time distributions 19 , all meson species here show surprisingly similar freeze­ out behavior - the freeze-out time distributions all closely resemble each other. Only the hyperons show an entirely different freeze-out behavior. Whereas the common freeze­ out characteristics of the mesons seem to hint at least at a partial thermalization, the hyperons show that even at SPS energies there exists no common global freeze­ out for all hadron species. The same observation applies also to the distribution of transverse freeze-out radii. Since these distributions have a large width, the average freeze-out radius clearly does not define a freeze-out volume and therefore estimates of the reaction volume or energy density based on average freeze-out radii have to be regarded with great scepticism. The large width of the freeze-out distributions is supported experimentally by HBT source analysis which indicate the emitting pion source to be "transparent" , emitting pions from everywhere rather than from a thin surface layer 32.
Unfortunately, neither freeze-out density, nor freeze-out time, is directly observ­ able. However, figure 9 shows that we can establish a correlation between high trans­ verse momenta and early freeze-out times, at least in heavy collision systems. In figure 9 the freeze-out time of pions is plotted versus their transverse momenta for p+p, S+S and Pb+Pb reactions at SPS energies. Naturally, the proton-proton system does not show any correlation, whereas in the heavy Pb+ Pb system a strong pcdependence of the freeze-out time is visible. Such a correlation is distinctly non-thermal. Selecting particles with high transverse momenta yields a sample of particles with predominantly early freeze-out times and high freeze-out densities.
Summary and Conclusions
We have performed a hadrochemical analysis of particle production and freeze-out in ultrarelativistic heavy ion collisions within the microscopic Ultrarealtivistic Quan­ tum Molecular Dynamics (UrQMD) transport approach. The equilibrium properties of UrQMD have been investigated in the infinite matter limit, yielding a hadron-gas equa­ tion of state with a limiting temperature of approximately 135 MeV, due to the popu­ lation of string degrees of freedom . Ratios of hadronic abundances for Vs N N "" 20 Ge V
22
0,01 U.QMD 1.0 • pions
20 ~U--.Q~M~D~1.0~-----O~~:-.I~S~Y-<~--S I~~-----' 18 • Pb+Pb
_O,Ofj cut YeM ± 1 • K+
'tI ~ K" ., "+1: :S! 0,05
'"
j -... -a_ ........
z t 'tI
O,g 0 10 20
o L-------~ ______________ ~ __ ~ 30 40
tr, ..... out (fm/c) 50 60 0.0 0.2 0,4 0,6 0,8 1.0 1,2 1,4
PI (GeV)
Figure 8. Normalized freeze-out time distribution Figure 9. Freeze-out time of pions as a function of for pions, kaons, antikaons and hyperons, As with transverse momentum for p+p, S+S and Pb+Pb the freeze-out radii, the times for the meson species reactions at CERN/SPS energies, For heavy are very similar. The hyperons again show a systems early freeze-out is correlated to high Pt. different behavior,
and freeze-out properties have been analyzed. A comparison to data shows good agree­ ment. Discrepancies can be found in the c/J/(p + w), KUA and 0,/3 ratios. The resulting ratios have been compared to the primordial abundances from a cocktail of elementary pp, pn and nn interactions and then analyzed with respect to their de­ pendence on secondary interactions and on rapidity. Hadron ratios for the symmetric heavy system Pb+ Pb far from the elementary primordial nucleon-nucleon values have been predicted, The strong dependence of the ratios on rapidity, the broad freeze-out distributions of different hadron species and differences in those distributions between hyperons and mesons cast strong doubt on the assumption of thermal and chemical equilibrium, which has been prevalent in previous analysis.
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D, Hahn and H, Stocker, Nuc!. Phys. A476, 718 (1988), D, Hahn and H, StOcker, Nuc!. Phys, A452, 723 (1986), H, Stocker and W, Greiner, Phys, Rep. 137, 277 (1986),
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12. J. Cleymans, M. I. Gorenstein, J. Stalnacke and E. Suhonen, Phys. Scripta 48,277 (1993). J. Cleymans and H. Satz, Z. Phys. C57, 135 (1993). J. Cleymans, D. Elliott, H. Satz, R.L. Thews, Z. Phys. C74,319 (1997)
13. P. Braun-Munzinger, J. Stachel, J. P. Wessels, and N. Xu, Phys. Lett. B344, 43 (1995), nucl-th/9410026 and Phys. Lett. B365, 1 (1996), nucl-th/9508020. P. Braun-Munzinger and J. Stachel, Nucl. Phys. A606, 320 (1996).
14. C. Spieles, H. StOcker, and C. Greiner, Z. Phys. C, in print (1997), nucl-th/9704008. C. Greiner and H. Stocker., Phys. Rev. D44, 3517 (1992).
15. S. E. Eiseman et al., Phys. Lett. B297, 44 (1992). J. Barrette et al., Z. Phys. C59, 211 (1993). T. Abbott et al., Phys. Rev. C50, 1024 (1994). G. S. F. Stephans et al., Nucl. Phys. A566, 269c (1994). S. E. Eiseman et al., Phys. Lett. B325, 322 (1994). J. Barrette et al., Phys. Lett. B351, 93 (1995).
16. E. Andersen et al., Phys. Lett. B294, 127 (1992). E. Andersen et al., Phys. Lett. B327, 433 (1994). M. Murray et al., Nucl. Phys. A566, 589c (1994). J. T. Mitchell, Nucl. Phys. A566, 415c (1994). M. Gadzicki et al., Nucl. Phys. A590, 197c (1995). S. Abatzis et al., Phys. Lett. B316, 615 (1993). D. D. Bari et al., Nucl. Phys. A590, 307c (1995).
17. F. Becattini and U. Heinz, Z. Phys. C76, 269 (1997), hep-ph/9702274. 18. H. W. Barz, B. L. Friman, J. Knoll, and H. Schultz, Nucl. Phys. A484, 661 (1988). 19. S. A. Bass, M. Belkacem, M. Bleicher, M. Brandstetter, C. Ernst, L. Gerland, C. Hartnack,
S. Hofmann, J. Konopka, G. Mao, L. Neise, S. Soff, C. Spieles, H. Weber, N. Amelin, J. Aichelin, H. Stocker and W. Greiner, to appear in Progr. Part. Nucl. Physics Vol. 41 (1998). M. Bleicher, C. Spieles, L. Gerland, S. A. Bass, M. Belkacem, M. Brandstetter, C. Ernst, S. Hof­ mann, J. Konopka, G. Mao, L. Neise, S. Soff, H. Weber H. Stocker and W. Greiner, to be sumitted to Phys. Rev. C
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C. Ernst, 1. Gerland, G. Mao, L. Neise, S. Soff, H. Weber, H. Stocker and W. Greiner, manuscript in preparation
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24
} National Superconducting Cyclotron Laboratory and Department of Physics and Astronomy Michigan State University East Lansing, Michigan 48824-1321, USA
2Department of Physics Grinnell College Grinnell, Iowa 50112, USA
3Department of Physics Linfield College McMinnville, Oregon 97128-6894, USA
INTRODUCTION
One of the premier challenges of the ultra-relativistic reaction physics program is to gain information on the space-time history of heavy-ion reactions. This is by no means a trivial undertaking, because all that is experimentally attainable is the measurement of the asymptotic momentum states of the final products of the reaction. Measuring two-particle correlations of hadrons emitted during the reaction provides at least an indirect way of obtaining space- time information.} Radronic probes, however, have large final state interactions and thus are not sensitive to the initial high-density and high­ temperature phase of a heavy-ion reaction. Consequently, any information embedded in hadronic dynamics is completely masked by multiple scatterings. Dileptons are not disturbed by the hadronic environment even though they are produced at all stages of the collisions as they have long mean free paths. They are dubbed "clean probes" of the collision dynamics. This is what we need, if we want to learn about possible phase transitions (quark-gluon-plasma formation, restoration of chiral symmetry, ... ) in the early stages of ultra-relativistic heavy-ion collisions.
There are at least two ways how to proceed in the investigation of experimental signals:
1. Compare the experimental results to the best model simulations incorporating all known information on conventional reaction dynamics and elementary processes .
• email: bauerlDns cl . rnsu. edu urI: http://lo7lo7lo7 . nscl. rnsu. edu;-bauer /
25
2. Compare the experimental results of nucleus-nucleus collisions to those from nucleon-nucleus and nucleon-nucleon collisions at equivalent energies, appropri­ ately scaled.
The last decade has taught us that neither mode of operation is free from danger, however (see, for example, the long-lasting confusion regarding the transverse-energy "puzzle" 2).
Method 2 was applied to the interpretation of di-Iepton pair signals (e+e-) by the CERES collaboration at CERN.3 The proton-induced reactions (p+Be and p+Au at 450 GeV) are consistent with predictions from primary particle production and subsequent radiative and/or Dalitz decays, suggesting that the e+ c- yields are fairly well understood. Yet, the heavy-ion data (S+Au at 200 GeV /n and Pb+Au at 158 GeV In) show a significant excess as compared to the same model for meson production and electromagnetic decays. When integrated over pair invariant mass up to 1.5 GeV, the number of electron pairs exceeded the "cockta.il" prediction by a factor of 5±2. It is clear that two-pion annihilation contrihutes in the heavy-ion reactions as fireball-like features emerge and support copious pion production." Vector dominance arguments would naturally lead to extra production around the rho mass. Yet, the excess is most pronounced between the two-pion threshold and the rho mass.
Theorists, of course, prefer method 1 above. There seemed to be some early consensus5 'that the best conventional physics explanations were not sufficient to explain the effect either in its magnitude or in its pair mass dependence. This would leave the door open to some very attractive speculations on the origin of this enhancement.
Medium modifications resulting in it shifted rho mass could be responsible.6 The mass shift postulated arises from a pa,rtial restoration of chiral symmetry. A mass shift as drastic as proposed in Ref. 6 would represent. a qualitatively new effect. Pre­ vious experience with resonances ill tll(' medium only exhibited effects like collisional broadening7 and only slight shifts of the centroids, mainly due to considerations of to­ tal available phase space.8 , 9, 10 Along these lines, conseqm~nces arising from a modified pion dispersion relation have been investigated considering finite temperature effectsll
and collisions with nucleons and 6 resonances. 12 Enhanced 'I' productioll, as suggested in Ref. 13, seems to be ruled out by inclusive photon measlll'emenbi. 14,"
The more conventional explanation of secondary scattering of pions and other resonances has also been studiedls focusing on the role of the CLI through 7r p ~ CLl ~
7r e+ e-. The contribution was shown to be relevant but not sufficient for interpreting the data. We extend the secondary scattering investigatioll in the present calculation by including non-resonance dilepton-producing 7r (J ~ 7r e+ c- reactions. In, 17
DYNAMICS
To describe the initial stages of ultra-relativistic heavy-ion collisiolls, it is necessary to use partons as the dynamical degrees of freedom. With this in mind, there are efforts underway to construct so-called parton cascades. 18, 19 These model are based on perturbative QCD and are thus attractive candidates for a. space-time transport theory in this energy regime. However, we have shown that there are severe problems with causality violations2o and with the time-ordering of soft-gluon emission. 21
Thus we feel that at the present time a more simple approach provides more reliable results: Geometrical folding of the results of event generators for the elementary processes. This approach is followed, for example, in the HIJING computer code. 22
26
The simulation we develop is similar to HIJING. It is based on a simple prescrip­ tion that uses QCD to characterize the individual nucleon-nucleon collisions and uses Glauber-type geometry to determine the scaling. The kinematics of the nucleon-nucleon collisions are handled by PYTHIA and JETSET,23 high energy event-generators using QCD matrix elements as well as the Lund fragmentation scheme. The elementary parton distribution functions are taken from the CTEQ collaboration.24
The geometrical folding employed by us is similar to the one used in Ref. 2. For each impact parameter, we determine the average number of nucleon nucleon collisions via the simple integration over density,
N(b) = (7NN J dx dy dZl dZ2 PA( Jx2 + y2 + Z12) PB( Jx2 + (y - b)2 + Z22) (1)
Using this average number, we probabilistically pick scattering partners for pro­ cessing via the PYTHIA event generator. PYTHIA chooses partons to participate in the hard scattering from each nucleon. The partons that are chosen, as well as the momentum fraction they carry, are based on known parton distributions.24 After the individual partons have had a hard scattering and are color-connected with the diquarks from the remaining nucleon, strings are formed. The kinematics of the frag­ ments from the string are determined by JETSET. Any partonic radiation that is not color-connected to either string goes directly into the nucleus-nucleus final state. This string is then put back into the nuclei and allowed to rescatter as a "wounded" nu­ cleon. The wounded nucleon has the string's momentum while its position is updated to halfway between the original nucleons' positions.
Dileptons from pseudoscalars (7r0 , '1/, '1/') and vectors (w, pO, ¢) produced in the primary scattering phase are not enough to account for the S+Au data. Our model also incorporates secondary scattering of hadronic resonances. All 7r sand P s formed during the primary collisions of nucleons will have a chance to scatter amongst themselves before decaying. The reactions we consider are of two types, one which produces a resonance that decays to dileptons and the other which goes to dileptons directly.
Of the first type, 7r+7r- -) l -) e+e- and 7r0p± -) al± -) 7r±e+e- have been included. To accomplish these types of scattering, pions and rhos must of course appear in the final state of the model described in the previous section. As the default, JETSET automatically decays all hadronic resonances, but it also contains provisions to prohibit them. We thus allow neutral pions to scatter from charged rhos when conditions are favorable.
Technically, the steps involved in secondary scattering are similar to those for primary scattering. The same geometrical considerations as for primary scattering apply, leading to an integral that is essentially similar to the one in Eq. (1), except that one now has to use different elementary cross sections, depending in the pair of scattering partners under consideration.
The cross section for creating a l resonance is taken to be
(0) _ 7r f partial2
(7 S - k2 (Vs - mres )2 + f Cul12/ 4 (2)
with k being the center-of-mass momentum. The full and partial decay widths for l-) 7r+7r- are set to 152 MeV.
The situation for creating an al resonance through 7r p scattering is handled some­ what differently than creating a pO through a 7r+7r- collision. Since our model scatters 7r'S and p's resonantly and non-resonantly, the cross section used to determine whether or not a pair will scatter should be the total cross section. The total cross section for 7r p scattering determines how many and how often the charged rhos scatter with pions.
27
Since data exists for 7r p scattering,25, 26 a parameterization can be used for the total cross section. Based on the general shape of the data, we use a simple Breit-Wigner shape for the function normalized by what the cross section should be near the al peak. The resultant cross section is parameterized for Vi ~ 0.9 GeY by
0.72 Gey2 mb a( 0) = (Vi _ 1.1 GeY)2 + r2/4) (3)
At this point, we have to point out that since the pions and rhos are scat­ tering inside the reaction zone, their dynamics are altered by the medium. Being of Bremsstrahlung type, these mechanisms are therefore susceptible to the Landau­ Pomeranchuk-Migdal effect.31 Pions and rhos involved in secondary scattering will un­ dergo frequent multiple scatterings, and not only with other pions and rhos. Therefore, the number of dileptons produced by this scattering is reduced. The reduction factor is dependent at minimum on the invariant mass of the lepton pair as well as the mean free path of the pions and rhos. We use a reduction 1- e- M \ where M is the invariant mass of the lepton pair and ,\ is the mean free path of the hadrons. For our purposes and level of estimation here, we set ,\ to some average value", 1 fm. 32
....., i -CI1
0.0 0.5 1.0 1.5 m [(GeV/c2 )]
Figure 1. Total dilepton invariant mass distributions for the reaction S + Au at 200 GeV per nucleon incident energy, including primary and secondary scattering in the model (thick histogram) as compared with CERES data (points). For comparison, we have also included (thin histogram) the result of our calculations without secondary scattering contributions.
28
The non-resonant component is estimated here by computing the sole process 7r 0 p± -+ 7r±e+ e-. The other 7r p channels that contribute to dilepton production involve Feynman graphs that result in a singularity and must be regulated in a full T-matrix or some other effective approach.27 Real photon studies28, 29 suggest that contributions from 7r± l -+ 7r±e+ e- and 7r'f p± -+ 7r°e+ e- are comparable to the process we calculated. Therefore we have assumed the same cross section and dilepton mass dependence for the other isospin channels not calculated here. To this level of estimate, isospin averaging and ignoring interference effects between these and the resonant al contributions is not worrisome. The prescription for directly scattering pions and rhos is very similar to the one used for resonance scattering, except that we calculate the scattering cross-section utilizing a Lagrangian proposed by Kapusta et al. 28
Finally, we should mention that a recent manuscript by Baier et ai.30 presents a calculation similar to ours, with results different from ours. The reason for this discrepancy is that Baier et al. only used the charged pion and neutral rho reaction, whereas our calculation focused on the charged rho and neutral pion reaction. In addition, the work by Baier et ai. contains kinematic constraints for the lepton pair that are not present in the experimental data and that were also avoided in our study.
RESULTS
A reasonable candidate for a successful model description of ultra-relativistic heavy ion collisions has to at least be able to reproduce the rapidity distributions and trans­ verse momentum spectra of the pions produced in the collisions. We have performed these test with our model and compared our results to available experimental data at CERN.I1 We will not repeat this analysis here, but only state the results: The total number of produced pions is reproduced to better than a factor of two; the shape of the dN I dy-distribution shows the correct degree of stopping; the slope of the transverse momentum spectra is reproduced. Thus we are confident that our calculations of the di-lepton spectra have the proper normalization.
In Ref. 17, we also compared our results for di-Iepton pair production in proton­ induced reactions at 450 GeV Ic to the data of the CERES collaboration. Again, we find very good agreement between our calculations and the experimental invariant mass distributions.
Finally, in Ref. 17 we have shown that the inclusion of the secondary scatter­ ing channels for the mesons has very little influence on the di-lepton pair invariant­ mass spectra in proton-nucleus collisions, but significantly improves the agreement for nucleus-nucleus collisions, both for the absolute normalization of the high-energy (Minv > 1 GeV) tails, and for the mass region around 0.5 GeV, in which the discrepancy between the CERES data and conventional calculations is largest.
The main result of our comparison for the S + Au collisions is shown in Fig. 1. The CERES data are represented by the plot symbols with their statistical error bars only. The result of our calculation is shown by the histogram. Several observations are in order:
1. The low-energy (up to 0.3 GeV) and high-energy (above 0.9 GeV) parts of the invariant mass spectrum are reproduced nicely. This, however is not too surprising - other models have accomplished more or less the same. And even without our rescattering contributions the low-energy part of the spectrum, mainly due to the Dalitz decay of the pion, is reproduced.
29
2. The spectrum is much flatter with the contributions of rescattering than without, i.e. the minimum around 0.5 Ge V is much less pronounced. Thus we are confident that the effect we are discussing here is a necessary ingredient in a complete description of the observed experimental data.
3. There is a remaining discrepancy in this region, with our calculations underpre­ dicting the data by approximately a factor of 3. This difference leaves open the possibility for additional medium effects as the ones discussed in the introduction.
Since we submitted our manuscript of Kef. 17 for publication, the CERES collab­ oration has produced additional data for Pb-projectiles at 158 GeV per nucleon beam energy. These data33 are shown in Fig. 2.
,....., -I -OIl o
0.0 0.5 1.0 1.5 m [(GeV/c 2 )]
Figure 2. Total dilepton invariant mass distributions for the reaction Pb + Au at 158 GeV per nucleon incident energy, including primary and secondary scattering in til" l1lodel (thick histogram) as compared with CERES data (points). The thin histogram is the result of a calculation that omits secondary scatterings.
Our preliminary calculations for the Pb + Au system di-Icpton invariant mass spectra are also shown in this figure (histogram). The same tendencies we discussed above for the S-induced reaction can also be observed for the heavier projectile. There is even a hint that the discrepancy between calculations and data is even bigger in the 0.2-0.7 Ge V invariant mass region than it is for the sulphur projectile.
If one compares the data for the two different projectiles, one finds that they are basically identical. Since we are dividing the di-lepton pair production numbers by
30
the numbers of charged particles in each rapidity bin, we are generating a differential branching ratio (as a function of lepton pair mass). What we can conclude from the experimental data is that this branching ratio does not drastically change as one in­ creases the projectile mass by a factor of almost 7. This is a surprising result, because the number of produced pions increases with the projectile mass. Thus the number of pi-pi collisions has to rise even stronger, and one would expect a bigger relative contribution for the pi-pi annihilation channel in the Pb-projectile reaction than in the S-projectile one, irrespective of the shift (or lack thereof) of the rho-resonance peak in medium. Our preliminary calculations seem to follow this tendency, but the data clearly do not.
CONCLUSIONS AND FUTURE PERSPECTIVES
We have introduced a new event generator for ultra-relativistic collisions. Our model is able to reproduce the phase-space distribution of pions produced in these collisions.17, 34
Within our model we have shown that secondary collisions of produced particles have and important influence on the observed di-lepton invariant mass spectra. Our results also indicate that the effect discussed by us is not a complete explanation of the observed di-lepton spectra.
Finally, we should mention that we have also compared our calculations to the HELlOS di-lepton data. For this dataset, we do not find a relevant disagreement between calculation and experiment.
It will be interesting to study the transverse momentum dependence of the di­ lepton pairs. Data should be available in the near future.
Acknowledgements
This research was supported by NSF grants PHY-9700938, PHY-9605207, PHY- 9403666, and PHY-9253505.
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31
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