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Edited by
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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
Softcover reprint o f the hardcover 1st edition 1998
http://www.plenum.com
10 9 8 7 6 5 4 3 2 1
Al l rights reserved
No part o f this book may be reproduced, stored in a retrieval
system, or transmitted in any form or by any means, electronic,
mechanical, photocopying, microfilming, recording, or otherwise,
without written
permission from the Publisher
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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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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