

 04 Aug 95

Dilepton Production at SPS Energies

\Lambda

W. Cassing, W. Ehehalt and C. M. Koy Institut f"ur Theoretische Physik, Universit"at Giessen

D-35392 Giessen, Germany

August 4, 1995

Abstract We present a nonperturbative dynamical study of e+e\Gamma production in proton-nucleus and nucleus-nucleus collisions at SPS energies on the basis of a covariant transport approach. For p + A reactions the dilepton yield for invariant masses m ^ 1.2 GeV is found to be dominated by the decays of the j; ae; ! and \Phi mesons in line with the findings of the CERES collaboration. For S + Au collisions at 200 GeV/A the dilepton yield is, however, dominated by ss+ss\Gamma annihilation due to the high pion densities achieved. Whereas for `free' meson masses and form factors the experimental cross section is slightly underestimated for 0.3 GeV ^ m ^ 0.45 GeV, different medium modifications of the ae-meson appear compatible with current CERES data.

\Lambda Work supported by BMFT and GSI Darmstadt.

yPermanent address: Cyclotron Institute and Physics Department, Texas A&M University, College Station, Texas 77843

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During the last few years a major effort in heavy-ion collisions up to bombarding energies of 200 GeV/A has been to probe the properties of hot and dense nuclear matter as well as its phase transition to the quark-gluon plasma. Apart from signatures associated with the quark-gluon degrees of freedom the partial restoration of chiral symmetry at high baryon density is of fundamental interest in its own right. Particle production plays a special role in this context [1] since mesonic and electromagnetic probes, that are not available in the initial stage of the reaction, carry information on the possible transition phase.

Contrary to mesons, electromagnetic signals are particularly well suited for an investigation of the violent phases of a high-energy heavy-ion collision because they can leave the reaction volume essentially undistorted by finalstate interactions. Whereas the direct photon signal is overwhelmed by the strong background of meson decay photons, dileptons (e+e\Gamma and _+_\Gamma pairs) are free from such problems. Indeed, dileptons from heavy-ion collisions have been observed by the DLS collaboration at the BEVALAC [2, 3, 4] and by the CERES [5] and HELIOS collaboration [6] at SPS energies.

Furthermore, dileptons can also be used as probes for the coupling of timelike photons to charged hadrons in the nuclear medium. The vector-meson dominance model assumes that this coupling proceeds through virtual q _q excitations of the QCD vacuum with the quantum numbers of the photon, i.e. through the vector mesons (mainly the ae-meson). Dileptons thus are expected to be sensitive to the properties of the ae-mesons in the medium since the latter predominantly decay still in the dense nuclear medium due to their short lifetime.

In fact, both the CERES and HELIOS collaborations have found an enhancement of dileptons in A + A collisions compared to p + A collisions for invariant masses 0.3 GeV ^ m ^ 0.6 GeV. Studies by Srivastava et al. [7] based on a quark-gluon scenario can not account for the excess dileptons. On the other hand, this enhancement has been interpreted by Li et al. [8] as a signature for chiral symmetry restoration, more precisely, as a signature

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for the dropping mass of the ae-meson in the dense medium. However, their analysis was based on an expanding fireball scenario in chemical equilibrium, which validity in S + Au collisions might be questionable. In this paper, we will thus carry out a partially related but extended study based on a nonequilibrium covariant transport model.

In continuation of our work in refs. [9, 10, 11, 12] we study the dynamics of proton-nucleus or nucleus-nucleus reactions by using a coupled set of covariant transport equations with scalar and vector self-energies of all hadrons involved. Explicitly propagated are nucleons, \Delta 's, N

\Lambda (1440), N\Lambda (1535) resonances as well as ss's, j's, ae's, !'s, \Phi 's, kaons and K\Lambda 's with their isospin degrees of freedom. For more detailed information on the self-energies employed we refer the reader to ref. [13], where the transport approach HSD1 is formulated and applied to nucleus-nucleus collisions from SIS to SPS energies.

In this investigation we calculate dilepton production taking into account the contributions from nucleon-nucleon, pion-nucleon and pion-pion bremsstrahlung, the Dalitz-decay of the \Delta , N\Lambda (1440), j ! fle+e\Gamma and ! ! ss0e+e\Gamma , the direct dilepton decays of the vector mesons ae; !; \Phi as well as ss+ss\Gamma annihilation. The nucleon-nucleon, pion-nucleon and ssss bremsstrahlung, the Dalitz-decay of the \Delta ; N \Lambda , ss0 and j are evaluated in the same way as described in refs. [9, 11].

The pion annihilation - which will turn out to play a specific role - proceeds through the ae-meson which decays into a virtual massive photon by vector meson dominance. The cross section is parametrized as in [9, 11, 14] as

oess

+ss\Gamma !e+e\Gamma (m) = 4ss

3 `

ff m'

2 s1 \Gamma 4m2ss

m2 jFss(m)j

2 ; (1)

where the free electromagnetic form factor of the pion is given by

jFss(m)j2 = m

4ae

(m2 \Gamma m0ae2)2 + m2ae\Gamma 2ae : (2) 1Hadron-String-Dynamics

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In eq. (2) m is the dilepton invariant mass, ff is the fine structure constant, and

mae = 775M eV ; m

0ae = 761M eV ; \Gamma ae = 118M eV :

Note that eq.(1) describes the free pion annihilation cross section; possible medium modifications will be discussed below.

For the cross section of the proton-neutron bremsstrahlung we use the phase-space corrected soft-photon approximation which has been shown to be a good approximation to a more fundamental one-boson-exchange calculation [9, 15]. This approximation might be questionable for pion-nucleon and pionpion bremsstrahlung, but due to their rather small contributions (see below) relative factors of 2-3 will not change the conclusions of our present study. Similar transport models for e+e\Gamma production are reported in refs. [16, 17, 18, 19, 20].

In addition to our previous calculations we now also include the ! Dalitzdecay given by [21]:

d\Gamma !!ss0e+e\Gamma

dm =

ff 3ss

\Gamma !!ss0fl

m (1 +

m2 m2! \Gamma m2ss )

2 \Gamma 4m

2!m2

(m2! \Gamma m2ss)2 !

3=2

\Theta jF!!ss0e+e\Gamma (m)j2 ; (3) where the form factor is parametrized as ([21])

F!!ss0e+e\Gamma (m) = 11 \Gamma m2=\Lambda 2

s (4)

with

\Lambda s = 0:65 GeV : (5)

The singularity for m = \Lambda s is avoided by introducing numerically a finite width in the denominator which is compatible with the data on F! in ref. [21]. The direct decays of the vector mesons to e+e\Gamma relative to the total width are taken as \Gamma \Phi !e+e\Gamma =\Gamma tot\Phi = 3.09\Theta 10\Gamma 4, \Gamma !!e+e\Gamma =\Gamma tot! = 7.1 \Theta 10\Gamma 5 and \Gamma ae!e+e\Gamma =\Gamma totae = 4.4 \Theta 10

\Gamma 5.

We have calculated the dilepton yields for p + Be and p + Au at 450 GeV, and for S + Au at 200 GeV/A bombarding energy. A comparison with

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the experimental data of the CERES collaboration [5] is shown in Fig. 1 for p + Be and p + Au including the dilepton acceptance cuts in pseudo-rapidity, i.e. 2:1 ^ j ^ 2:65, a cut of the transverse dilepton momenta for pT * 0.05 GeV/c as well as a cut on the opening angle of the dileptons \Theta * 35 mrad. Also, the experimental mass resolution has been included in evaluating the theoretical mass spectrum. The full solid curves in Fig. 1 display the sum of all individual contributions which is dominated by the decays of the mesons. The bremsstrahlung contributions (ssN, pN) as well as ss+ss

\Gamma annihilation are

of minor importance for both systems in line with the experimental cocktail analysis in ref. [5].

Before going over to the system S + Au at 200 GeV/A we need to check if the global reaction dynamics are reproduced by our transport calculation. This is obviously the case, as may be extracted from Fig. 2, where we compare our calculated rapidity distribution for protons (dashed line) and ss\Gamma (solid line) with the experimental data [22, 23]. The proton rapidity spectrum shows a narrow peak at target rapidity (ss -3.03) which is easily attributed to the spectators from the Au target. The bump at y ss -2, furthermore, is mainly due to rescattering of target nucleons. Please note that there is no longer any yield at projectile rapidity (y ss 3.03) which implies that all nucleons from the projectile have undergone inelastic scatterings. The CERES acceptance roughly covers the rapidity regime -1 ^ y ^ -0.4 where the pion density is large compared to the proton density.

We now turn to the calculations for e+e\Gamma production, where the experimental cuts have been employed again. Contrary to the p + Be and p + Au reactions, a cut on the transverse dilepton momenta pT * 0.2 GeV/c has been taken in line with the experimental acceptance [5]. The results of our calculation, where no medium effects are incorporated for all mesons, are displayed in Fig. 3 (upper thick solid line) in comparison to the data [5]. The open triangles present the experimental extrapolation for mesonic decays [5] whereas the thick solid line denoted by `cocktail' is the result of j; !; \Phi and primary ae decays from our calculation. Except for a single point at invariant

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mass m = 0.6 GeV our cocktail analysis coincides with that of the CERES collaboration such that we can attribute the additional yield seen experimentally (full dots) to the additional channels accounted for in our model. In fact, the ss+ss\Gamma annihilation component (dashed line) is found to dominate the dilepton spectrum for m * 0.3 GeV very much reminiscent of the situation at BEVALAC or SIS energies [9, 11, 17]. The additional bremsstrahlung contributions are of minor importance; here the pion-pion channels are smaller than proton-nucleon or even pion-nucleon channels. However, the shape of the experimental spectrum is not very well reproduced for 0.3 ^ m ^ 0.5 GeV and the spectrum is also slightly underestimated at invariant masses m ss 0.3-0.4 GeV. Compared with the results by Li et al. [8] - based on an expanding fireball scenario in chemical equilibrium - our ss+ss\Gamma annihilation contribution at low masses is somewhat larger while that from direct ! decay is slightly smaller.

Since the dilepton yield for 0.3 GeV ^ m ^ 1 GeV is dominated by the ss+ss

\Gamma annihilation channel and the electromagnetic form factor of the pion is

determined by the properties of the ae-meson [24], in-medium modifications of the latter are expected to affect the dilepton mass spectrum as previously shown in refs. [11, 25]. The actual modifications of the ae-meson in a dense baryonic environment, however, are still a matter of debate. It is thus hoped that low mass dileptons from heavy-ion collisions can shed some light on this issue.

From QCD inspired models [26] or estimates based on QCD sum rules [27, 28] it has been predicted that the ae-meson mass decreases with density. In order to explore the compatibility of such scenarios with the CERES data (as proposed by Li et al. [8]), we have performed calculations with a mediumdependent ae-mass according to Hatsuda and Lee [27], i.e.

m

\Lambda

ae ss m

0 ae (1 \Gamma 0:18aeB=ae0) * mu + md ss 14M eV; (6)

where aeB(t) is the actual baryon density during the decay of the ae-meson and ae0 ss 0.16 fm

\Gamma 3. The dropping of the ae-meson mass is associated with

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a scalar self-energy of the meson which is determined by the local baryon density; the propagation of the `quasi-particle' with effective mass m

\Lambda ae thus

couples to the baryon current during the expansion, and the meson becomes `on-shell' asymptotically due to a feedback of energy from the mean fields, which thus ensures that the total energy of the system is conserved.

The results of this simulation are shown in Fig. 4 in comparison with the CERES data. Again we find the ss+ss\Gamma annihilation to dominate the spectrum for invariant masses m * 0.3 GeV, and a significant enhancement of low mass dileptons is obtained. Our computation thus supports the proposal by Li et al. [8] that the enhanced dilepton yield might be due to a dropping ae-mass in the medium.

On the other hand, within the vector-dominance model Herrmann et al. [29] and Asakawa et al. [30] have predicted that the ae-mass does not change much with density, but instead the width of the ae-resonance should increase substantially. Similar, but less pronounced modifications, have been claimed by Chanfray et al. [31]. We also follow this assumption as in ref. [11] and explore if such medium effects might actually be seen in the CERES experiment.

In this respect we have performed calculations using a rough fit to the density-dependent pion form factor of Herrmann et al. [29] (cf. Fig. 14 of ref. [11]). In order to account for the effect of \Delta 's in matter we use an effective density aeN \Gamma ae\Delta =4 as pointed out in ref. [32]. The results are displayed in Fig. 5 in comparison to the CERES data [5] and are seen to agree also with the experimental results within the errors bars. Including a collisional broadening of the ae as calculated by Haglin [33] will further enhance the yield of low mass dileptons. Since the change of the pion form factor in the work of Herrmann et al. [29] is entirely due to conventional many-body effects, i.e. the coupling of the ss; ae; \Delta and nucleon degrees of freedom, better experimental data and further theoretical studies appear necessary to extract new physics from the CERES data.

In summary, we have studied e+e

\Gamma production in proton and heavy-ion

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induced reactions at SPS energies on the basis of the covariant transport approach HSD [13] which describes the hadronic processes quite reliably. We have incorporated the contributions from proton-nucleon, pion-nucleon and pion-pion bremsstrahlung, the Dalitz-decay of the \Delta , j and ! as well as ss+ss\Gamma annihilation and the direct dilepton decay of the vector mesons ae; !; \Phi . It is found that for p + Be and p + Au at 450 GeV the mesonic decays almost completely determine the dilepton yield, whereas in S + Au reactions the ss+ss

\Gamma annihilation channel takes over due to the high pion densities achieved.

The experimental data taken by the CERES collaboration [5] are slightly underestimated by the calculation when using free form factors for the pion and ae-meson.

Different in-medium effects on the ae-meson have been expected; here we have examined a shift of the ae-mass according to QCD sum rules as suggested by Hatsuda and Lee [27] and the broadening of the ae according to the approach by Herrmann et al. [29]. Although the dropping ae-mass scenario proposed by Li et al. [8] is compatible with the CERES data for S+Au, the large error bars in the data can not exclude the more conventional scenario of a broadening ae spectral function in the medium. To extract direct evidence for chiral symmetry restoration, we need both improved experimental data and further theoretical studies.

We gratefully acknowledge many helpful discussions with A. Drees, B. Friman, K. Haglin, U. Mosel, H. J. Specht and Gy. Wolf. One of us (C.M. Ko) likes to thank U. Mosel for the kind hospitality extended to him during his stay at the University of Giessen under a Humblodt Research Award. His work was also partially supported by the US National Science Foundation under grant No.  and the Welch foundation under Grant No. A-1110.

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References

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CERES/NA45 collaboration, Proceedings of the International Workshop XXIII on Gross Properties of Nuclei and Nuclear Excitations, Hirschegg, Austria, Jan. 1995, ed. by H. Feldmeier and W. N"orenberg, p. 151.

[6] I. Kralik and the HELIOS-3 collaboration, Proceedings of the International Workshop XXIII on Gross Properties of Nuclei and Nuclear Excitations, Hirschegg, Austria, Jan. 1995, ed. by H. Feldmeier and W. N"orenberg, p. 143.

[7] D. K. Srivastava, B. Sinha, and C. Gale, Phys. Rev. Lett., submitted. [8] G. Q. Li, C. M. Ko and G. E. Brown, Phys. Rev. Lett., submitted. [9] Gy. Wolf, G. Batko, W. Cassing et al., Nucl. Phys. A517 (1990) 615. [10] Gy. Wolf, W. Cassing, U. Mosel, and M. Sch"afer, Phys. Rev. C43 (1991)

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Ko and Q. Li, Phys. Rev. C37 (1988) 2270; Q. Li, J. Q. Wu, and C. M. Ko, Phys. Rev. C39 (1989) 849.

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[13] W. Ehehalt and W. Cassing, Nucl. Phys. A, submitted; . [14] C. Gale and J. Kapusta, Phys. Rev., C35 (1987) 2107. [15] M. Sch"afer, T. Bir'o, W. Cassing, and U. Mosel, Phys. Lett. B221 (1989)

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[16] L.H. Xia, C.M. Ko, L. Xiong and J.Q. Wu, Nucl. Phys. A485 (1988)

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[18] V.D. Toneev, A.I. Titov and K.K. Gudima, GSI-92-05 preprint (1992). [19] V. D. Toneev, E. L. Bratkovskaya and K. K. Gudima, Proceedings of

the International Workshop XXIII on Gross Properties of Nuclei and Nuclear Excitations, Hirschegg, Austria, Jan. 1995, ed. by H. Feldmeier and W. N"orenberg, p. 330.

[20] L. A. Winckelmann, H. St"ocker, W. Greiner, and H. Sorge, Phys. Lett.

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[21] L. G. Landsberg, Phys. Rep. 128 (1985) 301. [22] R. Bauer et al., Nucl. Phys. A566 (1994) 87c. [23] R. Santo et al., Nucl. Phys. A566 (1994) 61c. [24] T. Ericson and W. Weise, Pions and Nuclei, (Clarendon Press, Oxford,

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[28] M. Asakawa and C. M. Ko, Phys. Rev. C48 (1993) R526; Nucl. Phys.

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Fig. 1: Comparison of our calculations for the differential dilepton spectra (thick solid lines) with the experimental data [5] (full dots) for p + Be and p + Au at 450 GeV. The individual contributions from the vector meson decays and Dalitz decays as well as bremsstrahlung channels and ss+ss

\Gamma annihilation

are shown by the thin solid, dashed and dotted lines.

Fig. 2: Comparison of our calculations for the proton (dashed line) and ss

\Gamma rapidity distribution (solid line) in comparison to the experimental data

[22, 23] for S + Au at 200 GeV/A.

Fig. 3: Comparison of our calculations for the differential dilepton spectra (upper thick solid line) with the experimental data [5] (full dots) for S + Au at 200 GeV/A when employing no medium modification of the mesons. The triangles represent the experimental reconstruction from meson decay channels [5] which is compared to the corresponding sum from our calculation (thick solid line denoted by 'cocktail'). The individual contributions from the

11

vector meson decays and Dalitz decays as well as bremsstrahlung channels and ss+ss

\Gamma annihilation are shown by the thin solid, dashed and dotted lines.

Fig. 4: Comparison of our calculations for the differential dilepton spectra (thick solid line) with the experimental data [5] (full dots) for S + Au at 200 GeV/A when including a shift of the ae-meson mass (6) according to the prediction by Hatsuda and Lee [27]. The individual contributions from the vector meson decays and Dalitz decays as well as bremsstrahlung channels and ss+ss\Gamma annihilation are shown by the thin solid, dashed and dotted lines.

Fig. 5: Comparison of our calculations for the differential dilepton spectra (thick solid line) with the experimental data [5] (full dots) for S + Au at 200 GeV/A when including a broadening of the ae-meson according to the calculations by Herrmann et al. [29]. The individual contributions from the vector meson decays and Dalitz decays as well as bremsstrahlung channels and ss+ss\Gamma annihilation are shown by the thin solid, dashed and dotted lines.

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0.2 0.4 0.6 0.8 1.010 -9

10-8 10-7 10-6 10-5 p

T > 50 MeV/c2.1 < h < 2.65

<dnch/dh> = 3.1

all

450 GeV/A

p+Be

w -> pe+e- N* \Delta pN pN

h

r w \Phi

p+p-

(d 2 n

ee/d

hdm)/(dn

ch/d h) [50 MeV/c

2 ]-1

m [GeV/c2] Figure 1a

13

0.2 0.4 0.6 0.8 1.010 -9

10-8 10-7 10-6 10-5 p

T > 50 MeV/c2.1 < h < 2.65

<dnch/dh> = 7.0

all

450 GeV/Ap+Au

w -> pe+e- N *

\Delta pN

pN

h

r w \Phi

p+p-

(d 2 n

ee/d

hdm)/(dn

ch/d h) [50 MeV/c

2 ]-1

m [GeV/c2] Figure 1b

14

-4 -2 0 2 40 20 40 60 80

p-

p

S + Au 200 GeV/A

dN/dy

y Figure 2

15

0.2 0.4 0.6 0.8 1.010 -9

10-8 10-7 10-6 10-5 10-4

pp-brems

cocktail

pT > 0.2 GeV/c 2.1 < h < 2.65 <dnch/dh> = 125

all

200 GeV/AS+Au

w -> pe+e- N * \Delta pN

pN h

r w \Phi p+p-

(d 2 n

ee/d

hdm)/(dn

ch/d h) [100 MeV/c

2 ]-1

m [GeV/c2] Figure 3

16

0.2 0.4 0.6 0.8 1.010 -9

10-8 10-7 10-6 10-5 10-4

pp-brems pT > 0.2 GeV/c 2.1 < h < 2.65 <dnch/dh> = 125

all

200 GeV/AS+Au

w -> pe+e- N* \Delta pN pNh

r w \Phi p+p-

(d 2 n

ee/d

hdm)/(dn

ch/d h) [100 MeV/c

2 ]-1

m [GeV/c2] Figure 4

17

0.2 0.4 0.6 0.8 1.010 -9

10-8 10-7 10-6 10-5 10-4

pp-brems pT > 0.2 GeV/c 2.1 < h < 2.65 <dnch/dh> = 125

all

200 GeV/AS+Au

w -> pe+e- N* \Delta pN pNh

r w \Phi p+p-

(d 2 n

ee/d

hdm)/(dn

ch/d h) [100 MeV/c

2 ]-1

m [GeV/c2] Figure 5

18

