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Dilepton As a Possible Signature for the Baryon-Rich Quark-Gluon Plasma

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Dilepton As a Possible Signature for the Baryon-Rich Quark-Gluon Plasma PHYSICAL REVIE%' C VOLUME 41, NUMBER 2 FEBRUARY 1990 Dilepton as a possible signature for the baryon-rich quark-gluon plasma L. H. Xia, ' C. M. Ko, and C. T. Li Cyclotron Institute and Center for Theoretical Physics, Texas A&M University, College Station, Texas 77843 (Received 31 July 1989) In an expanding fireball model, we study dilepton production from high-energy heavy-ion col- lisions at the stopping regime. We find that the pion-pion annihilation gives the dominant contribu- tion to the dilepton yield at invariant masses between 2m„and 1 GeV. The total dilepton yield in this invariant mass region increases with the incident energy of the collision, but a saturation is seen once a baryon-rich quark-gluon plasma is formed in the initial stage. I. INTRODUCTION dilepton. It was suggested that the disappearance of the rho peak in the dilepton invariance mass spectrum might ' The ultimate goal of heavy-ion collisions at ultrarela- signal the formation of a quark-gluon plasma. ' De- tivistic energies is to create a deconfined quark-gluon tailed studies including the proper treatment of the ex- plasma. ' It is hoped that during the initial stage of the pansion dynamics, however, do not support such a possi- ' collision, a region of high-energy density will be produced bility. These studies are all concerned with the baryon so that a transition from the hadronic matter to the free quark-gluon plasma that might be produced in future quark-gluon plasma will take place. For future experi- RHIC energies. At the AGS, energies in the range of ments at the proposed relativistic heavy-ion collider about 15 GeV/nucleon, a dense hadronic matter will be (RHIC) a baryon free quark-gluon plasma is expected to formed if no quark-gluon plasma is created in the initial be created because of the increasing transparency of the stage. In the hadronic matter, dileptons can be produced nuclear matter with increasing collision energies. At from both pn bremsstrahlung and the m~ annihilation. present, the CERN experiments at both 60 GeV/nucleon For dense hadronic matter at high temperatures, it has and 200 GeV/nucleon indicate that the incident projec- been shown in Refs. 15 and 16 that the contribution from tile is not completely stopped by the target and a high- the stan annihilation is more significant than that from the ' energy density of many GeV/fm has been reached. The pn bremsstrahlung for dileptons of invariant masses in observation of the suppressed production of the J/4 par- the region of 2m to about 1 GeV, where m is the mass ticle has already stimulated great excitements as it might of pion. It is also found in Refs. 15-17 that the be a possible evidence for the formation of a quark-gluon modification of the pion dispersion relation by the dense plasma. However, it will not be considered as a nuclear matter because of the strong p-wave mN interac- definitive signature until a better understanding of the tion can lead to an enhanced production of dileptons at dissociation of J/4 by the hadronic particles is small invariant masses. This effect becomes more pro- achieved. For experiments carried out at the nounced as the density of the hadronic matter increases. Brookhaven National Laboratory Alternating Gradient On the other hand, if a baryon-rich quark-gluon plasma Synchrotron (AGS) at 14.5 GeV/nucleon, the analysis of is initially formed, then dileptons will be produced from the final transverse energy distribution indicates that the the qq annihilation. After the hadronization of the projectile is indeed completely stopped by the target and quark-gluon plasma, dileptons can also be produced from that a hadronic matter of density about five times the the hadronic matter via the pn bremsstrahlung and the normal nuclear matter density has been reached in the in- mm annihilation. Since the total entropy cannot decrease itial stage. Whether a baryon-rich quark-gluon plasma during the transition, the final hadronic matter will be at has been formed in such a collision is still uncertain. It a higher temperature and lower density than the initial ' has been argued in the past that the formation of a quark-gluon matter. If the quark-gluon plasma contrib- quark-gluon plasma may be signaled by an enhanced pro- utes mainly to dileptons with larger invariant masses, duction of kaons relative to that of pions. Data obtained then we expect a reduced production of dileptons with at the AGS indeed show an enhancement of a factor of 4 low invariant masses, compared with the case without the for K+/m. + ratio compared with that from the proton- formation of a quark-gluon plasma because of the low ha- proton and the proton-nucleus collisions. However, dronic matter density after its hadronization. In this theoretical studies show that a substantial enhancement case, it is of interest to measure the total yield of dilepton can be obtained by assuming either the formation of a with the invariant mass in the region of 2m to about 1 quark-gluon plasma or a dense hadronic matter in the ini- GeV as a function of the incident energy. The onset of a tial stage of the collision. ' " In view of the ambiguity baryon-rich quark-gluon plasma is thus signaled by the associated with these observables as signatures for the appearance of a plateau in this excitation function. quark-gluon plasma, the consideration of other observ- To substantiate this conjecture, we have carried out ables will be very useful. calculations for dilepton production based on the hydro- A very interesting suggestion in the past has been the dynamical description of heavy-ion collisions. In Sec. II, 41 572 1990The American Physical Society 41 DILEPTON AS A POSSIBLE SIGNATURE FOR THE BARYON-. 573 the nuclear phase diagram is introduced. The initial con- dg I k'dk (3b) dition of the fireball and its hydrodynamical expansion Q (k +P )/T 2~2 p e ' are described in Sec. III. The kinetic processes and the +1 hadronization model are discussed in Sec. IV. In Sec. V, dG P~ k dk G (3c) the elementary dilepton production processes are dis- 2 2 Jp k/T cussed. The results for dilepton production from high- energy heavy-ion collisions are presented in Sec. VI. Conclusions are given in Sec. VII. A brief report of this which lead to the total energy density in the quark-gluon work has already been published in Ref. 19. plasma e =eQ+e — q Q +eG+B II. NUCLEAR PHASE DIAGRAM 3p 30 T+3p T+ 2 +8 (4) Based on the quantum chromodynamics, it is generally believed that the nuclear matter exists in a deconfined where B is the bag constant. From the number and ener- phase of quarks and gluons when its density and tempera- gy densities, the pressure and entropy densities of the ture are high. The determination of the nuclear phase di- quark-gluon plasma are given by agram from the quantum chromodynamics however, a is, = — — diScult task. Instead, we shall use a simplified model to pq —,'(e 8) 8, construct the nuclear phase diagram. It is determined by 1 considering both the hadronic and the quark-gluon s =—(e+p 3p—n ). (6) matter as composed of noninteracting nonstrange parti- cles with the latter supplemented by a bag constant. This model of the nuclear phase diagram has been used previ- B. Equation of state for the hadronic phase ously in Refs. 20 and 21. As pointed out in these refer- ences, the inclusion of strange particles affects the phase For the hadronic matter, we include only nonstrange diagram only slightly. Since we shall look for qualitative stable hadrons (nucleon, pion, and eta) and their reso- signatures for the formation of a quark-gluon plasma, we nances (b,'s, N "s, p, and co) as in Refs. 20 and 21. In the believe that such a model will be suScient in the present case that their interactions can be neglected, the number work. For completeness, we describe briefly in the fol- density n;, the energy density e;, and the pressure p; of lowing the construction of the nuclear phase diagram in the ith particle are given by this simple model. d; „kdk n,. = ( — ) /T 2~2 p e e( p(. A. Equation of state for quark-gluon phase d, ek dk For the noninteracting quark-gluon matter consisting e;= — 2 p (, p)/ of the up and down quarks and the gluons, the quark e density the antiquark density and the den- nQ, nQ, gluon d, „e;'k dk sity can be written as nG 2 (E( )/T p e p( g (. k~dk — where e,. =(k +m; )'~ . In the above, + is for fermions Q 2 2 Jp (k P )/T e and —for bosons. The d; indicates the degeneracy, while dQ ~ k dk the chemical potential is denoted by p, . For baryons, we (lb) Q 2 (k+@ )/T have p; =b; pb, where b; is the baryon number and pb is 2 p e the baryon chemical potential. The total baryon number k 2dk and energy density, as well as the pressure of the hadron- nG = „=16((3)Tim. (1c) = = p e" — ic matter are then given by nb h g, b; n;, eh e;, and 2~ I 1 = g; ph g; p;, respectively. From these thermodynamical respectively. In the above, we have g(3}=1.20206, the quantities, the entropy density is quark degeneracy dQ = 12, the gluon degeneracy dG = 16, the chemical potential for the quark, and the tempera- 1 p ~h T(eh+Ph Pbnb, h } ture T.
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