In the framework of the relativistic quantum molecular dynamics approach (RQMD) we investigate antideuteron (d) observables in Au+Au collisions at 10.7 AGeV. The impact parameter dependence of the formation ratios d/p2 and d/p2 is calculated. In central collisions, the antideuteron formation ratio is predicted to be two orders of magnitude lower than the deuteron formation ratio. The d yield in central Au+Au collisions is one order of magnitude lower than in Si+Al collisions. In semicentral collisions di erent configuration space distributions of p s and d s lead to a large squeeze out e ect for antideuterons, which is not predicted for the p s

Bleicher, Marcus

Greiner, Walter

Jahns, André

Mattiello, Raffaele

Sorge, Heinz

Spieles, Christian

Stöcker, Horst

English

Hochschulschriftenserver - Universität Frankfurt am Main

arXiv:nucl-th/9506009 v1   10 Jun 1995Phasespace Correlations of Antideuterons inHeavy Ion Collisions∗M. Bleicher, C. Spieles, A. Jahns, R. Mattiello,H. Sorge, H. St¨ ocker and W. GreinerInstitut f¨ ur Theoretische PhysikJohann Wolfgang Goethe Universit¨ atFrankfurt am Main, GermanyAbstractIn the framework of the relativistic quantum molecular dynamics approach(RQMD) we investigate antideuteron (d) observables in Au+Au collisions at10.7 AGeV. The impact parameter dependence of the formation ratios d/p2and d/p2 is calculated. In central collisions, the antideuteron formation ratiois predicted to be two orders of magnitude lower than the deuteron forma-tion ratio. The d yield in central Au+Au collisions is one order of magnitudelower than in Si+Al collisions. In semicentral collisions diﬀerent conﬁgura-tion space distributions of p’s and d’s lead to a large “squeeze–out” eﬀect forantideuterons, which is not predicted for the p’s.∗Work supported by Bundesministerium f¨ ur Forschung und Technik, Deutsche Forschungsge-meinschaft, Gesellschaft f¨ ur Schwerionenforschung0To understand recent measurements of the antideuteron formation ratio (multiplicityof d divided by the p multiplicity squared, both at the same momentum per nucleon)in Si+Au collisions at the AGS, it has been suggested that the shape and size ofthe antinucleon source, which is diﬀerent from the nucleon source, has to be takeninto account [1, 2, 3]. Enhanced production of antibaryons and antimatter clustershas been proposed as potential signature of a quark–gluon plasma [4, 5]. The yieldof light (anti–)nuclei is connected to baryon density [6] and its spatial distributionin the later stages of the collision. This can be used to extract source sizes in analternative way to the HBT–analysis [7].Production processes which enhance the p yield can be counter–balanced by the an-nihilation in the baryon rich environment [6, 8]. This should be observable via the“anti–ﬂow” correlation between matter and antimatter [8].Strong annihilation distorts the conﬁguration space distribution of antibaryons andstrongly aﬀects the antideuteron production as shown below. The strong suppres-sion of antimatter cluster formation and their characteristic phasespace distributionof antideuterons for ﬁnite impact parameters is discussed. These phenomena can beexperimentally scrutinized to diﬀerentiate between annihilation assumptions. It canalso reveal details of the structure of the eventshape unaccessible by p or p data.The calculations presented here are based on a microscopic phase space approach,the relativistic quantum molecular dynamics model (RQMD 1.07–cascade mode)[9].This model is based on the propagation of all hadrons on classical trajectories inthe framework of Hamilton constraint dynamics. RQMD includes secondary interac-tions, e.g. the annihilation of produced mesons on baryons, which may lead to theformation of s channel resonances or strings. The absorption probability for ¯ p’s inthe baryonic medium is determined by the free pp annihilation cross section.Since RQMD does not include the production of light (anti–)nuclei dynamically, clus-ter formation is added after strong freeze–out. We calculate the deuteron and an-tideuteron formation probability by projecting the (anti–)nucleon pair phasespace onthe (anti–)deuteron wave function via the Wigner–function method as described in[10, 11]. The Hulth´ en parametrization [12] is used to describe the relative part ofthe (anti–)deuteron wavefunction. The yield of antideuterons (and deuterons, resp.)is given bydNd = 1234DPi,j ρWd (∆  R,∆  P)Ed3(pip + pjn).The sum goes over all n and p pairs, whose relative distance (∆  R) and relativemomentum (∆  P) are calculated in their rest frame at the earliest time after bothnucleons have ceased to interact. The factors 12 and 34 account for the statisticalspin and isospin projection on the (anti–)deuteron state. The calculation of the ¯ t isstraight forward, by exchanging the Hulth´ en parametrization of the ¯ d wavefunctionwith a 3–body harmonic oscilator wavefunction to describe the ¯ t [10]. We use theevent mixing technique to improve statistics.It has been shown that the RQMD/C–Model describes the Si(14.6AGeV)+Au an-tideuteron data reasonably well [3].The conﬁguration space distribution of midrapidity antideuterons is calculated atfreezeout in a cut perpendicular to the beam axis (∆z = ±0.5fm) for the Au(10.7AGeV)+Au, b=5 fm reaction (ﬁg. 1). Antimatter is preferentially emitted from thesurface of the ﬁreball – i.e. the region of hot and dense matter – in clear contrast tothe source of baryons, which spreads over the whole reaction volume. This can beunderstood as a consequence of antibaryon absorption, which produces deep holes inthe momentum– (at pcms ≈ 0 GeV/c) and even more so in the conﬁguration spacedistribution (at xcms ≈ 0 fm, ycms ≈ 0 fm, ﬁg. 1) of the antibaryons at freezeout[8, 1].The antideuteron formation happens perpendicular to the reaction plane, where theobserver gets an undistracted view directly into the hot and dense participant mat-ter. The suppression of p’s in the reaction plane is due to the fact that the baryonsannihilate p’s preferentially moving parallel to the impact parameter plane. Theanticluster formation probability decreases rapidly with the relative distance of thep, n constituents. The small decrease of the spatial p density (<30%) along thefootball–shaped region in the x-y–plane shows up very clearly in the d’s.The anisotropic conﬁguration space distribution of the d’s can be magniﬁed via theazimuthal (φ) distribution of antideuterons. φ is the angle between   pT and the x–axis(tanφ = |py|/px). Thus, a vector with φ = 0 degrees points into the direction of thex–axis.Fig. 2 shows the azimuthal distribution of midrapidity antiprotons (full line), an-tideuterons (long dashed) and antitritons (short dashed) in peripheral Au(10.7AGeV)+Aucollisions. The momentum distribution of p’s in the px-py–plane is slightly concaveand reﬂects the geometry of the almond shaped reaction zone.In contrast, the d distribution is shifted towards φ = 90◦, in line with the describedconﬁguration space distribution of the d’s. This looks like a ”squeeze–out” eﬀect. Itis expected that the eﬀect is even more pronounced for t’s. The asymmetry in theazimuthal angular distributions (d2Nd/dφ/dy|y=ymid) can be experimentally tested –once the reaction plane is determined. The exact reﬂection symmetry of ﬁg. 2 is dueto the fact that every event for the symmetric system has been reﬂected by φ = 90◦.Let us explore the reaction volume dependence of the (anti–)deuteron formation ratio.This can be done by varying the impact parameter b as shown in ﬁg. 3 (d/p2–ratio, fullcircles; d/p2–ratio, open squares). In thermodynamic approaches the (anti–)deuteronformation rate is proportional to the inverse volume of the sources. Those rates mea-sure the average phase–space distance of nucleons and antinucleons, respectively [8].The d formation ratio in central collisions (where up to 95% of the initially producedantinucleons are reabsorbed) is predicted to be roughly two orders of magnitude lowerthan the formation ratio of deuterons. This diﬀerence vanishes when going to higherimpact parameters or small systems (like Si+Al). It has to be pointed out that thiseﬀect is so strong that the absolute yield of d actually decreases from ≈ 10−7 d’sper Si+Al event to ≈ 10−8 d’s in central Au+Au collisions! If the antideuteron for-mation ratio is calculated within a momentum coalescence model with a momentumcutoﬀ parameter of ∆p = 120 MeV (d/p2–ratio, open circles), one ﬁnds only littlesensitivity to the impact parameter chosen. This strengthens the explanation of themostly conﬁguration space origin of this eﬀect. For very peripheral collisions the an-tideuteron formation ratio must decrease rapidly (not shown in the ﬁgure), becausethe production of two antibaryons is not allowed due to the limited available energy.The E814 collaboration might be able to measure these dependencies as they havedone for matter clusters [13].The predicted reaction volume dependence and the squeeze–out of anti–fragmentsreﬂects mainly the spatial distribution of antibaryons. Antimatter clusters providean exciting opportunity to measure the spatial properties of the exploding densematter.References[1] St. Mrowczynski: Phys. Lett. B308 (1993)216[2] A. Aoki et al.: Phys. Rev. Lett. 69 (1992)2345[3] J.L. Nagle, B.S. Kumar, M.J. Bennet, S.D. Coe, G.E. Diebold, J.K. Pope,A. Jahns, H. Sorge: Phys. Rev. Lett. 73 (1994)2417[4] U. Heinz, P.R. Subramanian, H. St¨ ocker, W. Greiner: J. Phys. G: Nucl.Phys. 12 (1986)1237[5] D. H. Rischke et al.: Phys. Rev. D41 (1990)111[6] S. Gavin, M. Gyulassy, M. Pl¨ umer, R. Venugoplan: Phys. Lett. B234(1990)175[7] J.L. Nagle, B.S. Kumar, M.J. Bennet, G.E.Diebold, J.K. Pope, H. Sorge,J.P. Sullivan: Phys. Rev. Lett. 73 (1994)1219[8] A. Jahns, C. Spieles, H. Sorge, H. St¨ ocker, W. Greiner: Phys. Rev. Lett.22 (1994); A. Jahns, C. Spieles, R.Mattiello, H. Sorge, H. St¨ ocker, W.Greiner: Phys. Lett. B308 (1994)3464[9] H. Sorge, H. St¨ ocker, W. Greiner: Ann. Phys. (N.Y.) 192 (1989) 266;[10] R. Mattiello, A. Jahns, H. Sorge, H. St¨ ocker, W. Greiner: Phys. Rev.Lett. 74 (1995)2180[11] M. Gyulassy, K. Frankel, E.A. Remler: Nucl. Phys. A402 (1983)596[12] L. Hulthen: Ark. Mat. Ast. Fys. 28, No.5[13] J. Barrette et al. (E814 collab): Phys. Rev. C50 (1994)1077Figure Captions :Figure 1Conﬁguration space distribution of midrapidity antideuterons in the reaction Au(10.7 AGeV)+Au,b=5fm at freezeout in a cut perpendicular to the reaction plane. The initial shapesof the colliding nuclei are also plotted.Figure 2Correlations of antiprotons lead to a “squeeze–out” for d and t in peripheral Au(10.7AGeV)+Aureactions due to a lower anticluster formation probability in the reaction plane.Figure 3Impact parameter dependence of the (anti–)deuteron to the (anti–)proton ratio squared(d/p2,full circles; d/p2, open squares). Open circles: the result of a simple momentumcoalescence model. The lines are to the eye.Figure 1-15 -10 -5 0 5 10 15X [fm]-15-10-5051015Y[fm]Au(10.7AGeV)+Au, b=5 fm, ZCMS 0 fm,Y=Ymid-15 -10 -5 0 5 10 15-15-10-5051015dNucleiFigure 20 20 40 60 80 100 120 140 160 1800.00.10.20.30.40.50.60.70.80.91.0d2N/dy/d|-0.3<y<0.3(%)Au(10.7AGeV)+Au,b=5fm,Y=YmidAnti-tritonsAnti-deuteronsAnti-protonsAnti-Cluster Squeeze-OutFigure 30 2 4 6 8 10Impactparameter b [fm]510-52510-42510-32510-2RatioAu(10.7AGeV)+Aud / p2d / p2d / p2Mom.Coal.Absorption!

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Phasespace Correlations of Antideuterons in Heavy Ion Collisions

Phasespace Correlations of Antideuterons in Heavy Ion Collisions

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