The regeneration of hadronic resonances is discussed for heavy ion collisions
at SPS and SIS-300 energies. The time evolutions of Delta, rho and phi
resonances are investigated. Special emphasize is put on resonance regeneration
after chemical freeze-out. The emission time spectra of experimentally
detectable resonances are explored.Comment: Proceedings of the Nuclear Physics Winter Meeting 2005 in Bormi

Bleicher, Marcus

Vogel, Sascha

English

arXiv

The regeneration of hadronic resonances is discussed for heavy ion collisions at SPS and SIS-300 energies. The time evolutions of Delta, rho and phi resonances are investigated. Special emphasize is put on resonance regeneration after chemical freeze-out. The emission time spectra of experimentally detectable resonances are explored

Hochschulschriftenserver - Universität Frankfurt am Main

arXiv:nucl-th/0505027 v1   10 May 2005Resonance Absorption and Regeneration in Relativistic Heavy Ion CollisionsSascha Vogel and Marcus BleicherInstitut f¨ ur Theoretische Physik,J.W. Goethe Universit¨ atMax-von-Laue-Str. 1, 60438 Frankfurt am Main, GermanyThe regeneration of hadronic resonances is discussed forheavy ion collisions at SPS and SIS-300 energies. Thetime evolutions of ∆,ρ and φ resonances are investigated.Special emphasize is put on resonance regeneration afterchemical freeze-out. The emission time spectra of exper-imentally detectable resonances are explored.The study of strongly decaying resonances is one ofmajor topics that came up in recent years [1]. Recently,detailed experimental studies of hadron resonances be-came available. Up to now ρ,Λ∗,Σ∗∆,K0∗ and Φ reso-nances have been reconstructed from hadron correlationsin heavy ion reactions at the full SPS and highest RHICenergy [2–9].This exciting new data poses serious constraints on ourunderstanding and modeling of hadronic interactions inthe late expansion stage of massive nuclear collisions.Especially the apparent suppression of K0∗ and Λ∗ res-onances (together with ∆ enhancement in central reac-tions compared to the thermal model estimates [10] ques-tions the notion of an instantaneous chemical freeze-outas assumed in thermal models. In fact, it demonstratesthat the ideas of a directly observable Quark-Gluon-Plasma (QGP) ﬁreball without a longliving hadronicstage in scenarios with strong supercooling [11] seems notin line with the experimental data. Whether hadronicstatistical models can be used to understand the reso-nance data is still not clear, see e.g. [12,13]First ideas how to understand a modiﬁcation of the res-onance yields had been brought forward by [8] where amodiﬁcation the inverse slope of the Φ meson was dis-cussed. Later this idea was picked up by [14] in terms ofa thermal models plus absorption afterburner. However,this thermal absorption model fell short of the data, be-cause it neglected the regeneration of hadron resonancesin the expansion stage.Comprehensive studies of ρ,K0∗,Σ,Λ and Λ∗ hadron res-onance yields and spectra within a transport approachwere presented in [15–17] for SPS and RHIC energies.For Pb+Pb collisions at 158 AGeV it was shown thatwithin the transport simulation a chemical freeze-out(where most of the inelastic interactions cease and elas-tic and pseudo-elastic interaction take over) around 6fm/c is present. However, it was also shown that elasticand pseudo-elastic reactions might still alter the recon-structable resonance yields and distributions due to ab-sorption of daughter particles and regeneration (refeed-ing).As shown in Fig. 1, recent data by the STAR Col-laboration [2] indicates interesting resonance to ground-state ratios as a function of centrality. E.g., the K0∗/Kand the Λ∗/(Λ+Σ0) ratios decrease, while the Φ/K and∆++1232/p ratios stay constant or might even show a slightincrease with centrality.FIG. 1. Compilation of measured particle ratios in pp andAu+Au collisions at√s = 200 AGeV as a function of cen-trality. Figure is taken from [2]Let us now investigate possible mechanisms that pro-duce at the same time a slight increase of the ∆++/pratio and a suppression of K∗/K ratio. As a tool weemploy the UrQMD model [18,19] which is based on thecovariant propagation of hadrons, resonances and strings.In the present calculations, modiﬁcations due to rescat-tering and regeneration are present in nearly all spectraand yields of short lived resonances. Especially for the∆1232 and the ρ0770, which both have lifetimes of approxi-mately 1-1.5 fm/c this eﬀect alters the spectra drastically.As will be shown next the calculation predicts a diﬀerencebetween reconstructable resonances and all decayed res-onances. Fig. 2 shows the rapidity distributions of the∆01232 and the ρ0770 for central Pb+Pb collision at theSPS energy of 158 AGeV. Full symbols depict the reso-nances which decayed during the collision and, in case ofthe ρ are reconstructable in the dileptonic decay channel.Open symbols show those resonances where the hadronicdecay products did not rescatter after their creation. In1Fig. 2 one observes a suppression by a factor of 6 for theρ meson and a suppression by a factor of 3 for the ∆. InFig 3 one observes a suppression by a factor of 7 for the ρand a suppression by a factor of 6 for the ∆. This can beunderstood because of the diﬀerent meson/baryon ratioat the diﬀerent energies, i.e. a higher baryon density at30 AGeV compared to 158 AGeV.-3 -2 -1 0 1 2 3y0102030405060708090dN/dyall decayedoreconstructableoall decayedoreconstructableoFIG. 2. Rapidity distributions of ∆01232 and ρ0770 for centralPb+Pb collisions at 158 AGeV. A strong suppression of inhadron correlations reconstructable resonances compared tothose reconstructable via leptons (indicated as ’all decayed’)is visible.-3 -2 -1 0 1 2 3y0102030405060708090dN/dyall decayedoreconstructableoall decayedoreconstructableoFIG. 3. Rapidity distribution of ∆01232 and ρ0770 for centralPb+Pb collisions at 30 AGeV. A strong suppression of inhadron correlations reconstructable resonances compared tothose reconstructable via leptons (indicated as ’all decayed’)is visible.Fig. 4 shows the decay time distribution of recon-structable resonances in Pb+Pb at 158 AGeV. Most re-constructable ∆01232’s and ρ0770’s stem from the late stageof the collision (tdecay ≥ 10 fm/c). The Φ1020 shows adiﬀerent behaviour, since it has a very small hadroniccross section and a lifetime of 44 fm/c, which leads to adecay of a large part of the Φ mesons outside the ﬁreball.0 5 10 15 20 25 30 35 40 45 50[fm/c]051015202530dN/d[fm-1]reconstructable 1020*100reconstructable 770reconstructable 1232FIG. 4. Decay time distribution of reconstructable reso-nances for Pb+Pb collisions at 158 AGeV. Detectable ∆1232and ρ770 resonances stem from late stages of the collision. TheΦ mesons decays mostly outside of the collision zone (Notethat the Φ distribution is multiplied by 100).In order to investigate the refeeding aspects two sce-narios are studied. The ﬁrst scenario allows for a quali-tative understanding of the refeeding process: Here, thecalculation is stopped roughly at the chemical freeze-outat 6 fm/c [15]. At this point all resonances are forced todecay. Then the calculation is continued. The full line inFig. 5 shows the time evolution of all ∆1232 resonancessince the beginning. The dotted line shows the time evo-lution of the ∆1232 resonances which regenerate after thecomplete decay at 6 fm/c. On clearly observes that theregeneration of the ∆ resonances is strong and allowsthe delta yield to regain its full strength after additional6 fm/c propagation.Let us now turn to the ρ resonance as shown in Figure6. The ρ770 does not reach its initial value as the ∆1232does. This is because of the smaller and strongly en-ergy dependent cross sections for the reaction ππ → ρ770compared to the reaction pπ → ∆1232. While for a break-up time of 6 fm/c regeneration of the rho is still possi-ble, absorption eﬀects take over when the system is morecooled down because most of the ππ interactions will beat√sππ ≪ mρ.20 5 10 15 20 25 30 35 40[fm/c]20406080100120140160NFIG. 5. Time evolution of the ∆ yield for Pb+Pb collisionat 158 AGeV. The full line is the evolution in the standardcalculation. The dashed line depicts the evolution of the ∆1232when all resonances were forced to decay at 6 fm/c.0 5 10 15 20 25 30 35 40[fm/c]020406080100120140NFIG. 6. Time evolution of the ρ yield for Pb+Pb collisionat 158 AGeV. The full line is the evolution in the standardcalculation. The dashed line depicts the evolution of the ρwhen all resonances were forced to decay at 6 fm/c.0 5 10 15 20 25 30 35 40[fm/c]0.00.51.01.52.02.53.03.54.0NFIG. 7. Time evolution of the Φ yield for Pb+Pb collisionat 158 AGeV. The full line is the evolution in the standardcalculation. The dashed line depicts the evolution of the Φwhen all resonances were forced to decay at 6 fm/c.Let us now probe this assumption with a particle withmore exotic decay branchings. Figure 7 depicts the num-ber of Φ resonances as a function of time - again forthe full calculation (full line) and the modiﬁed calcula-tion (dashed line). The multiplicity of the Φ meson reso-nance does not reach the value from the full calculation,but falls short by 40% even after additional 30 fm/c. Incontrast to the ρ and ∆ regeneration is diﬃcult in theΦ channel, because the probability for KK → Φ is sup-pressed due to the low Kaon densities and the small widthof the Φ.Let us now turn to a quantitative analysis of the re-generation processes as shown in Fig. 8. Here, we trackall decay products of a resonance. When a daughter par-ticle from a resonance decay directly reforms a resonanceof the same type in the next interaction it is marked as’regenerated’. Note that only ρ0770 into ρ0770 or ∆++1232 into∆++1232 are counted as directly ’regenerated’. This explainsthe low percentage of regenerated resonances in the earlystage of the collision, where resonances are directly pro-duced, e.g. from pp → ∆ + X.30 5 10 15 20 25 30 35 40 45 50t [fm/c]0510152025303540%ofreg.resonances 30 AGeV++158 AGeV++30 AGeVo158 AGeVo|y| 0.5FIG. 8. Ratio of regenerated/all decayed resonances asa function of time for Pb+Pb collisions at 30 AGeV and158 AGeV. Open symbols indicate the ∆ resonance, whilefull symbols show the ρ resonance.The Delta (open symbols) regeneration peaks around10-12 fm/c with a direct regeneration probability be-tween 25% (158 AGeV) and 30% (30 AGeV) and staysstrong throughout the ﬁnal expansion stage of the reac-tion. In contrast, the direct rho (full symbols) regenera-tion is weak (only 10-15% at both energies) and becomesnegligible after 12 fm/c.To summarize, the importance of the regeneration ofresonances in heavy ion collisions was studied. It wasshown that a full regeneration of the ∆1232 abundancieson time scales of 6 fm/c is possible within the presentmodel. In contrast to the rho, a large regeneration prob-ability of Deltas was found which might explain the slightenhancement of the ∆++/p ratio with centrality. Furtherinvestigation of the regeneration and absorption dynam-ics are currently under way.ACKNOWLEDGEMENTSThis work was supported by GSI, DFG and BMBF.The computational resources have been provided by theCenter for Scientiﬁc Computing at Frankfurt. S.V.thanks the organizers for the great time at Winter Meet-ing in Bormio.[1] P. Braun-Munzinger, Summary talk at the Quark Matter2004 Conference in Oakland, CA, USA.[2] C. Markert [STAR Collaboration], J. Phys. G 30 (2004)S1313 [arXiv:nucl-ex/0404003].[3] C. Markert [STAR Collaboration],arXiv:nucl-ex/0308029.[4] C. Markert [STAR Collaboration], J. Phys. G 28 (2002)1753 [arXiv:nucl-ex/0308028].[5] P. Fachini [STAR Collaboration], J. Phys. G 30 (2004)S565 [arXiv:nucl-ex/0305034].[6] P. Fachini, Acta Phys. Polon. B 35 (2004) 183[arXiv:nucl-ex/0311023].[7] P. Fachini, J. Phys. G 30 (2004) S735 [arXiv:nucl-ex/0403026].[8] S. C. Johnson, B. V. Jacak and A. Drees, Eur. Phys. J.C 18 (2001) 645 [arXiv:nucl-th/9909075].[9] S. S. Adler et al. [PHENIX Collaboration], Phys. Rev.C 71 (2005) 034908 [Erratum-ibid. C 71 (2005) 049901][arXiv:nucl-ex/0409015].[10] P. Braun-Munzinger, D. Magestro, K. Redlich andJ. Stachel, Phys. Lett. B 518 (2001) 41 [arXiv:hep-ph/0105229].[11] E. E. Zabrodin, L. V. Bravina, L. P. Csernai, H. St¨ ockerand W. Greiner, Phys. Lett. B 423, 373 (1998)[arXiv:hep-ph/9806207].[12] W. Broniowski, W. Florkowski and B. Hiller, Phys. Rev.C 68 (2003) 034911 [arXiv:nucl-th/0306034].[13] G. Torrieri, J. Letessier, J. Rafelski and S. Steinke, ActaPhys. Polon. B 35 (2004) 2911 [arXiv:nucl-th/0411007].[14] G. Torrieri and J. Rafelski, Phys. Lett. B 509 (2001) 239[arXiv:hep-ph/0103149].[15] M. Bleicher and J. Aichelin, Phys. Lett. B 530 (2002) 81[arXiv:hep-ph/0201123].[16] M. Bleicher, Nucl. Phys. A 715 (2003) 85 [arXiv:hep-ph/0212378].[17] M. Bleicher and H. St¨ ocker, J. Phys. G 30 (2004) S111[arXiv:hep-ph/0312278].[18] S. A. Bass et al., Prog. Part. Nucl. Phys. 41 (1998) 225[arXiv:nucl-th/9803035].[19] M. Bleicher et al., J. Phys. G 25 (1999) 1859 [arXiv:hep-ph/9909407].4

Resonance Absorption and Regeneration in Relativistic Heavy Ion Collisions

Abstract

Similar works

Full text

Available Versions

Hochschulschriftenserver - Universität Frankfurt am Main