We study the transverse expansion in central Pb+Pb collisions at the CERN SPS. Strong collective motion of hadrons can be created. This flow is mainly due to meson baryon rescattering. It allows to study the angular distribution of intermediate mass meson baryon interactions

Bass, Steffen A.

Bleicher, Marcus

Ernst, Christoph

Gerland, Lars

Greiner, Walter

Soff, Sven

Spieles, Christian

Stöcker, Horst

English

Hochschulschriftenserver - Universität Frankfurt am Main

arXiv:hep-ph/9803346 v1   13 Mar 1998The Origin of Transverse Flow at the SPSM. Bleicher, C. Spieles, C. Ernst, L. Gerland, S. Soﬀ, H. St¨ ocker, W. GreinerInstitut f¨ ur Theoretische Physik, J. W. Goethe-Universit¨ at,D-60054 Frankfurt am Main, GermanyS. A. Bass∗Department of Physics, Duke UniversityDurham, N.C. 27708-0305, USAAbstractWe study the transverse expansion in central Pb+Pb collisions at the CERNSPS. Strong collective motion of hadrons can be created. This ﬂow is mainlydue to meson baryon rescattering. It allows to study the angular distributionof intermediate mass meson baryon interactions.∗Feodor Lynen Fellow of the Alexander v. Humboldt Foundation1An important question raised in the recent year is: Is there collective transverse expansionand ﬂow at midrapidity in relativistic heavy ion collisions? This phenomenon has long beenpredicted [1,2] as a result of strong stopping and compression wave or shock wave formationwith subsequent hydrodynamical sideward momentum transfer. Flow of baryons and mesonshas been experimentally observed at the LBL/BEVALAC and at GSI/SIS in the 1 AGeVregime [3,4], as well as at the BNL/AGS [5,6].The question now has been raised whether the strong blue shift of the inclusive hadronspectra for high multiplicity events observed last year at the SPS Pb(160 AGeV)+Pb system[7–9] can be theoretically explained by a microscopic calculation. Here we report that theobserved strong increase of pt with mhadron can be due to the large fraction of secondarymeson baryon collisions.A heavy ion collision can be divided into three phases: Incoming nucleons interact witheach other, they produce secondary particles and gain transverse momentum. In the courseof the rescattering stage, the system may reach thermal (or even chemical) equilibrium, whilecollective transverse expansion develops. Finally the system dilutes, strong interactions cease- the system freezes out.The studies presented in this letter are performed within the UrQMD model [10], amicroscopic hadronic transport approach based on the covariant propagation of mesonicand baryonic degrees of freedom. It allows for rescattering and the formation and decay ofresonances and strings.Let us brieﬂy discuss how meson baryon reactions are modeled within UrQMD. In thelow energy region, i.e.√s < ∼ 2 GeV, the inelastic cross section is dominated by s-channelresonance formation. It is calculated from detailed balance according to the sum of thepossible ﬁnal state baryon resonances (e.g. π− + p → ∆0 or N∗):σMBtotal(√s) =XR=∆,N∗ jB,mB,jM,mM|JR,MR 2IR + 1(2IB + 1)(2IM + 1)(1)×πp2CMSΓR→MBΓtot(MR −√s)2 +Γ2tot4, (2)which depends on the total decay width Γtot, the partial decay width ΓR→MB, the spins of2the particles I and on the c.m. energy√s. According to its lifetime this resonance decaysisotropically in its local restframe into (one or more) mesons and a baryon.In the ultra high energy limit t-channel processes dominate the total cross section, whichcan be calculated from Regge theory [11]:σtotal = Xsǫ + Y s−η . (3)Here the ﬁrst term describes the pomeron exchange, while the second one is due to ρ, ω, f anda meson exchange, while s denotes the squared center of mass energy. The parameters areﬁxed by experimental data when available (π + N, K + N, ...). For completely unknowncross sections we employ additional rescaling factors from the additive quark model [12]under the assumption of a 40% reduced s-quark cross section (compared to u, d):σAQM = 40￿23￿m1+m2 ￿1 − 0.4s13 − m1￿ ￿1 − 0.4s23 − m2￿[mb] ,σMBunkown(√s) = σπN(√s)σMBAQMσπNAQMwith mi = 1(0) for particle i being a meson (baryon) and si being the number of(anti-)strange quarks in particle i. One or both particles are now excited to longitudi-nal color ﬂux tubes. Due to the extremely high relative momenta of the incident hadrons,the fragmentation of the strings leads to a strongly forward-backward peaked distributionof secondaries.Heavy ion collisions at the AGS and, even more so, at the SPS exhibit an intricatescenario: Here, the typical MB collision energies are in the range of 2-10 GeV, thus cannotbe assigned to one of the above discussed regimes. The necessity to bridge consistently fromone picture of meson baryon interactions to the other becomes apparent if we look at thefollowing reactions where a low momentum pion hits a nucleonπ + N(938) → ∆ → π + N(938) with an isotropic angular distribution, (4)π + N(2000) → String → π + N(2000) with a longitudinal angular distribution. (5)To investigate the inﬂuence of the modelling of meson baryon scattering on the collectivetransverse ﬂow, the UrQMD model was used in two diﬀerent modes:31. A complete downward extrapolation of the high energy longitudinal color ﬂux pictureto√s = 2 GeV (refered to as forward-backward peaked (f-b) variant) .2. An upward extrapolation of the resonance behaviour, i.e. an isotropic angular distri-bution of all outgoing particles in meson baryon reactions (indicated as (iso)).These changes aﬀect only MB collisions above the resonance region (√s > 2 GeV); all otherchannels, i.e. meson meson and baryon baryon reactions, remain unchanged.Let us start by comparing both scenarios to recent preliminary experimental data. InFig. 1 the mean transverse momentum of negatively charged particles (h− = π− + K− + p)as a function of rapidity in Pb+Pb, b < 3.2 fm at 160 AGeV is depicted. Open circles areNA49 data [8], open squares are calculated with the resonance extrapolation (iso) and fullsquares denote the high energy prescription (f-b). Overall good agreement for both ansatzeswith the data on the 10% level is found from projectile to target rapidity.Let us turn now to the transverse momentum spectra of baryons. Fig. 2 shows the”apparent temperature” of protons, ”T”, in Pb(160AGeV)+Pb for diﬀerent rapidities incomparison with preliminary NA49 data (open circles) [8]. The inverse slope ”T” is obtainedfrom a ﬁt to the transverse mass mT spectrum using1mTdNdmT∝ e−mT /T . (6)In both scenarios, the ”temperature” of the protons increases towards midrapidity. Themaximum ”temperatures” are 270 MeV (f-b, full squares) and 395 MeV (iso, open squares).Thus the isotropic meson baryon scattering prescription predicts a temperature at yCMexceeding the preliminary data by 30%.To gain further insight into the creation of transverse ﬂow, Fig. 3 discusses the meantransverse momenta of particles for diﬀerent mass bins at |y| < 0.5 in central Pb+Pbcollisions at the SPS. Circles show the p(160 AGeV)+p events, open squares indicate the(f-b) Pb+Pb events and the full black squares show the MB-(iso)tropic model. In addition,we ﬁt the resulting mass spectra with a simpliﬁed 2 parameter ﬁreball plus ﬂow model. The4full black line is the mean transverse momentum < pT(m,T0,βT) > for diﬀerent massesm calculated from a thermal distribution with temperature T0 = 160 MeV (to ﬁt the π)without any additional ﬂow (βT = 0). The dashed line shows the < pT(m,T0,βT) > froman expanding thermal source (T0 = 170 MeV) with an additional transverse ﬂow velocity ofβT = 0.34c. This yields in the saddle point approximation a rough value for the ”apparenttemperature” T [13]:T ≈ T0 + mβ2T . (7)The mean pT of all hadrons, from proton-proton reactions as well as from the high energynucleus-nucleus (f-b) scenario show no signiﬁcant diﬀerence to a non-expanding thermalsource. However, additional baryon ﬂow is visible due to further baryon baryon collisions.This results in a bump in the mean pT around m ≈ 1.1 GeV. In contrast, the isotropic (MB)model produces a hadronic source which expands more strongly in the transverse direction.A signiﬁcant transverse collective ﬂow velocity of 0.34c is observed in this calculation. Dueto its very small cross section in nuclear matter the Φ-meson aquires less transverse ﬂowcompared to other hadrons. Note that the error bars are only statistical. These are givenonly for the (f-b) Pb+Pb reaction, in the (MB iso) and p+p case they are about the same.The observed apparent ”temperatures” (inverse slopes) at midrapidity (|y| < 0.5) dependstrongly on the particle mass m as depicted in Fig. 4. The calculated proton-proton collisions(crosses) show about the same freeze-out ”temperature” T ≈ mπ for all particles from mπ tom = 2 GeV. In Pb(160 AGeV)+Pb, the ”T”-values increase -in contrast to the data- onlyweakly above the p+p values, if the forward backward scenario (MB) is applied. On theother hand, isotropic angular distributions for intermediate energy meson-baryon collisions(in line with the resonance picture) yield a linearly increasing apparent ”temperature” withthe particle mass for Pb(160 AGeV)+Pb, in agreement with the preliminary NA49 data.We conclude that strong transverse ﬂow can occur in massive reactions at the SPS.However, the hadron mass dependence of the apparent temperature is sensitive to thedetailed modelling of the meson-baryon rescattering process above the resonance region5(√sMB > 2 GeV) and below the high energy domain. Two distinct pictures of mesonbaryon scattering with√sMB > 2 GeV have been confronted: the high energy limit of longi-tudinal fragmenting color strings was extrapolated downward in energy, versus the conceptof resonance formation of meson baryon scattering with isotropic decay. Both models de-scribe the rapidity dependence of the transverse momentum of produced particles equallywell, while the isotropic scattering prescription predict the apparent proton temperaturesat midrapidity about 30% larger than preliminary data. However, strong increase of thetransverse slope does only build up in the high energy ’resonance model’.ACKNOWLEDGEMENTSThis work is supported by the BMBF, GSI, DFG and Graduiertenkolleg ’Schwerionen-physik’. M. Bleicher and S. Soﬀ acknowledge support by the Josef Buchmann Foundation.6REFERENCES[1] W. Scheid, H. M¨ uller, W. Greiner, Phys. Rev. Lett. 32 (1974) 741[2] L.P. Csernai, W. Greiner, H. St¨ ocker, I. Tanihata, S. Nagamiya, J. Knoll, Phys. Rev.C25 (1982) 2482;H. St¨ ocker, W. Greiner, Phys. Rep. 137 (1986) 277[3] K. H. Kampert, J. Phys. G17 (1989) 691[4] H. H. Gutbrod, A. M. Poskanzer, H. G. Ritter, Rep. Prog. Phys. 52 (1989) 1267[5] J. Barrette et al., (E877 Collaboration), Phys. Rev. C56 (1997) 3254[6] R. Mattiello, H. Sorge, H. St¨ ocker, W. Greiner, Phys. Rev. C55 (1997) 1443[7] I.G. Bearden et al., (NA44 Collaboration), Phys. Rev. Lett. 78 (1997) 2080[8] P. G. Jones et al., (NA49 Collaboration), Nucl. Phys. A610 (1996) 188c;G. Roland et al., (NA49 Collaboration), Nucl. Phys. A (1998) in print[9] T. Peitzmann (WA98 Collaboration), Talk given at the Quark Matter ’97, Nucl. Phys.A (1998) in print[10] S. A. Bass, M. Belkacem, M. Bleicher, M. Brandstetter, L. Bravina, C. Ernst, L. Ger-land, M. Hofmann, S. Hofmann, J. Konopka, G. Mao, L. Neise, S. Soﬀ, C. Spieles,H. Weber, L. A. Winckelmann, H. St¨ ocker, W. Greiner, Ch. Hartnack, J. Aichelin,N. Amelin, to be published in Prog. Part. Nucl. Phys. 41 (1998)[11] A. Donnachie, P.V. Landshoﬀ, Phys. Lett. B296 (1992) 227[12] K. Goulianos, Phys. Rep. 101 (1983) 169[13] K.S. Lee, U. Heinz, E. Schnedermann, Z. Phys. C48 (1990) 5257FIGURES-3 -2 -1 0 1 2 3y0.00.10.20.30.40.50.6meanpt(GeV/c)Pb(160AGeV)+Pb, b<3.2 fmh- (NA49)h- (UrQMD (iso))h- (UrQMD(f-b))FIG. 1. Average transverse momentum of h− = π− + K− + p in central Pb(160GeV)+Pbreactions at the SPS.-3 -2 -1 0 1 2 3y0.00.10.20.30.40.50.6Inv.Slope’’T’’(GeV)Pb(160AGeV)+Pb, b<3.2 fmp (NA49)p (UrQMD (iso))p (UrQMD (f-b))FIG. 2. Apparent temperature of protons as a function of rapidity in central Pb(160GeV)+Pbreactions at the SPS.80.0 0.5 1.0 1.5 2.0Particle Mass m (GeV)0.00.20.40.60.81.01.21.41.6meanpT(GeV/c)Transverse Momenta<pT>(T=170 MeV, T=0.34c,m><pT>(T=160 MeV,m)UrQMD (p+p)UrQMD (f-b)UrQMD (iso)FIG. 3. Mean pt at midrapidity (|y| < 0.5) as a function of particle mass in centralPb(160GeV)+Pb reactions (compared to p(160GeV)+p).0.0 0.5 1.0 1.5 2.0Particle Mass (GeV)100150200250300350400450Inv.SlopeT(MeV)Pb(160 AGeV)+Pb, b<3.2 fmUrQMD (p+p)UrQMD (f-b)UrQMD (iso)NA49FIG. 4. Midrapidity (|y| < 0.5) inverse slope parameter T as a function of particle mass incentral Pb(160GeV)+Pb reactions (compared to p(160GeV)+p).901234567890Transverse MomentaT=150 MeV +T=270 MeVT=160 MeVPb+PbP+PK p0.0 0.2 0.4 0.6 0.8 1.0 1.2Particle Mass (GeV)0.10.150.20.250.3Inv.SlopeT(GeV)P+PS+SPb+Pb+ K+ p

The origin of transverse flow at the SPS

The origin of transverse flow at the SPS

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