The dependence of pion and strangeness production on the number of
participant nucleons and collision energy is discussed for central A+A
collisions. A possible interpretation of the experimental results assuming
transition to QGP is sketched within a simple statistical approach.Comment: 13 pages, 5 figures, some modifications of text and figure

Gazdzicki, Marek

English

arXiv

The dependence of pion and strangeness production on the number of participant nucleons and collision energy is discussed for central A+A collisions. A possible interpretation of the experimental results assuming transition to QGP is sketched within a simple statistical approach

Gaździcki, Marek

Hochschulschriftenserver - Universität Frankfurt am Main

arXiv:hep-ph/9606473 v2   8 Jul 19961INSTITUT F¨ UR KERNPHYSIK, UNIVERSIT¨ AT FRANKFURT60486 Frankfurt, August–Euler–Strasse 6, GermanyIKF–HENPG/2–96Pion and Strangeness PuzzlesMarek Ga´ zdzicki1Institut f¨ ur Kernphysik, Universit¨ at Frankfurt, Frankfurt, GermanyAbstractDependence of pion and strangeness production on number of participant nucleonsand collision energy is discussed for central A+A collisions. A possible interpreta-tion of the experimental results assuming transition to QGP is sketched within asimple statistical approach.Talk given at STRANGENESS’96, Budapest, Hungary, May 15–17 1996to be published in the special issue of Heavy Ion PhysicsSeptember 5, 20051E–mail address: marek@ikf.physik.uni–frankfurt.de21. IntroductionMassive hadrons are eﬀective degrees of freedom in strongly interacting matter atlow energy density. We expect that in the matter at high enough energy density thedegrees of freedom are almost massless quarks and gluons. This new form of matterconjectured long ago [1] is called Quark Gluon Plasma (QGP) [2]. By studies ofthe transition to QGP and the QGP properties itself we can better understand thestructure of the QCD vaccum, the origin of the hadron masses and conﬁnement ofquarks inside hadrons.Relativistic nucleus–nucleus collisions (A+A) are used as a tool to studystrongly interacting matter under extreme conditions. In the laboratory we cancontrol two basic parameters determining the property of the matter: the size ofthe colliding nuclei and the collision energy. With the increasing size of the collidingnuclei we increase the volume of the created matter and its life time. Increasingcollision energy we increase the initial energy density of the created matter. Thusthe transition from hadronic matter (HM) to QGP should be observed as a changeof the collision properties studied as a function of the size of colliding nuclei and/orcollision energy.The characteristic feature of the transition from hadronic matter to QGP isan increase of the eﬀective number of degrees of freedom and the reduction of theirmasses [3]. The increase of the eﬀective number of degrees of freedom should causean increase of entropy production. Thus the produced entropy, at high energiesmainly determined by the multiplicity of pions, can be considered as one of theimportant observables in search for a transition to QGP [4]. The reduction of theeﬀective masses of the degrees of freedom should result in the weaker dependence ofthe ratio particle number/entropy on the temperature of matter (collision energy).The corresponding observable is the ratio strangeness/entropy [5, 6], at high energymainly determined by the ratio strangeness/pion; by strangeness we mean heretotal number of s and s quarks in the system. Note that entropy, strangeness andbaryon number are deﬁned in any form of strongly interacting matter like QGP orHM. Therefore their values (or ratios) can be followed through hadronization andfreeze–out stages of the collision when the distribution of entropy, strangeness andbaryon number among ﬁnal states hadrons takes place.We argue below that the existing data on pion and strangeness productionin central collisions of heavy nuclei indicate rapid changes occuring between BNLAGS (≈ 15 A GeV/c) and CERN SPS (≈ 200 A GeV/c) collision energies. Canthese changes be interpreted as due to transition from HM to QGP?This presentation reviews several recent works of Dieter R¨ ohrich and myself [7,8, 9] where the details of the analysis and the references to the original experimentalpapers used in the compilations [7, 9] are given.The paper is organized as follows. In the Section 2 the main properties of theanalysis of the experimental data are described. In Sections 3 and 4 the experi-mental results are presented. The dependence of pion and strangeness production3on the number of participant nucleons and collision energy is shown. The resultsare discussed in Section 5. The paper is closed by summary and conclusions givenin Section 6.2. AnalysisThe aim of this paper is to study basic features of pion and strangeness productionin nuclear collisions as a function of the size of the colliding nuclei and the collisionenergy. This goal suggests a speciﬁc way of data selection and presentation.Matter created in A+A collisions expands in a complicated way. This expan-sion depends on the size of the colliding nuclei and collision energy. In order toreduce the inﬂuence of the expansion on the results and allow comparison of thedata for various systems and energies we limit analysis to the data integrated overthe full momentum space.Comparison and interpretation of the data can be further simpliﬁed by con-centrating on the data for head–on collisions of identical nuclei. Thus in the presentpaper the analysis is limited to the central collisions of similar nuclei.Even in head–on collisions of identical nuclei not all nucleons participate inthe interaction. Therefore to study the volume dependence an average numberof participant nucleons,  NP , measured experimentaly for each reaction is usedinstead of the total number of nucleons in the colliding nuclei. The A+A results arecompared with the corresponding results for all inelastic nucleon–nucleon (N+N)interactions. In the case of N+N interactions the number of participant nucleonsis taken to be 2.The collision energy dependence is studied using the Fermi energy variable[10, 11]:F =(√sNN − 2mN)3/4√s1/4NN, (1)where√sNN is the c.m. energy for a nucleon–nucleon pair and mN is the massof the nucleon. There are several advantages in using F as an energy variable.The measured mean pion multiplicity in N+N interactions,  π NN, in the studiedcollision energy range is approximately proportional to F [7, 8, 12]. In the Lan-dau model [11] both the entropy and the initial temperature of the matter (for √sNN >> 2mN) are also proportional to F.3. Pion PuzzleThe dependence of the average pion multiplicity per participant nucleon,  π / NP ,on the number of participant nucleons is shown in Fig. 1 for three diﬀerent collisionenergies.Results for central collisions of identical nuclei (A > 30) are plotted togetherwith the results for N+N interactions. The  π / NP  ratio for central A+A col-4lisions at all energies is independent of  NP  [13]. At low energies (pLAB < 15A GeV/c) the value of the saturation level of the  π / NP  ratio for central A+Acollisions is signiﬁcantly lower than the corresponding value for N+N interactions.This eﬀect is called pion suppression in low energy A+A collisions. At high ener-gies pion enhancement is observed; the saturation level for central A+A collisionsis higher than the corresponding ratio for N+N interactions.The independence of the  π / NP  ratio of  NP  simpliﬁes a study of theenergy dependence for which data for various nuclei can be put together. Thediﬀerence between the ratio  π / NP  for central A+A collisions and N+N inter-actions:∆ π  NP = π AA NP AA− π NN NP NN(2)is plotted in Fig. 2 as a function of F.The diﬀerence is energy independent and equal to about –0.35 for low energycollisions (pLAB < 15 A GeV/c). The low energy scaling is violated by high energyresults (Pb+Pb at 158 A GeV/c and S+S at 200 A GeV/c), where the enhancementof pion production is observed. A possible origin of this unusual energy behaviour,called pion puzzle, is discussed in Section 5.4. Strangeness PuzzleTotal production of strangeness relative to pion production is studied using theratio [14]:ES = Λ  +  K + K  π , (3)where  Λ  is the mean multiplicity of produced Λ/Σ0 hyperons and  K + K  isthe mean multiplicity of kaons and antikaons. The dependence of the ES ratio on NP  is shown in Fig. 3 for three diﬀerent collision energies. The results for centralA+A collisions [16] are shown together with the results for N+N interactions. Dueto the fact that the data on strangeness production are sparse the data for colli-sions between non–equal mass nuclei are also included (C+Cu/Zr at 4.5 A GeV/c,Si+Au/Pb at 14.6 A GeV/c [15] and S+Ag at 200 A GeV/c).There is a signiﬁcant increase of the relative strangeness production (measuredby the ES ratio) when going from N+N interactions to central A+A collisions at allstudied collision energies. This increase is called strangeness enhancement. Itappears to be strongest at BNL AGS energy. The relative strangeness productionsaturates for large enough values of  NP  at AGS BNL and CERN SPS energies.The saturation eﬀect can not be established at 4.5 A GeV/c as the results forcollisions of heavy nuclei do not exist at this energy.The collision energy dependence of the ES ratio is shown in Fig. 4. Theresults for N+N interactions are shown in Fig. 4a. A monotonic increase of ESbetween Dubna energy (pLAB = 4.5 A GeV/c) and CERN SPS energy (pLAB =5200 A GeV/c) is observed. In the range from 15 A GeV/c to 200 A GeV/c the ESratio for N+N interactions increases by a factor of about 2. A qualitatively diﬀerentenergy dependence is observed for central A+A collisions. The rapid increase ofthe ES between Dubna and BNL AGS energies is followed by a weak change of theES between BNL AGS and CERN SPS collision energies (Fig. 4b).A possible interpretation of the strangeness puzzle – ’strange’ energy de-pendence of the relative strangeness production in A+A collisions – is discussed inthe next section.5. DiscussionThe saturation of the relative pion ( π / NP ) and strangeness (ES) productionwith the volume of the created system ( NP ) may be treated as an indicationthat both entropy and strangeness approached their equilibrium values. Thus theinterpretation of the results in terms of statistical models is suggested by the data.It can be argued [11, 17, 18] that both entropy and strangeness reach satura-tion at the early and hot stages of the collision and their values are only weaklyaﬀected by later stages of system evolution. Further interpretation of the presentresults is therefore based on the simpliﬁng assumption that the measured ﬁnal stateentropy and strangeness reﬂect the equilibrium values at high temperature stage.Thus studing the entropy and strangeness production one can try to deduce theproperties of matter (HM or QGP) at the early stage of the collision.Transition from HM to QGP causes an increase of the eﬀective number ofdegrees of freedom resulting in the increase of entropy production. As pointed outby Landau [11] the entropy of the system is approximately proportional to the pionmultiplicity [19]. The entropy contained in baryons and generated during theirthermalization process is not directly sensitive to the initial number of degreesof freedom and therefore should not be counted. Thus the relevant quantity isthe entropy contained in the produced particles – the inelastic entropy. Howeverduring the expansion process a fraction of the initially created inelastic entropy canbe transfered back to the baryonic environment. The experimental observation ofpion suppression at low energies (see Figs. 1 and 2) can be interpreted as a resultof the inelastic entropy transfer to baryons. Following arguments given in Ref. [8]one can estimate the inelastic entropy as:S ∼  π  + α    NP , (4)where α    NP  is a correction for the inelastic entropy transfer to baryons (α ≈−0.35). For simplicity the contribution from other produced particles (mainlykaons) is neglected in Eq. 4, but it is included in the ﬁnal evaluation of S pre-sented in Fig. 5a [8].The unusual increase of the relative pion production at CERN SPS energiesmay be interpreted as due to an increase of the eﬀective number of degrees of6freedom. In fact, in the generalized Landau model [8] the inelastic entropy isproportional to:S ∼ g1/4    NP    F, (5)where g is the eﬀective number of degrees of freedom. Thus the observed deviationof the data for A+A collisions from the Landau scaling:S NP ∼ F (6)can be interpretad as due to an increase of the eﬀective number of degrees of freedomwhen crossing the transition collision energy. The magnitude of this increase canbe estimated, within the generalized Landau model, as forth power of the ratio ofslopes of straight lines describing (see Fig. 5a) low and high energy A+A data:1.334 ≈ 3 [8]. A hypothetical dependence of S/ NP  on F is shown by solid lines inFig. 5a; the transition region is assumed to be at about pLAB = 30 A GeV/c [20].The second dominant eﬀect of the transition from HM to QGP is the reductionof the eﬀective masses of degrees of freedom. Basic thermodynamics tells us that formassless particles the ratio particle number/entropy is independent of temperature.For massive particles the ratio increases with T at low temperature approachingsaturation level (equal to the corresponding ratio for massless particles) at hightemperatures, T >> m. This property can be used to study the magnitude of theeﬀective mass of strangeness carriers in strongly interacting matter. The ES ratiois approximately proportional to the ratio number of strangeness carriers/entropy(strangeness/entropy) and therefore its temperature (collision energy, F) depen-dence should be sensitive to the eﬀective mass of strangeness carriers. Reduction ofthe mass of strangeness carriers should cause a weaker dependence of the ES ratioon the collision energy.The rapid increase of the ES ratio in the energy range of F < 2 GeV1/2 (seeFig. 4b) can be interpreted as due to large eﬀective mass of strangeness carriers(kaons or constituent strange quarks, mS ≈ 500 MeV ) in comparison to the tem-perature of matter, T < TC ≈ 150 MeV. At temperature above TC matter is inthe form of QGP and mass of strangeness carriers is equal to the mass of currentstrange quarks, mS ≈ 150 MeV, consequently mS ≤ T. Thus much weaker depen-dence of the ES ratio on F is expected in the high energy region where the creationof QGP takes place.The equilibrium value of the strangeness/entropy ratio is higher in HM thanin QGP at very high temperatures. This is due to the fact that it is proportional tothe ratio of the eﬀective number of strangeness degrees of freedom to the number ofall degrees of freedom. This ratio is lower in QGP than in hadronic matter. At lowtemperature, however, the strangeness/entropy ratio is lower in HM than in QGP.This is caused, as previously discussed, by the high mass of strangeness carriers inHM. Thus, in general, a transition to QGP may lead to an increase or a decreaseof the strangeness/entropy ratio depending at which temperatures of QGP andHM the comparison is made. A quantative estimation of the strangeness/entropy7dependence on temperature within simple models of QGP and HM can be found inRef. [6]. The estimated temperature of the crossover of QGP and HM dependencesis about 130 MeV [6]. The measured low values of the ES ratio at CERN SPSrelative to the values at BNL AGS can be interpreted as due to reduction of theES value at the transition to QGP. The hypothetical dependence of the ES ratioon F is indicated by the solid lines in Fig. 5b. The transition region is assumed tobe at about pLAB = 30 A GeV/c [20].6. Summary and ConclusionsThe experimenal data on pion and strangeness production indicate:(a) saturation of pion and strangeness production with the number of participantnucleons,(b) change in the collision energy dependence occuring between 15 A GeV/c and200 A GeV/c.Within a simple statistical approach the observed behaviour can be qualitativelyunderstood as due to:equilibration of entropy and strangeness production in collisions of heavy nuclei (a),transition from hadronic matter to QGP occuring between BNL AGS and CERNSPS energies (b).These observations hold already for the central S+S collisions, they are not uniqueto central Pb+Pb collisions.A quantitative description of the existing data within theoretical models andexperimental study of the energy dependence of pion and strangeness productionbetween BNL AGS and CERN SPS energies are needed for a ﬁnal clariﬁcation ofthe observed pion and strangeness puzzles.AcknowledgmentsI would like to thank Reinhard Stock for numerous discussions and comments .References1. J. C. Collins and M. J. Perry, Phys. Rev. Lett. 34 (1975) 151.2. E. V. Shuryak, Phys. Rep. C61 (1980) 71 and C115 (1984) 151.3. Quark Gluon Plasma 2, Ed. R. C. Hwa, World Scientiﬁc (1995)4. L. Van Hove, Phys. Lett. B118 (1982) 138.5. K. Redlich, Z. Phys. C27 (1985) 633.6. J. Kapusta and A. Mekjan, Phys. Rev. D33 (1986) 1304.7. M. Ga´ zdzicki and D. R¨ ohrich, Z. Phys. C65 (1995) 215.8. M. Ga´ zdzicki, Z. Phys. C66 (1995) 659.9. M. Ga´ zdzicki and D. R¨ ohrich, Z. Phys. C71 (1996) 55.810. E. Fermi, Prog. Theor. Phys. 5 (1950) 570.11. L. D. Landau, Izv. Akad. Nauk SSSR, Ser. Fiz. 17 (1953) 51,S. Z. Belenkij and L. D. Landau, Uspekhi Fiz. Nauk 56 (1955) 309.12. A. I. Golokhvastov, Dubna Report, JINR E2–89–364 (1989).13. The Pb+Pb data at 158 A GeV/c are taken from:M. Ga´ zdzicki et al. (NA49 Collab.), Nucl. Phys. A590 (1995) 197c.14. T. Alber et al. (NA35 Collab.), Z. Phys. C64 (1994) 195.15. S. E. Eiseman et al. (E810 Collab.), Phys. Lett. B297 (1992) 44,T. Abbott et al. (E802 Collab.), Phys. Rev. C50 (1994) 1024.16. The ES ratio for Pb+Pb collisions at 158 A GeV/c was estimated on thebasis of the preliminary NA49 results for kaon production presented at thisConference by S. Margetis.17. J. Letessier, A. Tounsi and J. Rafelski, Phys. Rev. C50 (1994) 406,J. Letessier, A. Tounsi and J. Rafelski, Acta Phys. Pol. 27 (1996) 1035 andreferences therein.18. K. Geiger, Nucl. Phys. A566 (1994) 257c and references therein.19. for detailed discussion of the inﬂuence of non-equilibrium processes at freeze–out see::J. Sollfrank and U. Heinz, Phys. Lett. 289 (1992) 132,S. Ochs and U. Heinz, University of Regensburg Report, TPR 96–09, hep–ph/9606458 (1996).20. C. M. Hung and E. V. Shuryak, Phys. Rev. Lett. 75 (1995) 40079Fig. 1. The dependence of the ratio  π / NP  on  NP  at three diﬀerent col-lisions energies (pLAB = 2.1, 14.6 and 200 A GeV/c). The data for Au+Au at11.6 A GeV/c and Pb+Pb at 158 A GeV/c were extrapolated to 14.6 A GeV/cand 200 A GeV/c, respectively. The data for central A+A collisions are indi-cated by circles and the data for N+N interactions by squares.10Fig. 2. The dependence of the diﬀerence ∆( π / NP ) (see Eq. 2) on thecollision energy measured by the Fermi energy variable, F (see Eq. 1).11Fig. 3. The dependence of the ES ratio (see Eq. 3) on  NP  at threediﬀerent collisions energies (pLAB = 4.5, 11.6–14.6 and 158–200 A GeV/c).The data for central A+A collisions are indicated by circles and the data forN+N interactions by squares.12Fig. 4. The dependence of the ES ratio (see Eq. 3) on the collision energymeasured by the Fermi energy variable, F (see Eq. 1) for N+N interactions(a) and central A+A collisions (b).13Fig. 5. (a) The dependence of the S/ NP  ratio (see Eq. 4) on the collisionenergy measured by the Fermi energy variable, F (see Eq. 1). The entropy, S,is measured in units given by pion entropy at freeze–out. A hypothetical depen-dence of S/ NP  ratio on F for central A+A collisions assuming transtion toQGP at pLAB = 30 A GeV/c is shown by solid lines. The data for central A+Acollisions are shown by circles and the data for N+N interactions by squares.(b) A hypothetical dependence of the ES ratio on F assuming transition toQGP at pLAB = 30 A GeV/c is shown by a solid lines. The data for centralA+A collisions are indicated by circles.

1035 and references therein.

257c and references therein.

71 and C115

for detailed discussion of the inﬂuence of non-equilibrium processes at freeze– out see::

The ES ratio for Pb+Pb collisions at 158 A GeV/c was estimated on the basis of the preliminary NA49 results for kaon production presented at this Conference by S.

Pion and Strangeness Puzzles

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