A recent paper on energy dependence of strangeness production in A+A and p+p interactions written by Dunlop and Ogilvie (Phys. ReV. C61 031901(R) (2000) indicates that there is a significant misunderstanding about the concept of strangeness enhancement and its role as a signal of Quark Gluon Plasma creation. In this comment we will try to clarify some essential points. 25.75.Dw, 13.85.Ni, 21.65.+

Gazdzicki, Marek

Gorenstein, Mark I.

Röhrich, Dieter

English

Gaździcki, Marek

Hochschulschriftenserver - Universität Frankfurt am Main

arXiv:hep-ph/0006236 v1   20 Jun 2000Comment on “Comparison of strangeness productionbetween A+A and p+p reactions from 2 to 160 A GeV”,by J. C. Dunlop and C. A. OgilvieMarek Ga´ zdzickiCERN, Geneva, Switzerland,Institut f¨ ur Kernphysik, Universit¨ at Frankfurt, Frankfurt, GermanyMark I. GorensteinBogolubov Institute for Theoretical Physics, Kiev, Ukraine,Institut f¨ ur Theoretische Physik, Universit¨ at Frankfurt, Frankfurt, GermanyDieter R¨ ohrichUniversity of Bergen, Bergen, Norway(September 29, 2005)AbstractA recent paper on energy dependence of strangeness production in A+Aand p+p interactions written by Dunlop and Ogilvie [1] indicates that there isa signiﬁcant misunderstanding about the concept of strangeness enhancementand its role as a signal of Quark Gluon Plasma creation. In this comment wewill try to clarify some essential points.PACS numbers: 25.75.Dw, 13.85.Ni, 21.65.+fTypeset using REVTEX1In a recent publication Dunlop and Ogilvie (DO) [1] studied the energy dependence ofstrangeness production and considered it from the point of view of a possible transition toQuark Gluon Plasma (QGP). In our opinion the DO paper does not reﬂect the status of thediscussion on these subjects correctly and it is even misleading. We, therefore, feel the needto comment on the observation of anomalous energy dependence of strangeness productionin nucleus–nucleus (A+A) collisions and its possible interpretation. In the ﬁrst section ofour comment we show that the data analysis part of the DO paper repeats our earlier workwithout, however, any reference to it. In the second section we argue that the DO proposalto search for the transition by studying the energy dependence of strangeness enhancementfactor is unjustiﬁed and misleading.I. Data on Strangeness ProductionIn 1994 the idea that the creation of a transient QGP state in the early stage of A+Acollisions should be reﬂected in the collision energy dependence of basic observables triggeredour analysis of results on hadron multiplicities in A+A and nucleon–nucleon (N+N) colli-sions. The work commenced from the relatively rich data on pion production [2]. In 1996this study was extended to strangeness production [3]. The basic experimental observationsconcerning strangeness here called strangeness anomaly were the following:• the strangeness to pion ratio in central A+A collisions increases rapidly with thecollision energy up to the top AGS (15 A GeV) energy; the ratio at top SPS (200A GeV) energy is approximately equal to the ratio at AGS;• a very diﬀerent energy dependence is observed for N+N interactions, a monotonicincrease is seen at all energies, between top AGS and SPS energies the ratio increasesby a factor of about 2.This strangeness anomaly is rediscovered in the very recent DO paper [1] on the basis ofdata on central Pb+Pb collisions at SPS energy (158 A GeV) [4] and Au+Au collisions atAGS energies [5]. After clarifying two points, the similarity becomes obvious:1.) In the original paper [3] the strangeness to pion ratio was quantiﬁed by the measure2ES ≡ Λ  +  K + K  π , (1)where  Λ ,  K + K  and  π  are mean multiplicities of Λ hyperons, K + K mesons and allpions, respectively. For the comparison of the A+A collisions to nucleon-nucleon interactionsthe N+N results were constructed by a proper averaging of p+p, n+p and n+n data. Theabove procedure yields the best experimental estimate of the total strangeness to pion ratio.Our compilations indicate that the K+/π+ ratio used in DO paper is closely (within 20–30%) related to the ES measure.2.) In refs. [2,3] the energy dependence of pion and strangeness production is presentedby using the Fermi energy measure:F ≡ (√s − 2m)3/4/√s1/4 ∼ =√s1/2 , (2)where√s is the c.m. energy for a nucleon–nucleon pair and m is the nucleon mass. Inthe statistical model of the early stage of the collision both entropy and the early stagetemperature are approximately proportional to F [8]. In the DO paper the dependence on√s is studied.Keeping these two technical diﬀerences in mind one observes that Figs. 1, 2, 3(5) and 4in the DO paper are almost identical to, respectively, Figs. 3(4) in [3], 1 in [2], 7(8) in [3](for the most recent version see also Fig. 3 in [6]) and Fig. 3 in [7]. Therefore, the analysispresented in the DO paper fully conﬁrms the observations made in refs. [3,6,7] ( however,without any references to these papers).II. Interpretation of Strangeness AnomalyThe anomalous energy dependence of the strangeness to pion ratio in A+A collisions(see the previous section) was established experimentally and its connection with a possibleobservation of transition to QGP in A+A collisions between AGS and SPS was stressed inRefs. [3,8]. Note also that it serves as one of the basic arguments for the current studyof the low energy (40 A GeV) Pb+Pb collisions at CERN SPS [9]. In contrast to thissuggestion it is proposed in the DO paper that in order to search for the transition to QGP3one should study the energy dependence of the strangeness enhancement factor, i.e. theincrease of the strangeness to pion ratio between N+N and A+A collisions. The idea ofstrangeness enhancement as a QGP signal was formulated about 20 years ago [10] and wasbased on the estimate that the strangeness equilibration time in QGP is of the same order(≈ 10 fm/c) as the expected life time of the ﬁreball created in A+A collisions. Thus inthe case of QGP formation the strangeness content is expected to approach its equilibriumvalue in QGP. This equilibrium value is signiﬁcantly higher (factor 2 or more dependingon energy) than the strangeness production in elementary N+N interactions. Furthermoreit was estimated that the strangeness production in secondary hadronic interactions whichmay follow initial N+N interactions is small [11]. Therefore, if QGP is not formed, thestrangeness yields would be expected to be much lower than those predicted by equilibriumQGP calculations1. For experimental and theoretical reasons it is convenient to analyse thestrangeness to pion ratio in an actual study of strangeness production. Then a simple andelegant signature of QGP creation appeared: a transition to QGP should be signalled byan increase of the strangeness to pion ratio from the value close to that measured in N+Ninteractions at the corresponding energy to the level given by QGP in equilibrium. Thisidea motivated study of the strangeness to pion ratio in A+A collisions relatively to thecorresponding ratio in N+N interactions as a function of nuclear mass number and collisionenergy.The comparison of the above expectations with the data was for the ﬁrst time possiblein 1988 when the preliminary results from S and Si beams at SPS and AGS were presented.Experiment NA35 reported [12] that in central S+S collisions at 200 A GeV the strangenessto pion ratio is two times higher than in N+N interactions at the same energy per nucleon.1In the DO discussion of the results of the data analysis performed within hadron gas models theusage of the model parameters γS (strangeness saturation factor) and λS (strangeness suppressionfactor) have apparently been confused.4Surprisingly even larger enhancement (a factor of about 3) was measured by E802 in Si+Acollisions at AGS [13]. Recent data on central Au+Au collisions at low AGS energies [5]complete the picture: strangeness enhancement is observed at all energies, it is even strongerat lower energies than at the SPS energy. Thus the interpretation in line with the originalconcept (strangeness enhancement → QGP) was put in question from the very beginningby the AGS data. At the low AGS energies one does not expect the creation of QGPand therefore one should not observe substantial strangeness enhancement. ConsequentlyAGS measurements of strangeness enhancement larger than that at SPS clearly leads tothe following conclusion: the simple concept of strangeness enhancement as a signal ofQGP is incorrect. Furthermore the observed enhancement is very large (factor several),indicating that a potential connection between strangeness measured in A+A collisions andthat produced in initial N+N interactions is lost. Therefore, the proposal of the DO paperto search for the transition to QGP by studying the energy dependence of the strangenessenhancement factor should be treated as unjustiﬁed and misleading, it is not based on anyspeciﬁc model or at least an intuitive physical picture.From our point of view it is more natural to concentrate on the strangeness to pionratio in A+A collisions instead of relating it to N+N interactions, which may only introduceadditional problems into the data interpretation. This suggestion is justiﬁed by the statisticalmodel of the early stage of A+A collisions [8] which, for a reasonable selection of the modelparameters, predicts a transition to QGP between AGS and SPS energies and explains theobserved strangeness anomaly by the presence of this transition. We would like to stressonce more the simplicity of the argument, which relies on the basic assumption of the modelthat in both conﬁned and deconﬁned matter a maximum entropy state is created at the earlystage of the collisions. In conﬁned matter the mass of strange and non–strange degrees offreedom are expected to be of the order of kaon and pion masses (mS ∼ = 0.5 GeV, mNS ∼ = 0.14GeV), respectively, and the temperature is T < TC ∼ = 0.170 GeV. Thus, strange degrees offreedom are heavy (mS > T) and non-strange light (mNS < T). Therefore, in the statisticalmodel one obtains approximately5 nS  nNS ∼T 3/2 exp(−mS/T)T 3 , (3)which is an increasing function of T for T < TC(< 2mS/3). In QGP mS ∼ = 0.170 GeV andmNS ∼ = 0.01 GeV. Both strange and non-strange degrees of freedom are light (m ≤ T), andtherefore one gets approximately nS  nNS ∼ = const(T) . (4)Consequently within the statistical model of the early stage we ﬁnd a simple explanationfor a fast increase of the strangeness to pion ratio at low energies (Eq. 3) and its rapidsaturation at high energies (Eq. 4) provided that the threshold for QGP creation is crossed.Two striking predictions follow from our approach.1.) Very similar strangeness to pion ratio is predicted for SPS, RHIC and LHC energies.This follows from the observations that the model predicts the transition to QGP to occurbelow top SPS energy (and above top AGS energy) and that in QGP the ratio  nS / nNS is almost independent of temperature (collision energy).2.) A non–monotonic (or kinky) energy dependence of the strangeness to pion ratio ispredicted in the vicinity of the transition region. This is due to the fact that the modelpredicts the transition to occur at an energy where the strangeness to entropy (pion) ratioin the conﬁned matter is higher (or equal) than in the QGP. Thus an initial fast increase ofthe ratio is expected to be followed by a decrease (or a saturation) to the level expected inan equilibrium QGP. The decrease starts at the onset of the transition region (≈ 30 A GeV)and ends when the pure QGP phase is produced (≈ 60 A GeV) [8].In Fig. 1 the discussd above predictions of the statistical model of the early stagecalculated for TC = 200 MeV [8] are confronted with the experimental data on strangenessto pion ratio. In the case of TC = 170 MeV the onset of transition takes place at the top AGSenergy and the non–monotonic behaviour is substituted by a kink in the energy dependence.In general, one might try to extend the model calculations to N+N interactions; in thiscase, however, canonical, and at low energy even micro-canonical, calculations are needed.6Note that this introduces additional dependence on model assumptions and parameters andtherefore also from the point of view of our model study of strangeness enhancement factoronly confuses the interpretation of the data.We hope to have shown that the idea to search for QGP by studying the strangenessenhancement factor, as proposed by DO, is unjustiﬁed and may lead to misleading conclu-sions.AcknowledgementsWe thank M. van Leeuwen for comments on the manuscript. We acknowledge the ﬁnan-cial support of BMBF and DFG, Germany.7REFERENCES[1] J. C. Dunlop and C. A. Ogilvie, Phys. Rev. C61, 031901(R) (2000).[2] M. Ga´ zdzicki and D. R¨ ohrich, Z. Phys. C65, 215 (1995).[3] M. Ga´ zdzicki and D. R¨ ohrich, Z. Phys. C71, 55 (1996).[4] J. B¨ achler et al. (NA49 Collab.), Nucl. Phys. A661, 45 (1999).[5] L. Ahle et al. (E866 and E917 Collab.), Phys. Lett. B476, 1 (2000).[6] M. Ga´ zdzicki, Acta Phys. Pol. B30, 3611 (1999).[7] D. R¨ ohrich, Acta Phys. Pol. B29 3277 (1998).[8] M. Ga´ zdzicki and M. I. Gorenstein, Acta Phys. Pol. B30, 2705 (1999).[9] J. B¨ achler et al. (NA49 Collab.), Status and Future Programme of the NA49 Experiment,Addendum–2 to Proposal SPSLC/P264, CERN/SPSC 98–4 January 1998.[10] J. Rafelski and B. M¨ uller, Phys. Rev. Lett. 48, 1066 (1982).[11] P. Koch, B. M¨ uller and J. Rafelski, Phys. Rept. 142, 167 (1986).[12] M. Ga´ zdzicki et al. (NA35 Collab.), Nucl. Phys. A498, 375c (1989).[13] P. Vincent et al. (E802 Collab.), Nucl. Phys. A498, 67c (1989).[14] T. Alber et al. (NA35 Collab.), Z. Phys. C64, 195 (1994),J. B¨ achler et al. (NA35 Collab.), Z. Phys. C58 367 (1993),J. B¨ achler et al. (NA35 Collab.), Nucl. Phys. A661, 45c (1999),L. Ahle et al. (E802 Collab.), Phys. Rev. C60, 044904 (1999),L. Ahle et al. (E802 Collab.), Phys. Rev. C59, 2173 (1999),L. Ahle et al. (E802 Collab.), Phys. Lett. B476, 1 (2000),J. Barrette et al. (E877 Collab.), Nucl. Phys. A661, 198c (1999),J. Barrette et al. (E877 Collab.), nucl–ex/9910004,8S. Ahmed et al. (E981 Collab.), Phys. Lett. B382, 35 (1996).[15] R. E. Ansorge et al. (UA5 Collab.), Nucl. Phys. B328, 36 (1989) and references therein.9FIGURESFIG. 1. Collision energy dependence of strangeness to pion ratio for central nucleus–nucleus[14] collisions (closed points), nucleon–nucleon [3] and p + ¯ p [15] interactions (open points). Thepredictions of the statistical model of the early stage for A+A collisions are indicted by solid line.Within the model one expects a non–monotonic dependence of the strangeness to pion ratio in thevicinity of the transition region and its saturation at the value characteristic for equilibrium QGPat high energies.10

Comment on 'Comparison of strangeness production between A + A and p + p reactions from 2 to 160 A GeV', by J. C. Dunlop and C. A. Ogilvie

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