We found that the experimental results on transverse mass spectra of kaons produced in central Pb+Pb (Au+Au) interactions show an anomalous dependence on the collision energy. The inverse slopes of the spectra increase with energy in the low (AGS) and high (RHIC) energy domains, whereas they are constant in the intermediate (SPS) energy range. We argue that this anomaly is probably caused by a modification of the equation of state in the transition region between confined and deconfined matter. This observation may be considered as a new signal, in addition to the previously reported anomalies in the pion and strangeness production, of the onset of deconfinement located in the low SPS energy domain

Bugaev, Kyrill A.

Gazdzicki, Marek

Gorenstein, Mark I.

Physics Letters B

English

arXiv

We found that the experimental results on transverse mass spectrum of kaons produced in central Pb+Pb (Au+Au) collisions show an anomalous dependence on the colliding energy. The inverse slope of the spectrum increases with the energy in the low (AGS) and high (RHIC) energy domains, whereas it remains constant in the intermediate (SPS) energy range. We argue that this anomaly is probably caused by the modification of the equation of state in the transition region between confined and deconfined matter. This observation may be considered as a new signal, in addition to the previously reported anomalies in the pion and strangeness production, of the onset of deconfinement located in the low SPS energy domain

Gaździcki, Marek

Hochschulschriftenserver - Universität Frankfurt am Main

Transverse activity of kaons and deconfinement phase transition in nucleus–nucleus collisions

Gorenstein, M I

Gazdzicki, M

Bugaev, K A

CERN Document Server

Transverse Activity of Kaonsand the Deconfinement Phase Transitionin Nucleus–Nucleus CollisionsM.I. Gorensteina,b, M. Gaz´dzickic,d and K.A. Bugaeva,e,a Bogolyubov Institute for Theoretical Physics, Kiev, Ukraineb Institut fu¨r Theoretische Physik, Universita¨t Frankfurt, Germanyc Institut fu¨r Kernphysik, Universita¨t Frankfurt, Germanyd Swietokrzyska Academy, Kielce, Polande Gesellschaft fu¨r Schwerionenforschung (GSI), Darmstadt, GermanyAbstractWe found that the experimental results on transverse mass spectra of kaons pro-duced in central Pb+Pb (Au+Au) interactions show an anomalous dependence onthe collision energy. The inverse slopes of the spectra increase with energy in thelow (AGS) and high (RHIC) energy domains, whereas they are constant in the in-termediate (SPS) energy range. We argue that this anomaly is probably caused bya modification of the equation of state in the transition region between confined anddeconfined matter. This observation may be considered as a new signal, in additionto the previously reported anomalies in the pion and strangeness production, of theonset of deconfinement located in the low SPS energy domain.1The statistical model of the early stage, SMES, of nucleus-nucleus (A+A) collisionssuggests [1] that the onset of the deconnement phase transition at the early stage ofthe collisions may be signaled by the anomalous energy dependence of several hadronicobservables. In particular, following earlier suggestions [2], the behavior of strangeness andpion yields in the transition region was studied in detail. Recent measurements [3] of pionand kaon production in central Pb+Pb collisions at the CERN SPS indeed indicate thatthe transient state of deconned matter is created in these collisions for energies largerthan about 40 AGeV. The present data show a maximum of the strangeness to pionratio at this energy. An exact position and the detailed structure of this maximum willbe claried by the soon expected new results from the 2002 Pb run at 20 and 30 AGeV.In the present letter we discuss another well known observable, which may be sensi-tive to the onset of deconnement, the transverse momentum, pT , spectra of producedhadrons. It was suggested by Van Hove [4] more than 20 years ago to identify the decon-nement phase transition in high energy proton{antiproton interactions by an anomalousbehavior (a plateau-like structure) of the average transverse momentum as a function ofhadron multiplicity. Let us briefly recall Van Hove’s arguments. According to the generalconcepts of the hydrodynamical approach the hadron multiplicity reflects the entropy,whereas the transverse hadron activity reflects the combined eects of temperature andcollective transverse expansion. The entropy is assumed to be created at the early stageof the collision and is approximately constant during the hydrodynamic expansion. Themultiplicity is proportional to the entropy, S = s  V , where s is the entropy density andV is the eective volume occupied by particles. During the hydrodynamic expansion, sdecreases and V increases with sV , being approximately constant. The large multiplicityat high energies means a large entropy density at the beginning of the expansion (andconsequently a larger volume at the end). A large value of s at the early stage of thecollisions means normally high temperature T0 at this stage. This, in turn, leads to anincrease of transverse hadron activity, a flattening of the transverse momentum spectra.Therefore, with increasing collision energy 1 one expects to observe an increase of both thehadron multiplicity and average transverse momentum per hadron. However, the presenceof the deconnement phase transition would change this correlation. In the phase transi-tion region the initial entropy density (and hence the nal hadron multiplicity) increaseswith collision energy, but temperature T0 = TC and pressure p0 = pC remain constant.The equation of state presented in the form p(ε)/ε versus energy density ε shows a mini-mum (the ‘softest point’ [5, 6]) at the boundary of the (generalized [6]) mixed phase andthe quark gluon plasma. Consequently the shape of the pT spectrum is approximatelyindependent of the multiplicity or collision energy. The transverse expansion eect mayeven decrease when crossing the transition region [4]. Thus one expects an anomaly inthe energy dependence of transverse hadron activity: the average transverse momentumincreases with collision energy when the early stage matter is either in pure conned orin pure deconned phases, and it remains approximately constant when the matter is inthe mixed phase.1In the original Van Hove suggestion the correlation between average transverse momentum andhadron multiplicity was discussed for proton-antiproton collisions at fixed energy. Today we have thepossibility to study A+A collisions at different energies.2A simplied picture with T = TC = const inside the mixed phase is changed if thecreated early stage matter has a non{zero baryonic density. It was however demonstrated[7] that the main qualitative features (T = const, p = const, and a minimum of thefunction p(ε)/ε vs ε) are present also in this case. In the SMES model [1], which correctlypredicted the energy dependence of pion and strangeness yields, the modication of theequation of state due to the deconnement phase transition is located between 30 andabout 200 AGeV. Thus the anomaly in energy dependence of transverse hadron activitymay be expected in this energy range. Do we see this anomaly in the experimental data?The experimental data on transverse mass (mT =√m2 + p2T , where m is a particlemass) spectra are usually parameterized by a simple exponential dependence:dNmT dmT= C exp(−mTT ), (1)where the inverse slope parameter T  is sensitive to both the thermal and collective motionin the transverse direction. In the parameterization (1) the shape of the mT spectrum isfully determined by a single parameter, the inverse slope T . In particular, the averagetransverse mass, hmT i, can be expressed as:hmT i = T  + m + (T)2m + T . (2)The energy dependence of the inverse slope parameter tted to the K+ and K− spectrafor central Pb+Pb (Au+Au) collisions is shown in Figs. 1 and 2. The results obtained atAGS [8], SPS [3] and RHIC [9] energies are compiled. The striking features of the datacan be summarized and interpreted as follows. The T  parameter increases strongly with collision energy up to the lowest (40AGeV) SPS energy point. This is an energy region where the creation of connedmatter at the early stage of the collisions is expected. Increasing collision energyleads to an increase of the early stage temperature and pressure. Consequently thetransverse activity of produced hadrons, measured by the inverse slope parameter,increases with increasing energy. The T  parameter is approximately independent of the collision energy in the SPSenergy range. In this energy region the transition between conned and deconnedmatter is expected to be located. The resulting modication of the equation of state\suppresses" the hydrodynamical transverse expansion and leads to the observedplateau structure in the energy dependence of the T  parameter. At higher energies (RHIC data) the T  again increases with collision energy. Theequation of state at the early stage becomes again sti, the early stage temperatureand pressure increase with collision energy. This results in increase of T  withenergy.The anomalous energy dependence of the mT spectra is a characteristic feature of thekaon data. Why is this the case? How do the mT spectra of other hadrons look like? The3answer is rather surprising: among the measured hadron species the kaons are the bestand unique particles for observing the eect of the modication of the equation of statedue to the onset of deconnement. The arguments are as follows. The kaon mT{spectra are only weakly aected by the hadron re{scattering andresonance decays during the post{hydrodynamic hadron cascade [10, 11]. A simple one parameter exponential t (1) is quite accurate up to mT −m = 1 GeVfor K+ and K− mesons in A+A collisions at all energies. This means that the energydependence of the average transverse mass hmT i and average transverse momentumhpT i for kaons is qualitatively the same as that for the parameter T . This simpliesthe analysis of the experimental data. The high quality data on mT spectra of K+ and K− mesons in central Pb+Pb(Au+Au) collisions are available in the full range of relevant energies.The \hydro QGP + hadron cascade" approach [10, 11] predicts a strong modicationof the mT -spectra of protons and lambdas during the hadron cascade stage in A+Acollisions at both the SPS and RHIC. As the hadron gas expands, the pions excite and  resonances and transform some part of their transverse energy in the nucleonand hyperon sectors. Therefore, the hadron re{scattering and resonance decays lead tosignicant increase (about 40% [11]) of the inverse slope parameters T  for (anti)nucleonsand (anti)lambdas at the expense of the pion transverse energy (also see discussion inRef. [12]). These changes of the slopes T  are not directly related to the equation of stateof the matter at the early stage. It is rather dicult to separate these hadron-cascadeeects and in any case, this separation will be strongly model dependent. Note also thata simple exponential t (1) neither works for pi-mesons (T low−pT > Thigh−pT ) [13] norfor protons and lambdas (T low−pT < Thigh−pT ). This means that the average transversemasses, hmT i, and their energy dependence are not connected to the behaviour of theslope parameters in the simple way described by Eq. (2): one should separately considerboth T low−pT and Thigh−pT slopes for these hadrons (see Ref. [11] for details).The transverse activity of Ω hyperons and φ mesons should, as in the case of kaons, besensitive to the matter equation of state at the early stage of the collisions. These particlesseem to decouple just after the hydrodynamic expansion stops, they do not participatein the hadron cascade stage [10, 11, 12, 14]. Unfortunately the spectra of Ω hyperonsare measured only at top SPS and RHIC energies [15]. More data exist for φ mesonproduction [16]. However, the large uncertainties in the experimental results do not allowto draw a denite conclusion on the possible anomaly in the energy dependence of mTspectra.In conclusion, we observe an anomalous energy dependence of transverse mass spectraof K+ and K− mesons produced in central Pb+Pb (Au+Au) collisions. The inverse slopesof the mT{spectra increase with energy in the AGS and RHIC energy domains, whereasthey remain constant in the intermediate SPS energy range. We argue that this anomaly iscaused by a modication of the equation of state in the transition region between connedand deconned matter. This observation may be considered as a new signal, in addition4to the previously reported anomalies in energy dependence of the pion and strangenessproduction, of the onset of deconnement located at the low SPS energies.Acknowledgments. We thank W. Greiner and R. Renfordt for discussions and com-ments. M. G. has been partially supported by Bundesministerium fur Bildung undForschung (Germany) and the Polish Committee of Scientic Research under grant 2P03B04123.References[1] M. Gazdzicki and M.I. Gorenstein, Acta Phys. Polon. B30, 2705 (1999) and refer-ences therein.[2] M. Gazdzicki and D. Ro¨hrich, Z. Phys. C65, 215 (1995) and Z. Phys. C71, 55 (1996).[3] S. V. Afanasiev et al. (NA49 Collab.), Phys. Rev. C66, 054902 (2002).[4] L. Van Hove, Phys. Lett. B118, 138 (1982).[5] E.V. Shuryak and O.V. Zhirov, Phys. Lett. B89, 253 (1979).[6] C.M. Hung, E.V. Shuryak, Phys. Rev. Lett. 75, 4003 (1995).[7] C.M. Hung, E.V. Shuryak, Phys. Rev. C57, 1891 (1998).[8] L. Ahle et al. (E866 and E917 Collab.), Phys. Lett. B490, 53 (2000).[9] D. Ouerdane et al. (BRAHMS Collab.), nucl-ex/0212001,C. Adler et al. (STAR Collab.), nucl-ex/0206008.[10] S. Bass and A. Dumitru, Phys. Rev. C61, 064909 (2000).[11] D. Teaney, J. Lauret and E.V. Shuryak, Phys. Rev. Lett. 86, 4783 (2001) and nucl{th/0110037.[12] K.A. Bugaev, M. Gazdzicki and M.I. Gorenstein, hep-ph/0211337.[13] S. Afanasiev et al. (NA49 Collab.), nucl-ex/0209002,C. Adler et al. STAR Collab.), Phys. Rev. Lett. 87, 262301 (2001),C. Adler et al. (STAR Collab.), Phys. Rev. Lett. 89, 092301 (2002),K. Adcox et al. (PHENIX Collab.), Phys. Rev Lett. 88, 242301 (2002),K. Adcox et al. (PHENIX Collab.), Phys. Rev. Lett 89, 092302 (2002).[14] K.A. Bugaev, M. Gazdzicki, M.I. Gorenstein, Phys. Lett. B544, 127 (2002).[15] S. Afanasiev et al. (NA49 Collab.), nucl-ex/0208014,F. Antinori et al. (WA97 Collab.), J. Phys. G27, 375 (2001),G. van Buren et al. (STAR Collab.), nucl-ex/0211021.5[16] S. Afanasiev et al. (NA49 Collab.), Phys. Lett. B491, 59 (2000),B. Alessandro et al. (NA50 Collab.), Phys. Lett. B555, 147 (2003),F. Laue et al. (STAR Collab.), J. Phys. G28, 2051 (2002),R. K. Seto et al. (E917 Collab.), Nucl. Phys. A661, 506c (1999).6100 101 102 s1/2 (GeV)100150200250300350 T* (MeV)AGSSPSRHIC− −K+Figure 1: The energy dependence of the inverse slope parameter T  for K+ mesonsproduced at mid-rapidity in central Pb+Pb (Au+Au) collisions at AGS [8] (triangles),SPS [3] (squares) and RHIC [9] (circles) energies.7100 101 102 s1/2 (GeV)100150200250300350 T* (MeV)AGSSPSRHIC− −K−Figure 2: The energy dependence of the inverse slope parameter T  for K− mesonsproduced at mid-rapidity in central Pb+Pb (Au+Au) collisions at AGS [8] (triangles),SPS [3] (squares) and RHIC [9] (circles) energies.8

Transverse Activity of Kaons and the Deconfinement Phase Transition in Nucleus--Nucleus Collisions

arXiv:hep-ph/0303041 v1   5 Mar 2003Transverse Activity of Kaonsand the Deconﬁnement Phase Transitionin Nucleus–Nucleus CollisionsM.I. Gorensteina,b, M. Ga´ zdzickic,d and K.A. Bugaeva,e,a Bogolyubov Institute for Theoretical Physics, Kiev, Ukraineb Institut f¨ ur Theoretische Physik, Universit¨ at Frankfurt, Germanyc Institut f¨ ur Kernphysik, Universit¨ at Frankfurt, Germanyd Swietokrzyska Academy, Kielce, Polande Gesellschaft f¨ ur Schwerionenforschung (GSI), Darmstadt, GermanyAbstractWe found that the experimental results on transverse mass spectra of kaons pro-duced in central Pb+Pb (Au+Au) interactions show an anomalous dependence onthe collision energy. The inverse slopes of the spectra increase with energy in thelow (AGS) and high (RHIC) energy domains, whereas they are constant in the in-termediate (SPS) energy range. We argue that this anomaly is probably caused bya modiﬁcation of the equation of state in the transition region between conﬁned anddeconﬁned matter. This observation may be considered as a new signal, in additionto the previously reported anomalies in the pion and strangeness production, of theonset of deconﬁnement located in the low SPS energy domain.1The statistical model of the early stage, SMES, of nucleus-nucleus (A+A) collisionssuggests [1] that the onset of the deconﬁnement phase transition at the early stage ofthe collisions may be signaled by the anomalous energy dependence of several hadronicobservables. In particular, following earlier suggestions [2], the behavior of strangeness andpion yields in the transition region was studied in detail. Recent measurements [3] of pionand kaon production in central Pb+Pb collisions at the CERN SPS indeed indicate thatthe transient state of deconﬁned matter is created in these collisions for energies largerthan about 40 A GeV. The present data show a maximum of the strangeness to pionratio at this energy. An exact position and the detailed structure of this maximum willbe clariﬁed by the soon expected new results from the 2002 Pb run at 20 and 30 A GeV.In the present letter we discuss another well known observable, which may be sensi-tive to the onset of deconﬁnement, the transverse momentum, pT, spectra of producedhadrons. It was suggested by Van Hove [4] more than 20 years ago to identify the decon-ﬁnement phase transition in high energy proton–antiproton interactions by an anomalousbehavior (a plateau-like structure) of the average transverse momentum as a function ofhadron multiplicity. Let us brieﬂy recall Van Hove’s arguments. According to the generalconcepts of the hydrodynamical approach the hadron multiplicity reﬂects the entropy,whereas the transverse hadron activity reﬂects the combined eﬀects of temperature andcollective transverse expansion. The entropy is assumed to be created at the early stageof the collision and is approximately constant during the hydrodynamic expansion. Themultiplicity is proportional to the entropy, S = s   V , where s is the entropy density andV is the eﬀective volume occupied by particles. During the hydrodynamic expansion, sdecreases and V increases with s V , being approximately constant. The large multiplicityat high energies means a large entropy density at the beginning of the expansion (andconsequently a larger volume at the end). A large value of s at the early stage of thecollisions means normally high temperature T0 at this stage. This, in turn, leads to anincrease of transverse hadron activity, a ﬂattening of the transverse momentum spectra.Therefore, with increasing collision energy 1 one expects to observe an increase of both thehadron multiplicity and average transverse momentum per hadron. However, the presenceof the deconﬁnement phase transition would change this correlation. In the phase transi-tion region the initial entropy density (and hence the ﬁnal hadron multiplicity) increaseswith collision energy, but temperature T0 = TC and pressure p0 = pC remain constant.The equation of state presented in the form p(ε)/ε versus energy density ε shows a mini-mum (the ‘softest point’ [5, 6]) at the boundary of the (generalized [6]) mixed phase andthe quark gluon plasma. Consequently the shape of the pT spectrum is approximatelyindependent of the multiplicity or collision energy. The transverse expansion eﬀect mayeven decrease when crossing the transition region [4]. Thus one expects an anomaly inthe energy dependence of transverse hadron activity: the average transverse momentumincreases with collision energy when the early stage matter is either in pure conﬁned orin pure deconﬁned phases, and it remains approximately constant when the matter is inthe mixed phase.1In the original Van Hove suggestion the correlation between average transverse momentum andhadron multiplicity was discussed for proton-antiproton collisions at ﬁxed energy. Today we have thepossibility to study A+A collisions at diﬀerent energies.2A simpliﬁed picture with T = TC = const inside the mixed phase is changed if thecreated early stage matter has a non–zero baryonic density. It was however demonstrated[7] that the main qualitative features (T ∼ = const, p ∼ = const, and a minimum of thefunction p(ε)/ε vs ε) are present also in this case. In the SMES model [1], which correctlypredicted the energy dependence of pion and strangeness yields, the modiﬁcation of theequation of state due to the deconﬁnement phase transition is located between 30 andabout 200 A GeV. Thus the anomaly in energy dependence of transverse hadron activitymay be expected in this energy range. Do we see this anomaly in the experimental data?The experimental data on transverse mass (mT =qm2 + p2T, where m is a particlemass) spectra are usually parameterized by a simple exponential dependence:dNmT dmT= C exp￿−mTT ∗￿, (1)where the inverse slope parameter T ∗ is sensitive to both the thermal and collective motionin the transverse direction. In the parameterization (1) the shape of the mT spectrum isfully determined by a single parameter, the inverse slope T ∗. In particular, the averagetransverse mass,  mT , can be expressed as: mT  = T∗ + m +(T ∗)2m + T ∗ . (2)The energy dependence of the inverse slope parameter ﬁtted to the K+ and K− spectrafor central Pb+Pb (Au+Au) collisions is shown in Figs. 1 and 2. The results obtained atAGS [8], SPS [3] and RHIC [9] energies are compiled. The striking features of the datacan be summarized and interpreted as follows.• The T ∗ parameter increases strongly with collision energy up to the lowest (40A GeV) SPS energy point. This is an energy region where the creation of conﬁnedmatter at the early stage of the collisions is expected. Increasing collision energyleads to an increase of the early stage temperature and pressure. Consequently thetransverse activity of produced hadrons, measured by the inverse slope parameter,increases with increasing energy.• The T ∗ parameter is approximately independent of the collision energy in the SPSenergy range. In this energy region the transition between conﬁned and deconﬁnedmatter is expected to be located. The resulting modiﬁcation of the equation of state“suppresses” the hydrodynamical transverse expansion and leads to the observedplateau structure in the energy dependence of the T ∗ parameter.• At higher energies (RHIC data) the T ∗ again increases with collision energy. Theequation of state at the early stage becomes again stiﬀ, the early stage temperatureand pressure increase with collision energy. This results in increase of T ∗ withenergy.The anomalous energy dependence of the mT spectra is a characteristic feature of thekaon data. Why is this the case? How do the mT spectra of other hadrons look like? The3answer is rather surprising: among the measured hadron species the kaons are the bestand unique particles for observing the eﬀect of the modiﬁcation of the equation of statedue to the onset of deconﬁnement. The arguments are as follows.• The kaon mT–spectra are only weakly aﬀected by the hadron re–scattering andresonance decays during the post–hydrodynamic hadron cascade [10, 11].• A simple one parameter exponential ﬁt (1) is quite accurate up to mT −m ∼ = 1 GeVfor K+ and K− mesons in A+A collisions at all energies. This means that the energydependence of the average transverse mass  mT  and average transverse momentum pT  for kaons is qualitatively the same as that for the parameter T ∗. This simpliﬁesthe analysis of the experimental data.• The high quality data on mT spectra of K+ and K− mesons in central Pb+Pb(Au+Au) collisions are available in the full range of relevant energies.The “hydro QGP + hadron cascade” approach [10, 11] predicts a strong modiﬁcationof the mT-spectra of protons and lambdas during the hadron cascade stage in A+Acollisions at both the SPS and RHIC. As the hadron gas expands, the pions excite ∆and Σ∗ resonances and transform some part of their transverse energy in the nucleonand hyperon sectors. Therefore, the hadron re–scattering and resonance decays lead tosigniﬁcant increase (about 40% [11]) of the inverse slope parameters T ∗ for (anti)nucleonsand (anti)lambdas at the expense of the pion transverse energy (also see discussion inRef. [12]). These changes of the slopes T ∗ are not directly related to the equation of stateof the matter at the early stage. It is rather diﬃcult to separate these hadron-cascadeeﬀects and in any case, this separation will be strongly model dependent. Note also thata simple exponential ﬁt (1) neither works for π-mesons (T ∗low−pT > T ∗high−pT) [13] norfor protons and lambdas (T ∗low−pT < T ∗high−pT). This means that the average transversemasses,  mT , and their energy dependence are not connected to the behaviour of theslope parameters in the simple way described by Eq. (2): one should separately considerboth T ∗low−pT and T ∗high−pT slopes for these hadrons (see Ref. [11] for details).The transverse activity of Ω hyperons and φ mesons should, as in the case of kaons, besensitive to the matter equation of state at the early stage of the collisions. These particlesseem to decouple just after the hydrodynamic expansion stops, they do not participatein the hadron cascade stage [10, 11, 12, 14]. Unfortunately the spectra of Ω hyperonsare measured only at top SPS and RHIC energies [15]. More data exist for φ mesonproduction [16]. However, the large uncertainties in the experimental results do not allowto draw a deﬁnite conclusion on the possible anomaly in the energy dependence of mTspectra.In conclusion, we observe an anomalous energy dependence of transverse mass spectraof K+ and K− mesons produced in central Pb+Pb (Au+Au) collisions. The inverse slopesof the mT–spectra increase with energy in the AGS and RHIC energy domains, whereasthey remain constant in the intermediate SPS energy range. We argue that this anomaly iscaused by a modiﬁcation of the equation of state in the transition region between conﬁnedand deconﬁned matter. This observation may be considered as a new signal, in addition4to the previously reported anomalies in energy dependence of the pion and strangenessproduction, of the onset of deconﬁnement located at the low SPS energies.Acknowledgments. We thank W. Greiner and R. Renfordt for discussions and com-ments. M. G. has been partially supported by Bundesministerium fur Bildung undForschung (Germany) and the Polish Committee of Scientiﬁc Research under grant 2P03B04123.References[1] M. Ga´ zdzicki and M.I. Gorenstein, Acta Phys. Polon. B30, 2705 (1999) and refer-ences therein.[2] M. Ga´ zdzicki and D. R¨ ohrich, Z. Phys. C65, 215 (1995) and Z. Phys. C71, 55 (1996).[3] S. V. Afanasiev et al. (NA49 Collab.), Phys. Rev. C66, 054902 (2002).[4] L. Van Hove, Phys. Lett. B118, 138 (1982).[5] E.V. Shuryak and O.V. Zhirov, Phys. Lett. B89, 253 (1979).[6] C.M. Hung, E.V. Shuryak, Phys. Rev. Lett. 75, 4003 (1995).[7] C.M. Hung, E.V. Shuryak, Phys. Rev. C57, 1891 (1998).[8] L. Ahle et al. (E866 and E917 Collab.), Phys. Lett. B490, 53 (2000).[9] D. Ouerdane et al. (BRAHMS Collab.), nucl-ex/0212001,C. Adler et al. (STAR Collab.), nucl-ex/0206008.[10] S. Bass and A. Dumitru, Phys. Rev. C61, 064909 (2000).[11] D. Teaney, J. Lauret and E.V. Shuryak, Phys. Rev. Lett. 86, 4783 (2001) and nucl–th/0110037.[12] K.A. Bugaev, M. Ga´ zdzicki and M.I. Gorenstein, hep-ph/0211337.[13] S. Afanasiev et al. (NA49 Collab.), nucl-ex/0209002,C. Adler et al. STAR Collab.), Phys. Rev. Lett. 87, 262301 (2001),C. Adler et al. (STAR Collab.), Phys. Rev. Lett. 89, 092301 (2002),K. Adcox et al. (PHENIX Collab.), Phys. Rev Lett. 88, 242301 (2002),K. Adcox et al. (PHENIX Collab.), Phys. Rev. Lett 89, 092302 (2002).[14] K.A. Bugaev, M. Ga´ zdzicki, M.I. Gorenstein, Phys. Lett. B544, 127 (2002).[15] S. Afanasiev et al. (NA49 Collab.), nucl-ex/0208014,F. Antinori et al. (WA97 Collab.), J. Phys. G27, 375 (2001),G. van Buren et al. (STAR Collab.), nucl-ex/0211021.5[16] S. Afanasiev et al. (NA49 Collab.), Phys. Lett. B491, 59 (2000),B. Alessandro et al. (NA50 Collab.), Phys. Lett. B555, 147 (2003),F. Laue et al. (STAR Collab.), J. Phys. G28, 2051 (2002),R. K. Seto et al. (E917 Collab.), Nucl. Phys. A661, 506c (1999).6100 101 102 s1/2 (GeV)100150200250300350 T* (MeV)AGSSPSRHIC−−K+Figure 1: The energy dependence of the inverse slope parameter T ∗ for K+ mesonsproduced at mid-rapidity in central Pb+Pb (Au+Au) collisions at AGS [8] (triangles),SPS [3] (squares) and RHIC [9] (circles) energies.7100 101 102 s1/2 (GeV)100150200250300350 T* (MeV)AGSSPSRHIC−−K−Figure 2: The energy dependence of the inverse slope parameter T ∗ for K− mesonsproduced at mid-rapidity in central Pb+Pb (Au+Au) collisions at AGS [8] (triangles),SPS [3] (squares) and RHIC [9] (circles) energies.8

and nucl– th/0110037.

and references therein.

Transverse activity of kaons and the deconfinement phase transition in nucleus-nucleus collisions

AbstractWe found that the experimental results on transverse mass spectrum of kaons produced in central Pb+Pb (Au+Au) collisions show an anomalous dependence on the colliding energy. The inverse slope of the spectrum increases with the energy in the low (AGS) and high (RHIC) energy domains, whereas it remains constant in the intermediate (SPS) energy range. We argue that this anomaly is probably caused by the modification of the equation of state in the transition region between confined and deconfined matter. This observation may be considered as a new signal, in addition to the previously reported anomalies in the pion and strangeness production, of the onset of deconfinement located in the low SPS energy domain

Gorenstein, M.I

Gaździcki, M

Bugaev, K.A

Elsevier - Publisher Connector 

Transverse activity of kaons and deconfinement phase transition in nucleus–nucleus collisions 

Physics Letters B 567 (2003) 175–178
www.elsevier.com/locate/npe
Transverse activity of kaons and deconfinement phase transition
in nucleus–nucleus collisions
M.I. Gorenstein a,b, M. Gaz´dzicki c,d, K.A. Bugaev a,e
a Bogolyubov Institute for Theoretical Physics, Kiev, Ukraine
b Institut für Theoretische Physik, Universität Frankfurt, Germany
c Institut für Kernphysik, Universität Frankfurt, Germany
d ´Swie¸tokrzyska Academy, Kielce, Poland
e Gesellschaft für Schwerionenforschung (GSI), Darmstadt, Germany
Received 16 June 2003; accepted 24 June 2003
Editor: L. Montanet
Abstract
We found that the experimental results on transverse mass spectrum of kaons produced in central Pb+Pb (Au+Au) collisions
show an anomalous dependence on the colliding energy. The inverse slope of the spectrum increases with the energy in the low
(AGS) and high (RHIC) energy domains, whereas it remains constant in the intermediate (SPS) energy range. We argue that
this anomaly is probably caused by the modification of the equation of state in the transition region between confined and
deconfined matter. This observation may be considered as a new signal, in addition to the previously reported anomalies in the
pion and strangeness production, of the onset of deconfinement located in the low SPS energy domain.
 2003 Elsevier B.V. Open access under CC BY license.The statistical model of the early stage, SMES, of
nucleus–nucleus (A+ A) collisions suggests [1] that
the onset of deconfinement phase transition at the early
stage of the collisions may be signaled by the anom-
alous energy dependence of several hadronic observ-
ables. In particular, following earlier suggestions [2],
the behavior of strangeness and pion yields in the
transition region was studied in detail. Recent mea-
surements [3,4] of pion and kaon production in cen-
tral Pb + Pb collisions at CERN SPS indeed indicate
that the transient state of deconfined matter is cre-
ated in these collisions for energies larger than about
E-mail address: marek.gazdzicki@cern.ch (M. Gaz´dzicki).0370-2693 2003 Elsevier B.V.
doi:10.1016/j.physletb.2003.06.043
Open access under CC BY license.30 AGeV. The present data show a maximum of the
strangeness to pion ratio at this energy. An exact posi-
tion and the detailed structure of this maximum will be
clarified by the expected soon new results on Pb + Pb
collisions at 20 AGeV.
In the present Letter we discuss another well-
known observable, which may be sensitive to the on-
set of deconfinement, the transverse momentum, pT ,
spectra of produced hadrons. It was suggested by Van
Hove [5] more than 20 years ago to identify the de-
confinement phase transition in high energy proton–
antiproton interactions with an anomalous behavior
(a plateau-like structure) of the average transverse mo-
mentum as a function of hadron multiplicity. Let us
briefly recall the Van Hove’s arguments. According to
176 M.I. Gorenstein et al. / Physics Letters B 567 (2003) 175–178the general concepts of the hydrodynamical approach
the hadron multiplicity reflects the entropy, whereas
the transverse hadron activity reflects the combined
effects of temperature and collective transverse ex-
pansion. The entropy is assumed to be created at the
early stage of the collision and is approximately con-
stant during the hydrodynamic expansion. The multi-
plicity is proportional to the entropy, S = s · V , where
s is the entropy density and V is the effective volume
occupied by particles. During the hydrodynamic ex-
pansion, s decreases and V increases with s · V be-
ing approximately constant. The large multiplicity at
high energies means a large entropy density at the be-
ginning of the expansion (and consequently a larger
volume at the end). The large value of s at the early
stage of the collisions means normally high tempera-
ture T0 at this stage. This, in turn, leads to an increase
of transverse hadron activity, a flattening of the trans-
verse momentum spectrum. Therefore, with increasing
collision energy1 one expects to observe an increase
of both the hadron multiplicity and average transverse
momentum per hadron. However, a presence of the
deconfinement phase transition would change this cor-
relation. In the phase transition region the initial en-
tropy density (and hence the final hadron multiplic-
ity) increases with collision energy, but temperature
T0 = TC and pressure p0 = pC remain constant. The
equation of state presented in a form p(ε)/ε versus
ε shows a minimum (the ‘softest point’ [6,7]) at the
boundary of the (generalized [7]) mixed phase and the
QGP. Consequently the shape of the pT spectrum is
approximately independent of the multiplicity or colli-
sion energy. The transverse expansion effect may even
decrease when crossing the transition region [5]. Thus
one expects an anomaly in the energy dependence of
transverse hadron activity: the average transverse mo-
mentum increases with collision energy when the early
stage matter is either in pure confined or in pure decon-
fined phases, and it remains approximately constant
when the matter is in the mixed phase.
A simplified picture with T = TC = const inside
the mixed phase is changed if the created early
1 In the original Van Hove suggestion the correlation between av-
erage transverse momentum and hadron multiplicity were discussed
for proton–antiproton collisions at fixed energy. Today we have an
advantage to use A+A collisions at different energies.stage matter has a nonzero baryonic density. It was
however demonstrated [8] that the main qualitative
features (T ∼= const, p ∼= const, and a minimum of the
function p(ε)/ε vs ε) are present also in this case.
In the SMES model [1], which correctly predicted
energy dependence of pion and strangeness yields,
the modification of the equation of state due to
deconfinement phase transition is located between 30
and about 200 AGeV. Thus the anomaly in energy
dependence of transverse hadron activity may be
expected in this energy range. Do we see this anomaly
in the experimental data?
The experimental data on transverse mass (mT =√
m2 + p2T , where m is a particle mass) spectra
are usually parameterized by a simple exponential
dependence:
(1)dN
mT dmT
= C exp
(
−mT
T ∗
)
,
where C is the normalization constant, and the inverse
slope parameter T ∗ is sensitive to both the thermal
and collective motion in the transverse direction. At
small pT the T ∗ parameter can be expressed within
the hydrodynamical approach as
(2)T ∗ = Tf + 12mv¯
2
T ,
where Tf is the kinetic freeze-out temperature and v¯T
is the mean transverse flow velocity. In the parameter-
ization (1) the shape of the mT spectrum is fully deter-
mined by a single parameter, the inverse slope T ∗. In
particular, the average transverse mass, 〈mT 〉, can be
expressed as
(3)〈mT 〉 = T ∗ +m+ (T
∗)2
m+ T ∗ .
The energy dependence of the inverse slope para-
meter fitted to the K+ and K− spectra for central
Pb+Pb (Au+Au) collisions is shown in Figs. 1 and 2.
The results obtained at AGS [9], SPS [3,4] and RHIC
[10] energies are compiled. The striking features of the
data can be summarized and interpreted as following.
• The T ∗ parameter increases strongly with colli-
sion energy up to the point at the lowest
(30 AGeV) SPS energy. This is an energy re-
gion where the creation of confined matter at the
M.I. Gorenstein et al. / Physics Letters B 567 (2003) 175–178 177Fig. 1. The energy dependence (s1/2 is c.m. energy per nu-
cleon–nucleon pair) of the inverse slope parameter T ∗ for K+
mesons produced at midrapidity in central Pb + Pb (Au + Au) col-
lisions at AGS [9] (triangles), SPS [3,4] (squares) and RHIC [10]
(circles) energies.
Fig. 2. The energy dependence (s1/2 is c.m. energy per nu-
cleon–nucleon pair) of the inverse slope parameter T ∗ for K−
mesons produced at midrapidity in central Pb + Pb (Au + Au) col-
lisions at AGS [9] (triangles), SPS [3,4] (squares) and RHIC [10]
(circles) energies.
early stage of the collisions is expected. Increas-
ing collision energy leads to an increase of the
early stage temperature and pressure. This results
in larger final values of both Tf and v¯T in Eq. (2).
Consequently the transverse activity of produced
hadrons, measured by the inverse slope parameter,
increases with increasing energy.
• The T ∗ parameter is approximately independent
of the collision energy in the SPS energy range,
30–158 AGeV. In this energy region the transi-
tion between confined and deconfined matter isexpected to be located. The resulting modification
of the equation of state “suppresses” an increase
of both Tf and v¯T , and this leads to the observed
plateau structure in the energy dependence of the
T ∗ parameter.
• At RHIC (the c.m. energies per nucleon–nucleon
pair
√
s = 130 GeV and 200 GeV) the T ∗ is
significantly larger than at SPS energies. In the
RHIC energy domain the equation of state at the
early stage becomes again stiff, the early stage
temperature and pressure increase with collision
energy. This results in increase of the transverse
flow v¯T and, consequently, in increase of T ∗ (2)
between SPS and RHIC energies.
The anomalous energy dependence of the mT
spectra is a characteristic feature of the kaon data.
Why is it the case? How do the mT spectra of other
hadrons look like? The answer is rather surprising:
among measured hadron species the kaons are the best
and unique particles for observing in their transverse
momentum spectra the effect of the modification of
equation of state due to the onset of deconfinement.
The arguments are as following.
• A simple one parameter exponential fit (1) is quite
accurate up to mT −m∼= 1 GeV for K+ and K−
mesons in A + A collisions at all energies. This
means that the energy dependence of the average
transverse mass 〈mT 〉 (3) and average transverse
momentum 〈pT 〉 for kaons is qualitatively the
same as that for the parameter T ∗. This simplifies
analysis of the experimental data.
• The shape of kaons mT spectra is only weakly af-
fected by the hadron rescattering and resonance
decays during the post-hydrodynamic hadron cas-
cade [11,12].
• The high quality data on mT spectra of K+
and K− mesons in central Pb + Pb (Au + Au)
collisions are available in the full range of relevant
energies.
In contrast to kaons mT spectra, a simple expo-
nential fit (1) does not work accurately in a wide pT -
region for other hadrons: T ∗low-pT > T
∗
high-pT for ‘light’
pions, and T ∗low-pT < T
∗
high-pT for protons, lambdas
and other ‘heavy’ hadrons (for the SPS and RHIC
energies see discussion of hydrodynamic results in
Ref. [13] and the data in Ref. [14]). This means that
178 M.I. Gorenstein et al. / Physics Letters B 567 (2003) 175–178the average transverse masses, 〈mT 〉, and their energy
dependence are not connected to the behavior of the
slope parameters in a simple way (3): one should sep-
arately consider both T ∗low-pT and T
∗
high-pT for each of
hadron species.
The “hydro QGP + hadron cascade” approach
Refs. [11,12] predicts a strong modification of the mT
spectra of protons and lambdas during the hadron cas-
cade stage in A + A collisions at both the SPS and
RHIC. As the hadron gas expands, the pions excite
∆ and Σ∗ resonances and transfer a fraction of their
transverse energy to the nucleon and hyperon sectors.
Therefore, the hadron rescattering and resonance de-
cays lead to an essential increase (about 40% [12]) of
the inverse slope parameters T ∗ for (anti)nucleons and
(anti)lambdas at the expense of the pion transverse en-
ergy (also see discussion in Ref. [15]). These changes
of the slopes T ∗ are not directly related to the equa-
tion of state of the matter at the early stage. It is rather
difficult to separate these hadron cascade effects and,
in any case, this separation will be strongly model de-
pendent.
The transverse activity of Ω hyperons and φ
mesons should, as in the case of kaons, be sensitive
to the matter equation of state at the early stage
of the collisions. These particles seem to decouple
just after the hydrodynamic expansion stops, they
do not participate in the hadron cascade stage [11–
13,15]. Unfortunately, the spectra of Ω hyperons
are measured only at top SPS and RHIC energies
[16]. More data exist for φ meson production [17].
However, the large uncertainties in the experimental
results do not allow for precise enough study of energy
dependence.
In conclusion, we observe the anomalous energy
dependence of transverse mass spectra of K+ and
K− mesons produced in central Pb + Pb (Au + Au)
collisions. The inverse slope of the mT spectrum
increases with the energy in the AGS and RHIC energy
domains, whereas it is constant in the intermediate
SPS energy range. We argue that this anomaly is
caused by the modification of the equation of state in
the transition region between confined and deconfined
matter. This observation may be considered as a
new signal, in addition to the previously reported
anomalies in energy dependence of the pion and
strangeness production, of the onset of deconfinement
located in the low SPS energy domain.Acknowledgements
We thank W. Greiner for discussions and com-
ments. Partial support by Bundesministerium für Bil-
dung und Forschung and by Polish Committee of Sci-
entific Research under grant 2P03B04123 (M.G.) is
acknowledged.
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Transverse activity of kaons and the deconfinement phase transition in nucleus-nucleus collisions

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