In a previous paper, we have shown that a double phi peak structure appears
in the dilepton invariant mass spectrum if a first order QCD phase transition
occurs in ultrarelativistic heavy ion collisions. Furthermore, the transition
temperature can be determined from the transverse momentum distribution of the
low mass phi peak. In this work, we extend the study to the case that a smooth
crossover occurs in the quark-gluon plasma to the hadronic matter transition.
We find that the double phi peak structure still exists in the dilepton
spectrum and thus remains a viable signal for the formation of the quark-gluon
plasma in ultrarelativistic heavy ion collisions.Comment: 8 pages, 9 uuencoded postscript figures included, Latex, LBL-3572

C. M. Ko

C. S. Song

D. Seibert

E. Shuryak

F. R. Brown

H. C. Jean

H. Shiomi

J. Kapusta

K. Geiger

M. Asakawa

M. Hermann

N. H. Christ

P. Lévai

R. D. Pisarski

S. Gao

T. Hatsuda

English

arXiv

Journals published by the American Physical Society can be found at http://publish.aps.org

Asakawa, M.

Ko, Che Ming.

OAKTrust Digital Repository (Texas A&M Univ)

PHYSICAL REVIEW C VOLUME 50, NUMBER 6 DECEMBER 1994Secondary phi meson peak as an indicator of a +CD phase transitionin ultrarelativistic heavy-ion collisionsM. Asakawa*Nuclear Science Division, MS 70A $80-7, Laurrence Berkeley Laboratory, Berkeley, California 9/790C. M. Ko~Cyclotron Institute and Physics Department, Texas ASM University, College Station, Texas 778/8-8866(Received 26 May 1994)In a previous paper, we have shown that a double phi peak structure appears in the dileptoninvariant mass spectrum if a first order /CD phase transition occurs in ultrarelativistic heavy-ion collisions. Furthermore, the transition temperature can be determined from the transversemomentum distribution of the low mass phi peak. In this work, we extend the study to the case thata smooth crossover occurs in the quark-gluon plasma to the hadronic matter transition. We 6ndthat the double phi peak structure still exists in the dilepton spectrum and thus remains a viablesignal for the formation of the quark-gluon plasma in ultrarelativistic heavy-ion collisions.PACS number(s): 25.75.+r, 12.38.Mh, 24.85.+pIn a previous paper [1],we have proposed that a doublephi peak structure in the dilepton invariant mass spec-trum &om ultrarelativistic heavy-ion collisions can beused to confirm the phase transition &om quark-gluonplasma to hadronic matter. Furthermore, the transversemomentum distribution of the low mass phi peak allowsus to determine the transition temperature.The low mass phi peak results &om the decay of phimesons with reduced in-medium masses during the tran-sition. The reduction of the phi meson mass in hothadronic matter is a result of the partial restorationof chiral symmetry [2—4]. In normal efFective field the-ory, hadron masses do not decrease at finite temperatureand/or density [5,6]. This result is, however, incomplete,because it neglects the modification of the vacuum due tomedium effects. In QCD, the vacuum can be describedin terms of expectation values of quark and gluon opera-tors, i.e., condensates. The correlation function for cur-rent operators defined by quark fields can be calculatedas a sum of condensates in the deep Euclidean regionand can be identified as the hadron spectral function inthe timelike region. Values of the correlation function inthese two regions are related to each other through thedispersion relation. The behavior of condensates at finitetemperature and/or density can be calculated with theappropriate approximation. Using these condensates onone side of the dispersion relation and the hadron spec-trum function &om an effective theory on the other side,it has been shown that hadron masses should decreasein the medium in order to satisfy the dispersion relation[7]. In effective field theory, the vacuum effect can alsoElectronic address: yukinsdssd. lbl. gov~ Electronic address: koOcomp. tamu. edube included via nucleon-antinucleon polarization. Recentstudies show that this indeed leads to a reduction of vec-tor meson masses at finite temperature and/or density[S-11].If a first order phase transition occurs between thequark-gluon plasma and the hadronic matter in heavy-ion collisions as assumed in Ref. [1], the system spends arelatively long time in the inixed phase (about 10—15 fm)during which the phi meson mass stays almost constantat a value difFerent &om that in &ee space. Since theduration of the mixed phase is not negligible comparedto the lifetime of the phi meson in vacuum ( 45 fm), alow mass phi peak besides the normal one thus appearsin the dilepton spectrum. As the transverse fIow duringthe mixed phase is not appreciable, the transverse mo-mentum distribution of the low mass phi meson is largelydetermined by the temperature of the mixed phase andprovides thus information on the transition temperature.In the scenario described in Ref. [1], we have ignoredthe following effects: (i) the collisional broadening of thephi meson width due to its interaction with hadrons, (ii)the increase of the phi meson width in the mixed phasedue to its interaction with partons in the quark-gluonphase, and (iii) the possibility of a smooth transition fromquark-gluon plasma to hadronic matter instead of themixed phase. If these effects are large, then the secondaryphi peak proposed in Ref. [1] may not appear. EfFects(i) and (ii) have recently been studied in Refs. [12] and[13], respectively. It has been found that the collision ofthe phi meson with hadrons increases its width to about10 MeV while its interaction with partons adds anotherfew MeV in the width. The resulting phi meson widthremains small enough to make the secondary phi peakvisible. In this paper, we shall study if the double phipeak structure is still present in the dilepton spectrum inthe case of a smooth transition &om quark-gluon plasma0556-2813/94/50(6)/3064(5)/$06. 00 50 3064 1994 The American Physical Society50 SECONDARY PHI MESON PEAK AS AN INDICATOR OF A. . . 3065to hadronic matter.According to recent lattice calculations [14], the QCDphase transition is a crossover but very close to the Brstorder one. There exists a sudden change in the entropyIdensity within a temperature interval of less than 10MeV [15]. To incorporate these features of the QCDphase transition, we parametrize the temperature depen-dence of the entropy density s of hot matter as follows:ms'(T) 1 —tanh ( & ') + nsq(T) 1+ tanh ( & ')m 1 —tanh( & ') +n 1+tanh( & )msq(T) 1 —tanh ( r ') + nsq(T) 1+ tanh ( & )(m + n) + (n —m) tanh ( & ')where sg(T) = 12aTs and eq(T) = 148aTs with a =z2/90 are the bag model entropy densities with two fia-vors in the hadron and the quark phases, respectively; T,is the critical temperature; m, n, and I' are constants.The typical width of the phase transition is given by 2I'with I' 5 MeV according to lattice calculations. Fortemperatures that satisfy ~T —T,~)& I', the entropy den-sity given by Eq. (1) approaches asymptotically to sp, (T)and sq(T), respectively, for T below and above T,. Wehave introduced m and n to include the possibility of anasymmetric phase transition. The case m/n = 1 corre-sponds to a symmetric phase transition. For m/n ) 1,the transition is asymmetric, and the entropy densitychanges more in the quark phase than in the hadronphase. 'The pressure P and the energy density e can bestraightforwardly evaluated &om the entropy density. Inthis paper, we take the chemical potential to be zero,as we are interested in the central region of ultrarela-tivistic heavy-ion collisions, where the baryon density isexpected to almost vanish. Then, the pressure and theenergy density are given byTP(T) = s(t)Ch,0e(T) = Ts(T) —P(T).We note that only one of the three quantities s, P, ande is independent at fixed temperature T and chemicalpotential. In Figs. 1—3, we show s, P, and e by solidlines as functions of temperature. The parameters usedin evaluating these quantities are T, = 180 MeV, I' = 5MeV, and m/n = 1. The dashed lines show the equationof state obtained &om the standard bag model.In the following calculations, we use the same temper-ature dependence of the phi meson mass as in Ref. [1].This is shown in Fig. 4. The decrease of the phi me-son mass is mainly due to the presence of a considerablenumber of strange particles at high temperatures. Thedetails can be found in Re&. [1, 16]. We note that theresult shown in Fig. 4 has been calculated independentlyof T,. As in Ref. [1],the rho meson mass is taken to havethe temperature dependenceand the omega meson mass is independent of temper-ature. The difference in the temperature dependenceof vector meson masses is due to the difference in theirisospin [17]. There are some ambiguities in the predic-tion of QCD sum rules on hadron masses in hot anddense matter. These are largely related to the temper-ature and/or density dependence of the four-quark con-densate, which is usually evaluated using the factoriza-tion approximation. Although the four-quark condensateis important for rho and omega meson masses, it is, how-ever, less important for the phi meson mass as a result ofthe large strange quark mass. Therefore, we expect thatthe phi meson mass at finite temperature and/or densitycalculated in QCD sum rules is more reliable than rhoand omega meson masses. We would like to point outthat the double phi peak structure in the dilepton spec-trum depends more on the existence of the shift of the phimeson mass at finite temperature than the magnitude ofx 10I160 180T [MeV]I200Strictly speaking, if the phase transition is a crossover, thedistinction between the hadron phase and the quark-gluonphase does not exist. Here ere assume, however, that thesystem is in the quark-gluon phase if T & T and the hadronphase if T (T,.FIG. 1. Entropy density as a function of temperature.The number ofSavors is taken to be 2 and T is 180 MeV. Solidand dashed lines correspond, respectively, to the crossovertransition with I' = 5 MeV and m jn= 1, and the Srst orderphase transition arith the bag model equation of state.3066 M. ASAKAWA AND C. M. KO SO\ I Ix 10950900160 180T [MeV]200 850 100 120 140 160T [MeV]180FIG. 2. Same as Fig. 1 for the energy density. FIG. 4. Temperature-dependent phi meson mass in hothadronic mat ter.the shift.We assume that in ultrarelativistic heavy-ion collisionsthe system has a cylindrical symmetry and is in thermalequilibrium. All forxnulas used in the following calcula-tion are given in Ref. [1]. In particular, we include anormalized smearing function of Gaussian forxn for thephi meson mass in order to take into account the exper-ixnental xnass resolution:(M ~ (y)) —LM —mp(T)j /2n0' 270where n is a constant and is taken to be 10 MeV [18].Since the collisional broadening of the phi meson is atmost of the order of 0 [12], we do not need to includeit explicitly as it can be considered as included alreadyI.n 0'.Assuming boost invariance, we have carried out a hy-drodynamical calculation with transverse flow for a cen-tral collision of ~~Au +~9~Au. We have mocMed the codeof Ref. [19] to include the smooth quark-gluon plasma tohadronic transition. %'e have used the following valuesfor the parameters [1, 20]: the initial proper time Tp1 fm and the initial radial velocity at the surface of thecylinder, eo ——0; the initial temperature To = 250 MeV,the critical temperature T = 180 MeV and the &eeze outtemperature Ty = 120 MeV; one-half of the typical widthof the crossover transition, I' = 5 MeV, and the asym-metry factor of the crossover, m/n = l. Unless specifiedotherwise, we use these default values in the calculation.In addition, we have assumed that the volume &actionof the hadron phase is 1 and 0 at T ( T, and T & T„respectively.In Fig. 5, we show by the solid line the invariant massdistribution of lepton pairs dN/dMdy. We see that thesecond phi peak between the omega meson and the nor-mal phi meson is still visible as in the case of a Grst orderphase transition [1]. The low mass phi peak is, however,soxnewhat broadened as the temperature in the presentcase does not stay exactly at the same value during thetransition. For comparison, we have also plotted in Fig. 5the result for an asymmetric case by the dashed line. Theasymmetric factor is chosen to be m/n = 3. In this case,the entropy density drops much more in the quark-gluonphase than in the hadron phase. This makes, however,practically no difference in the dilepton spectrum as thetemperature stays near the critical temperature T, = 180MeV (dotted line in Fig. 6) for a relatively long time inboth the symmetric and the asymmetric cases which areshown in Fig. 6 by the solid and the dashed lines, re-spectively. To understand this, we take the Bjorken scal-ing solution without transverse expansion and denote thecritical entropy density as s, which is given byV -2-10x 1010-6-0.6 0.8M [GeV]160I180T [MeV]I200FIG. 3. Same as Fig. 1 for the pressure.FIG. 5. Dilepton invariant mass spectrum at central ra-pidity. The solid curve is the result from the hydrodynami-cal calculations arith the default parameter set. The dashedcurve is obtained by changing the asymmetry factor of thephase transition rn/n to 3 and the dotted curve by changingthe vridth parameter of the transition I' to 10 MeV.50 SECONDARY PHI MESON PEAK AS AN INDICATOR OF A. . . 3067-2-10-4-100 10 20 30t [fm]-6-0.6 0.8 1M [GeV]FIG. 6. Temperature as a function of proper time. Thesolid line corresponds to the case using the default parametersand the dashed line is obtained by changing m/n to 3. Thedotted line is the critical temperature used in the calculation.FIG. 7. Dilepton invariant mass spectrum at central ra-pidity. The default parameters are used except that the ini-tial temperature is To —175 MeV for the solid line. For thedashed line, in addition, the vridth parameter of the transitionI' is changed to 10 MeV.map(T, ) + nsv(T, )m+AThe duration Dv for which the temperature remains al-most constant is then approximately given bygapa~(Tp)as(T, )7.psq (Tp)ap, (T,)gapa~(Tp)8cse(T )sp, (T,)sq(T. ) + nasp, (T,) nSince a~(T,)/ss(T, ) is very large (= 37/3), A7; is barelyafFected by any reasonable change of the asymmetry fac-tor.In Fig. 5, we have also shown by the dotted line thecase of a broader crossover with I' = 10 MeV. The sec-ond peak is seen to be broader and closer to the normalphi peak. If the effective I' becomes very large due tofinite size eKects in heavy-ion collisions, no separate sec-ond peak becoxnes visible as the temperature cannot stayat an almost constant value during the evolution of thesystem. We have found that the maximum I' below' whichthe second peak can be seen is around 20 MeV for thedefault parameter set. Since the w'idth of the crossoveris 2I', I' = 20 MeV is already an extremely large value.In Ref. [1], we have pointed out that for a first orderphase transition the second phi peak does not appear ifthe initial temperature is less than the critical tempera-ture. This is not the case for a smooth crossover as shownin Fig. 7 by the solid and dashed lines for I' = 5 and 10MeV, respectively. The initial temperature in these cal-culations is taken to be 175 MeV and is less than thecritical temperature. The reason for this is that for thecrossover transition the texnperature does not stay ex-actly at T but around T, and so the second phi peak isexpected to be visible if T —To + I' is satis6ed even ifTo & T . The result of our numerical calculation supportsthis.If the critical texnperature is small, it is possible thatthe second phi peak may not be observed due to thesmall separation &om the normal phi meson peak. InFig. 8, we show by the solid line the result &om theI I I1 I ) IV -2-101010 0.6 0.8 1M [GeV]FIG. 8. Dilepton invariant mass spectrum at central ra-pidity. For the solid line, the default parameters me usedexcept that the critical temperature is T = 160 MeV. Forthe dashed line, in addition, the width parameter of the tran-sition I' is changed to 10 MeV.calculation with a lower critical temperature T, = 160MeV. The second peak is still visible. However, if thewidth parameter I' of the crossover transition is larger,the second phi peak becomes broader and merges to thenormal one. This is shown by the dashed line in Fig.8 for a larger width parameter, I' = 10 MeV, and thesame critical temperature T = 160 MeV. We note thatas in a first order transition our results do not changequalitatively for higher initial temperatures [21—23] aslong as the critical temperature is kept the same [1].In Ref. [1], we have also pointed out that the crit-ical temperature for the /CD phase transition can beextracted reasonably accurately from the transverse mo-mentum distribution of the low mass phi meson peakin the dilepton spectrum. A similar proposal to measurethe phase transition temperature with the transverse mo-ment»m distribution of dileptons &om rho mesons wasproposed by Seibert [24]. The method with the phi me-son, however, has several advantages over the latter one:(i) The second peak originates exclusively from the mat-ter near the critical temperature, and so the signal tonoise ratio is large. (ii) The transverse fiow is still small3068 M. ASAKAWA AND C. M. KO 50////////////////IIlII300T0 [MeV]400FIG. 9. The slope parameter of the hi mmomentum distribe p i eson transversen ution as a function of the inititure. Except for th ' ' le & ial tempera-e initial temperature the deeters are used. Solid ande fault param-as ed curves corres ond to e ine is the critical temperature used ' thin e ca culation.near the phase transition. Therefore tht di t 'bis ri ution of the secondfaithfull the c ' 'peak reBects morey e ritical temperature. (iii) The hipea e the samee ransition temperature can also be extracted &oeson pea in t e case o' ion. n ig. 9, we show the slo ethe dilepton d' t b t'p parameter ofa funct' tis ri ution at small transverse momenta asion o he initial temperature. The solid curthe slope parameter of t}e lower mass peak at about 916MeV. It changes only slightly as the initial tern erate normal phi meson peak at 1019 MeV cas e initia temperature increases due to theresultant development of an ain e a ron hasthppreciable transverse Bowh d p e. We note especially the suddcrease of the slo ee p parameter of the normal phi mesonpeak in the region T,—I' T Tp y as the temperature increases.ensity c anges ra idln summary, due to the reduction of the phi mesonmass in hot matter and the sudde en change of the en-ropy ensity at the phase transitio d t'i ion, a istinct ow masspea esides the normal one appears in the d'1trum even ifrs e i epton spec-t"e quark-gluon plasma to hadrtransition in heav -'onic matterc y-ion collisions is not 6rst ord Ther. isa series o investigations on th e possi i ity ofrare ativistic heavy-ion collisions. With all fac-tors which could potentially weaken the double phi peakcritical temperature of the /CD hase ture u rare'ativistic heavy-ion experiments.M.A. was supported by the Director Office f EResearch OfBce of High Energy and Nuclear Ph sicsDivisions of High Ener Ph s'gy ysics and Nuclear Physicso e .S. Department of Ener un.K. was supported in part by00098. C.Me ational Science Foundation under Grant N . PHo Y-[1] M. Asakswa and C. M. Ko Ph(1 . Pisarski, Phys. Lett. 110B, 155 (1982).[3] T. Hatsuda and T. Kunihiro Ph s R(1985).ni ' o, y . ev. Lett. 55, 158[ ] . stsuda, Nucl. Phys. A544 27 (19 ).4 T Ha5] C. S. Son] g, Phys. Rev. D 49, 1556 (1994).rmann, B.L. Friman, and W. Norenber6 M. He[7] M. Asakawa and C. M. Ko Ph, ys. Rev. C 48, R526( 93); Nucl. Phys. A580, 399 (1993).[8] S. Gso, R. K. Su snd P.(1994)., , K. N. Yu, Phys. Rev C 49, 407 ~ ~9] H.-C. Jean J P] . n, . gekarewicz, and A. G. WilliamsRev. C 49, 1981 (1994).[10] H. Shiomi and T. Hatsuds Ph s. Ly . B 334, 281[11] C. S. Son P. W.g, Xia, and C. M. Ko, Texas ASM Uni-versity report, 1994.. R. Brown, F. P. Butler, H. Chen, N. H. Christ Z7 ~Dong, W. ShaKer, L. I. Unger, and A.e . , 2491 (1990).[ ] . . hr|st, Nucl. Phys. A544, 81c (1992).15NHC[16] M. Asakswa and C. M. Ko Nu(1994)., cl. Phys. A572, 732[17] T. Hatsuda, Y. Koike, snd S. H. Lee. , N 1. Phy . B394,[18] PHENIX Co1993.a oration, Conceptual Deszgn eport,[19] P. Levsi and B. Muller Ph s.' ' ", y. R . L tt. 87, 1519(1991).. Asakawa, C. M. Ko, and P. Lev ', ai, Phys. Rev. Lett.1993).[21] K. Gei er snd 8 , , 1992);g B. Muller, Nucl. Phys. B369 600(1992).eiger, Phys. Rev. D 48 4965 (1992 . 46, 4986[22 E. Shur sk Py , hys. Rev. Lett. 88, 3270 (1992); E. Shurysksnd L. Xiong, ibid. 70, 2241 (1993).apusta, L. McLerran, and D. K. Sriv23 J. KLett. B 283, 145 1992)., ~ astava, Phys.. Seibert, Phys. Rev. Lett. 88, 147 (24 D Se' 6 1992).

Secondary Phi-Meson Peak as an Indicator of a Qcd Phase-Transition in Ultrarelativistic Heavy-Ion Collisions

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Physical Review C

Secondary phi meson peak as an indicator of a QCD phase transition in ultrarelativistic heavy-ion collisions

Texas A&M University

Ko, C.M.

eScholarship - University of California