Mass Shift of Charmonium near Deconfining Temperature and Possible Detection in Lepton-Pair Production

Abstract

The mass shift of charmonium near the critical temperature of the deconfining transition is investigated by a c-c potential model through the change of the string tension. On the basis of the results, detection of the shift by lepton-pair production is discussed by the use of the hydrodynamical model of ultrarelativistic nucleus-nucleus collisions. It is shown that the mass shift is detectable if the critical temperature is not lower than 300 MeV. PACS numbers: 12.38.Mh, 12.40.Ee, 12.40.Qq, 25.70.Np Although there has been increasing support for the existence of deconfinement and/or chiral restoring transitions at finite temperature or high density in theoretical 1 and numerical 2 investigations, the possibility of detection of these transitions and the new phases is not yet clear. 3 On this problem, the hadronic mass shift related to the restoration of chiral symmetry has been discussed recently. 4,5 Despite the uniqueness of the phenomenon, detectability of the effect in actual collisions is still uncertain. In this Letter, we present some results for the mass shift of charmonium and the change of its leptonic width with variation of string tension, which is expected to be temperature dependent. Recent works in Monte Carlo simulation 6 " 8 and model investigation 9 ' 10 suggest critical behavior of the string tension near the deconfining transition. Further, we discuss detection of the mass shift by leptonpair production in heavy-ion collisions based on hydrodynamical development. 11 " 13 We see that the effect could be detectable if the deconfining temperature is not lower than 300 MeV.The computation of the mass shift adopted here is based on the c-c potential modelwhere the first term is the gluon-exchange Coulombic term given by Buchmuller and Tye, 14 i.e., with A = 250 MeV and b Q -9 (three flavors).Since we consider the string tension k at finite temperature, our present interest is to solve for c-c states under variation of k. Generally speaking, the Coulombic term might also be temperature dependent. Here we restrict ourselves to variation of the string tension, because the long-range part, kr, would primarily show a finite-temperature effect below the critical temperature. The mass of the charm quark in the potential model may also be temperature dependent. In the case of heavy quarks, this would be a minor effect and is omitted in the present calculation. We shall comment further on this in later discussions.Calculations are made by a variational method with variation of the string tension. In the calculation of the leptonic width, the reliability of the value of the variational wave function at the origin is rather poor. So we adopt the values from the sum rule for the potential, i.e., l^(0)| 2 =(/^/27r)<rfK/rfr).(In Fig. 1, the dependence of masses and widths on the string tension is shown. We fix the charm-quark mass m c to be 1.41 GeV and we can reproduce the results of Buchmuller and Tye at k = 0.18 GeV 2 . We see that both quantities decrease gradually as the string tension decreases. The ob...

Glueball properties at finite temperature in SU(3) anisotropic lattice QCD

“…In contrast to the effective model approaches, which have been extensively used to study the thermal properties of hadrons [2,6], only a few lattice QCD studies have been performed for the pole-mass of thermal hadrons so far [13,14,15,16]. Instead, the screening mass has been extensively studied with the lattice QCD [12,17,18,19] by analyzing the spatial correlations of the hadronic correlators.…”

“…QCD at finite temperature is one of the most interesting subjects in the quark hadron physics [1,2,3]. At low temperature, quarks and gluons are confined in the color-singlet objects, hadrons, due to the nonperturbative effect of the strong interactions among them.…”

“…As the temperature increases up close to T c , the inter-quark potential is known to change significantly [10,11]. As far as the heavy quarkonia are concerned, for instance J/ψ, the change of the interquark potential may be followed by the changes in the structures of hadrons, which may lead to significant mass shifts as a consequence [2]. One also expects significant mass shifts of the light hadrons, for instance, σ-meson [6], which is due to the partial chiral restoration.…”

“…Even below T c , one is interested in the hadronic mass shift [2,6,7], because it can be one of the most important pre-critical phenomena of the QCD phase transition at finite temperature (and also at finite density). In this respect, from the experimental side for instance, CERES Collaboration [8] has proposed the high-energy heavy-ion collision data, which may indicate the mass shift of ρ-meson, and extensive theoretical efforts have been made aiming at understanding of its true implications [9].…”

Quarkonium at Finite Temperature

“…Changes of charmonium states have been regarded as one of the most important probes of plasma formation [1], because the potential model calculations predict the mass shift of charmonium near T c [2], and J/ψ suppression above T c [3]. However, lattice QCD simulations have indicated that the thermal properties of hadronic correlators are much more involved than weakly interacting almost free quarks [4].…”