Masses ofJ/ψandηcin the Nuclear Medium: QCD Sum Rule Approach

Abstract

We investigate the masses of the lowest cc states, the J͞c and h c , in nuclear matter using QCD sum rules. Up to dimension four, the differences between the operator product expansions in vacuum and in medium arise from the density-dependent change in the gluon condensate and from a new contribution proportional to the nucleon expectation value of the twist-2 gluon operator. Both terms together give an attractive shift of about 5 -10 MeV to the J͞c and h c masses in nuclear matter.[S0031-9007(99)09014-6] PACS numbers: 14.40. Gx, 11.55.Hx, 24.85. + p Investigating the behavior of heavy quark systems in a nuclear medium is of great interest, for several reasons. First, the ongoing discussion of J͞c suppression in ultrarelativisitic heavy-ion collisions as a possible quarkgluon plasma signal requires detailed knowledge about the in-medium interactions of the J͞c under "normal," nonplasma conditions. Furthermore, as Brodsky et al. [1] pointed out, multigluon exchange can lead to an attractive potential between a cc meson and a nucleon, such that, for example, the h c could form bound states even with light nuclei. In more recent calculations the estimated charmonium binding energy in nuclear systems was found to be of the order of 10 MeV [2][3][4][5].In the present paper we study the in-medium behavior of the J͞c and h c using QCD sum rules [6]. The QCD sum rule approach connects the spectral density of a given current correlation function via a dispersion relation with the QCD operator product expansion (OPE). Inmedium QCD sum rules have so far been applied only for light quark systems, in order to study possible shifts of the in-medium masses of nucleons [7-9] and vector mesons [10]. Such calculations suffer from uncertainties, e.g., due to assumptions about factorization of fourquark condensates which may not be justified. As we shall see, in-medium QCD sum rules applied to heavy quark systems are expected to be more reliable. Up to dimension four, the order to which the vacuum sum rules for hadrons involving heavy quarks are commonly expanded, all condensate parameters are quite well known and there are no ambiguities in the OPE. We also find that uncertainties caused by possibly large hadronic inmedium decay widths are much smaller than for lightquark systems.Our starting point is the time ordered current-current correlation function of two heavy quark currents in nuclear matter (n.m.), P͑v,q͒ i Z d 4 x e iq?x ͗jT ͓ j͑x͒j͑0͔͒j͘ n.m. . (1) Here q ͑v, q͒, and j͘ n.m. is the ground state of nuclear matter which we take to be at rest. For the J͞c we take the vector current j V m cg m c and for the h c , we use the pseudoscalar current j P icg 5 c. In the region of large and positive Q 2 q 2 2 v 2 we can express the correlation function through an operator product expansion (short distance expansion) [11] and write the left hand side of Eq. (1) asHere the O n are operators of (mass) dimension n, renormalized at a scale m 2 , and C n are the perturbative Wilson coefficients which, in the medium at rest, generally ...

Charmonium spectroscopy in strong magnetic fields by QCD sum rules:S-wave ground states

“…(9) in Ref. [49]. Carrying out the replacement (48) in the expression therein, we obtain the twist-2 term in Eq.…”

“…The general forms of the Wilson coefficients for the twist-2 gluon condensate were calculated both in the pseudoscalar and the vector channels [49]. One can apply those expressions to the present cases in external magnetic fields by replacing the expectation value of the operator as…”

“…It is noteworthy that the dominant effects in finite temperature/density comes into the OPE only through dimension-4 gluon condensates that are related to the energy momentum tensor of which the matrix elements are well estimated both at finite temperature from lattice QCD [51,52,55,56,58] and at normal nuclear matter density from measurements in deep inelastic scatterings [49]. Recently, it has also been shown that the strength of the charmonium wave function at the origin obtained from the QCDSR follows precisely that obtained from solving the Schrödinger equation with a finite temperature free energy potential extracted from lattice QCD [59].…”

“…This structure in QCD sum rules indicates that we could investigate how changes in properties of QCD vacuum in the OPE manifest themselves in hadron properties in external environments. Indeed, the QCD sum rules at finite temperature/density [46][47][48] have been applied to heavy quarkonia [49][50][51][52][53][54][55][56][57][58][59], light mesons [60,61], and heavy-light mesons [62] in the last two decades, and very recently those in strong external magnetic fields [33,34].…”

QCD sum rules and thermal properties of Charmonium in the vector channel

“…Non-gluonic operators are highly suppressed [5], [12] so that they can be safely ignored. We have considered also a gluonic twist-two term in the OPE introduced in [13], and computed on the lattice in [14]. Its impact is small,(2-6)%, and plays no appreciable role in the results.…”