Finite density QCD sum rules for nucleons

Abstract

It is shown how the QCD sum rules can be applied for the investigation of the density dependence of the nucleon parameters. These characteristics can be expressed through the expectation values of QCD operators in nuclear matter. In certain approximations the expectation values are related to the observables. First applications of the approach reproduced some of the basic features of nuclear physics, providing also a new knowledge. The program of the future work is presented. The difficulties of the approach are discussed.

Properties of nucleon in nuclear matter: once more

“…Using the explicit form of the interpolating current in the correlation function of Eq. (1) and contracting out all quark pairs via Wick's theorem, we find (14) where S = C S T C, S u,d are light-quark propagators and T r [...] denotes the trace of the gamma matrices. In coordinate-space, the light-quark propagator at the nuclear medium has the following form in the fixed-point gauge [15,41]:…”

“…Only in [10], the authors extended the Ioffe current (β = −1) with β being the mixing parameter in the interpolating current of the nucleons to −1.15 ≤ β ≤ −0.95 using the mass sum rules. For some studies of the nucleon mass shift in the nuclear medium for the Ioffe current and properties of other hadrons in a dense medium, see for instance [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. The effects of four-quark condensate on the nucleon parameters have also been studied in [29].…”

Chemical potential dependence of chiral quark condensate in Dyson–Schwinger equation approach of QCD

“…where pν = ( p, p 4 + iµ), the complex functions A, C and B can be defined by the quark equation with an effective gluon propagator. With a δ-function in momentum space for the effective gluon propagator (Munczek-Nemirovsky model [39]), it has been found that, in the D-S equation approach [20,24], the quark condensate increases with chemical potential, which is not consistent with the behavior given in composite operator approach of QCD [13], dilute instanton liquid model [21], Nanbu-Jona-Lasinio (NJL) model [23] and other approaches [14,16,22,25]. Looking over the characteristic of the Munczek-Nomirovsky model, which gives an infinity at zero exchanged momentum, we propose that the discrepancy of the variation behaviors of the chiral quark condensate against the chemical potential arises from the overestimated sudden enhancement in the far infrared region.…”

“…Meanwhile many approaches in the framework of continuous field theory of QCD have been implemented to study the chiral symmetry breaking and its restoration in dense strongly interacting matter at zero temperature, and different models gave different behaviors at finite chemical potential (see for example Refs. [13,14,15,16,17,18,19,20,21,22,23,24,25,26]). However, there is still not any work to take into account the effect of the chemical potential dependence of the effective gluon propagator.…”

Impact of nucleon mass shift on the freeze-out process

“…Now we will turn to the in-medium nucleon pole mass M N (n, T ), which is the very characteristics which enters the EoS (10), [44]. In general, a nucleon propagating in a hot and dense hadronic enviroment can be regarded as a quasi particle, described by the in-medium nucleon correlator…”