Screening without screening: Baryon energy at high baryon density

Jeff Greensite,Evan Owen

doi:10.1103/physrevd.100.034503

Abstract

We compute the Coulomb interaction energy of dense sets of static quarks in a compact volume (much smaller than the lattice volume) containing one quark per lattice site. The quark color charges are combined into either a set of three-quark nucleon states, or into a non-factorizable "one big hadron" state. In both cases we find that the energy per quark is roughly constant as the volume of quarks increases. A surprise is that if we construct the nucleon states from sets of three quarks chosen at random in the volume, then the energy per quark remains roughly constant, even as the average distance between quarks in a nucleon state grows as the volume increases. This energy dependence of a nucleon in a dense medium is at odds with the behavior of an isolated nucleon as quark separation increases, and for static quarks it is not easily explicable in terms of some version of Debye screening.

Highlights

The study of QCD at high baryon density is constrained by the unsolved sign problem
In Coulomb gauge the V operators are tensors, independent of position and gauge field, which contract quark indices into global color singlets, and the Coulomb energy is computed on the lattice from the correlators hV log a1
In the past it was found that the Coulomb energy in a static quark-antiquark pair rises linearly with quark separation [3,4]; contains a Lüscher term [4]; and is arranged into a flux tube which is somewhat more narrow than the minimal energy configuration [6], rather than being spread out over all space as one might naively expect

Summary

INTRODUCTION

The study of QCD at high baryon density is constrained by the (as yet) unsolved sign problem. In this article we will study the Coulomb interaction energy of a dense system of static quark charges in a fixed volume, and for this problem we will see that standard Monte Carlo methods will suffice. This consists of division of the quarks into 2p sets of three quarks (not necessarily nearest neighbors), and contraction of the quark charges in each set into a color singlet. The point to notice is that unlike the MN state, a DQP state cannot be factorized into two or more subsets of color singlets It is, in a sense, one big hadron, where every quark interacts in some way with every other quark.

COLOR CONTRACTIONS

Gauge invariance and Coulomb energy

The multiplicities of MN and DQP contractions

SPATIAL ARRANGEMENTS AND COULOMB ENERGIES

COULOMB ENERGY IN A DENSE MEDIUM

CONCLUSIONS