Chiral symmetry restoration at finite temperature within the Hamiltonian approach to QCD in Coulomb gauge

TL;DR

This paper investigates the chiral phase transition in QCD at finite temperature using a Hamiltonian approach in Coulomb gauge, revealing a second-order transition with a critical temperature around 92-118 MeV.

Contribution

It introduces a novel Hamiltonian framework for studying chiral symmetry restoration at finite temperature in QCD, employing a spatial compactification method.

Findings

Identifies a second-order chiral phase transition at approximately 92 MeV.

Shows the critical temperature increases to 118 MeV when adjusting the Coulomb string tension.

Demonstrates the approach's consistency with traditional finite-temperature QCD results.

Abstract

The chiral phase transition of the quark sector of QCD is investigated within the Hamiltonian approach in Coulomb gauge. Finite temperature T is introduced by compactifying one spatial dimension, which makes all thermodynamical quantities accessible from the ground state on the spatial manifold $\small\mathbb{R}^2 \times S^1(1/T)$. Neglecting the coupling between quarks and transversal gluons, the equations of motion of the quark sector are solved numerically and the chiral quark condensate is evaluated and compared to the results of the usual canonical approach to finite-temperature Hamiltonian QCD based on the density operator of the grand canonical ensemble. For zero bare quark masses, we find a second-order chiral phase transition with a critical temperature of about 92 MeV. If the Coulomb string tension is adjusted to reproduce the phenomenological value of the quark condensate, the critical temperature increases to 118 MeV.