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 ${\mathbb{R}}^{2}\ifmmode\times\else\texttimes\fi{}{S}^{1}(1/T)$. 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.
Highlights
Understanding the phase diagram of quantum chromodynamics (QCD) is still one of the most challenging problems in particle physics [1,2]
Lattice calculations can shed some light on its structure for vanishing baryon density but still suffer from the so-called sign problem in the general case of finite densities [1,3]
In the past two decades several nonperturbative continuum approaches, which do not suffer from the sign problem, have been developed [4], one of them being the variational approach to Hamiltonian QCD in Coulomb gauge [5], see Ref. [6] for a recent review
Summary
Understanding the phase diagram of quantum chromodynamics (QCD) is still one of the most challenging problems in particle physics [1,2]. Lattice calculations can shed some light on its structure for vanishing baryon density but still suffer from the so-called sign problem in the general case of finite densities [1,3]. To overcome this problem, in the past two decades several nonperturbative continuum approaches, which do not suffer from the sign problem, have been developed [4], one of them being the variational approach to Hamiltonian QCD in Coulomb gauge [5], see Ref. Thereby, finite temperatures were introduced by compactifying one spatial dimension using the alternative formulation of finite-temperature Hamiltonian quantum field theory proposed in Ref. While the pseudocritical temperatures of the chiral and, respectively, deconfinement phase transition were in good agreement with lattice data, the width of the transition region and the order of the chiral phase transition turned out to be at odds with the lattice
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