Magnetic field effects on the static quark potential at zero and finite temperature

TL;DR

This study explores how a constant magnetic field influences the static quark-antiquark potential at zero and finite temperatures, revealing anisotropic effects and suppression of confinement, with implications for understanding QCD phase transitions.

Contribution

It provides continuum limit results for the static potential under magnetic fields and characterizes the anisotropic deformation of the string tension and related parameters.

Findings

Magnetic field induces a significant anisotropy in the string tension.

The string tension decreases with increasing magnetic field, potentially vanishing at high fields.

Magnetic fields suppress the confining potential even before inverse magnetic catalysis appears.

Abstract

We investigate the static $Q\bar{Q}$ potential at zero and finite temperature in the presence of a constant and uniform external magnetic field $\vec{B}$, for several values of the lattice spacing and for different orientations with respect to $\vec{B}$. As a byproduct, we provide continuum limit extrapolated results for the string tension, the Coulomb coupling and the Sommer parameter at $T = 0$ and $B = 0$. We confirm the presence in the continuum of a $B$-induced anisotropy, regarding essentially the string tension, for which it is of the order of 15\% at $|e| B \sim 1~{\rm GeV}^2$ and would suggest, if extrapolated to larger fields, a vanishing string tension along the magnetic field for $|e| B \gtrsim 4$ GeV$^2$. The angular dependence for $|e| B \lesssim 1$ GeV$^2$ can be nicely parametrized by the first allowed term in an angular Fourier expansion, corresponding to a quadrupole deformation. Finally, for $T \neq 0$, the main effect of the magnetic field is a general suppression of the string tension, leading to a precocious loss of the confining properties: this happens even before the appearance of inverse magnetic catalysis in the chiral condensate, supporting the idea that the influence of the magnetic field on the confining properties is the leading effect originating the decrease of $T_c$ as a function of $B$.