Thermo-magnetic evolution of the QCD strong coupling

TL;DR

This paper investigates how the strong coupling constant in QCD evolves under different thermal and magnetic conditions, revealing behaviors that could explain inverse magnetic catalysis observed in lattice QCD.

Contribution

It provides a detailed analysis of the thermo-magnetic evolution of the strong coupling across various regimes, including zero and high temperature, small and large magnetic fields.

Findings

At zero temperature, $\alpha_s$ increases with magnetic field strength.

At high temperature, $\alpha_s$ increases when magnetic field exceeds temperature squared.

At high temperature, $\alpha_s$ decreases when temperature squared exceeds magnetic field.

Abstract

We study the one-loop gluon polarization tensor at zero and finite temperature in the presence of a magnetic field, to extract the thermo-magnetic evolution of the strong coupling $\alpha_s$. We analyze four distinct regimes, to wit, the small and large field cases, both at zero and at high temperature. From a renormalization group analysis we show that at zero temperature, either for small or large magnetic fields, and for a fixed transferred momentum $Q^2$, $\alpha_s$ grows with the field strength with respect to its vacuum value. However, at high temperature and also for a fixed value of $Q^2$ we find two different cases: When the magnetic field is even larger than the squared temperature, $\alpha_s$ also grows with the field strength. On the contrary, when the squared temperature is larger than the magnetic field, a turnover behavior occurs and $\alpha_s$ decreases with the field strength. This thermo-magnetic behavior of $\alpha_s$ can help explain the inverse magnetic catalysis phenomenon found by lattice QCD calculations.