Thermomagnetic evolution of the QCD strong coupling

Abstract

We study the one-loop gluon polarization tensor at zero and finite temperature in the presence of a magnetic field, to extract the thermomagnetic evolution of the strong coupling ${\ensuremath{\alpha}}_{s}$. 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 ${Q}^{2}$, ${\ensuremath{\alpha}}_{s}$ 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, ${\ensuremath{\alpha}}_{s}$ also grows with the field strength. On the contrary, when the squared temperature is larger than the magnetic field, a turnover behavior occurs, and ${\ensuremath{\alpha}}_{s}$ decreases with the field strength. This thermomagnetic behavior of ${\ensuremath{\alpha}}_{s}$ can help explain the inverse magnetic catalysis phenomenon found by lattice QCD calculations.