The unbearable smallness of magnetostatic QCD corrections

TL;DR

This paper calculates one-loop corrections to the magnetostatic QCD action at dimension six, revealing that these corrections are small in the deconfined phase and discussing their implications for pressure and Wilson loops.

Contribution

It provides a simplified expression for one-loop corrections to magnetostatic QCD at dimension six, including their physical relevance, which was previously not explicitly detailed.

Findings

Corrections are small in the deconfined phase.

The correction term is explicitly expressed at dimension six.

Dimension eight contributions are also discussed.

Abstract

One loop corrections to the magnetostatic QCD action are evaluated to dimension six in the magnetostatic fields.The result is remarkably simple $${1\over 4}\int d\vec x (F^a_{ij})^2 - {g_M^2 N \over {32\pi m_E^3}} \int d\vec x\Bigg({1\over{60}}(D_m^{ab} F^b_{mr})^2 + {1\over 180} f^{abc} F^a_{mn} F^b_{nr }F^c_{rm} \Bigg)(1+\mathcal{O}(g_M^2)).$$ In all of the deconfined phase the correction is quite small. The term of $\mathcal{O}(g^2_M)$ is the dimension eight contribution and is only presented in a covariant derivative basis. We discuss their physical relevance for the pressure and the spatial Wilson loop.