The unbearable smallness of magnetostatic QCD corrections

Abstract

One loop corrections to the magnetostatic QCD action are evaluated to dimension six in the magnetostatic fields.The result is remarkably simple $$\frac{1}{4}\int d\vec{x}(F_{ij}^a{)}^2-\frac{g_M^{2}N}{32\pi m_E^3}\int d\vec{x}(\frac{1}{60}(D_m^{ab}{F}_{mr}^b{)}^2+\frac{1}{180}{f}^{abc}{F}_{mn}^a{F}_{nr}^b{F}_{rm}^c)(1+\mathcal{O}(g_M^2)).$$ In all of the deconfined phase the correction is quite small. The term of $\mathcal{O}(g_M^2)$ 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.