# Soft thermal contributions to 3-loop gauge coupling

Journal of High Energy Physics, May 2018

Abstract We analyze 3-loop contributions to the gauge coupling felt by ultrasoft (“magnetostatic”) modes in hot Yang-Mills theory. So-called soft/hard terms, originating from dimension-six operators within the soft effective theory, are shown to cancel 1097/1098 of the IR divergence found in a recent determination of the hard 3-loop contribution to the soft gauge coupling. The remaining 1/1098 originates from ultrasoft/hard contributions, induced by dimension-six operators in the ultrasoft effective theory. Soft 3-loop contributions are likewise computed, and are found to be IR divergent, rendering the ultrasoft gauge coupling non-perturbative at relative order $\mathcal{O}\left({\alpha}_{\mathrm{s}}^{3/2}\right)$. We elaborate on the implications of these findings for effective theory studies of physical observables in thermal QCD.

This is a preview of a remote PDF: https://link.springer.com/content/pdf/10.1007%2FJHEP05%282018%29037.pdf

M. Laine, P. Schicho, Y. Schröder. Soft thermal contributions to 3-loop gauge coupling, Journal of High Energy Physics, 2018, 37, DOI: 10.1007/JHEP05(2018)037