We calculate the $O\left(a\right)\mathrm{}$ improvement coefficient $c_{\mathrm{SW}}$ in the Sheikholeslami-Wohlert quark action for various improved gauge actions with six-link loops. We employ a conventional perturbation theory introducing the fictitious gluon mass to regularize the infrared divergence. Our results for some improved gauge actions are in agreement with those previously obtained with the Schrödinger functional method.

• Received 13 June 2003

DOI:https://doi.org/10.1103/PhysRevD.68.094019