On the one-loop Yukawa coupling beta-function to order $Yg^2$ in a general $alpha$ gauge and its gauge independence

Abstract

We present the calculation of the one-loop Yukawa coupling beta function to order $Yg^2$ in a general a gauge, where Y and g are Yukawa and gauge couplings. We show explicitly how the gauge parameter a cancels out from the beta - function and demonstrate how some familiar results are obtained from it.