Two-loop renormalization of tan(beta) and its gauge dependence

Abstract

Renormalization of two-loop divergent corrections to the vacuum expectation values (v_1, v_2) of the two Higgs doublets in the minimal supersymmetric standard model, and their ratio $\tan\beta=v_2/v_1$, is discussed for general R_{\xi} gauge fixings. When the renormalized (v_1, v_2) are defined to give the minimum of the loop-corrected effective potential, it is shown that, beyond the one-loop level, the dimensionful parameters in the R_{\xi} gauge fixing term generate gauge dependence of the renormalized $\tan\beta$. Additional shifts of the Higgs fields are necessary to realize the gauge-independent renormalization of $\tan\beta$.