Two-loop renormalization of tanβ and its gauge dependence

Renormalization of two-loop divergent corrections to the vacuum expectation values (v1,v2) of the two Higgs doublets in the minimal supersymmetric standard model, and their ratio tanβ=v2/v1, is discussed for general Rξ gauge fixings. When the renormalized (v1,v2) 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 Rξ gauge fixing term generate gauge dependence of the renormalized tanβ. Additional shifts of the Higgs fields are necessary to realize the gauge-independent renormalization of tanβ.