On the two–loop Yukawa corrections to the MSSM Higgs boson masses at large tan β

We complete the effective potential calculation of the two–loop, top/bottom Yukawa corrections to the Higgs boson masses in the Minimal Supersymmetric Standard Model, by computing the O(αt + αtαb + α2b) contributions for arbitrary values of the bottom Yukawa coupling. We also compute the corrections to the minimization conditions of the effective potential at the same perturbative order. Our results extend the existing O(αt ) calculation, and are relevant in regions of the parameter space corresponding to tanβ ≫ 1. We extend to the Yukawa corrections a convenient renormalization scheme, previously proposed for the O(αbαs) corrections, that avoids unphysically large threshold effects associated with the bottom mass and absorbs the bulk of the corrections into the one–loop expression. For large values of tanβ, the new contributions can account for a variation of several GeV in the lightest Higgs boson mass.