A convergent scheme for one-loop evolutions of the Yukawa couplings in the MSSM

Integrated forms of the one-loop evolution equations are given for the Yukawa couplings in the MSSM, valid for any value of $\tan \beta$, generalizable to virtually any number of Yukawa fermions, and including all gauge couplings. These forms turn out to have nice mathematical convergence properties which we prove, and we determine the ensuing convergence criteria. Furthermore, they allow to write down general sufficient and necessary conditions to avoid singularities in the evolution of the Yukawa couplings over physically relevant energy ranges. We also comment briefly on the possible use of these features for physics issues and give a short numerical illustration.