New formulas and predictions for running fermion masses at higher scales in SM, 2HDM, and MSSM

Abstract.

Including contributions of scale-dependent vacuum expectation values, we derive new analytic formulas and obtain substantially different numerical predictions for the running masses of quarks and charged leptons at higher scales in the SM, 2HDM and MSSM. These formulas exhibit significantly different behaviours with respect to their dependence on gauge and Yukawa couplings from those derived earlier. At one-loop level, the masses of the first two generations are found to be independent of the Yukawa couplings of the third generation in all three effective theories in the small mixing limit. Analytic formulas are also obtained for the running of $\tan\beta(\mu)$ in 2HDM and MSSM. Other numerical analyses include a study of the third generation masses at high scales as functions of the low-energy values of $\tan\beta$ and the SUSY scale $M_{\mathrm{S}}=M_Z-10^4$ GeV.