O α S 2 $$ \mathcal{O}\left({\alpha}_S^2\right) $$ corrections to the running top-Yukawa coupling and the mass of the lightest Higgs boson in the MSSM

Abstract

In this paper we propose a method to compute the running top-Yukawa coupling in supersymmetric models with heavy mass spectrum based on the "running" and "decoupling" procedure. In order to enable this approach we compute the two-loop SUSY-QCD radiative corrections required in the decoupling process. The method has the advantage that large logarithmic corrections are automatically resummed through the Renormalization Group Equations. As phenomenological application we study the effects of this approach on the SUSY-QCD corrections to the prediction of the lightest Higgs boson mass at three-loop accuracy. We observe a significant reduction of the renormalization scale dependence as compared to the direct method, that is based on the conversion relation between the running and pole mass for the top quark. The effect of resummation of large logarithmic contributions consists in an increased prediction for the Higgs boson mass, an observation in agreement with the previous analyses.

Higgs mass prediction in the MSSM at three-loop level in a pure $$\overline{{\text {DR}}}$$ DR ¯ context

“…7 we compare our results to the three-loop calculation presented in Ref. [68], assuming the input parameters for the "heavy sfermions" scenario defined in detail in the example folder of Ref. [69].…”

“…In the left panel the blue circles show the H3m result, including only the terms of O α t + α t α s + α t α 2 s , where the MSSM DR top mass is calculated using the "running and decoupling" procedure described in Ref. [68]. The black crosses show the same result, except that the DR top mass H3m with m at the SUSY scale is taken from the spectrum generator FlexibleSUSY+Himalaya.…”

O α s α t $$ \mathcal{O}\left({\alpha}_s{\alpha}_t\right) $$ (non)decoupling effects within the top-sector of the MSSM

“…Namely, they can be derived from the measured top, W and Z boson, and Higgs pole masses. However, such a determination will get very large radiative corrections for heavy supersymmetric particle [24]. Figure 3 and figure 5 of ref.…”

“…The SUSY-QCD contributions for ζ g , ζ mt and ζ yt in the same limit as in the present paper are available from ref. [24]. In addition, two-loop Yukawa contributions to ζ m b and ζ mτ were computed in the limit of heavy Higgses (including the lightest one) in ref.…”

“…Figure 3 and figure 5 of ref. [24] display the explicit comparison of the method based on running and decoupling procedure (similar with that presented in the current paper) and the direct calculation starting from the relation between the pole and the running top quark mass within the SUSY-QCD, using the code TSIL [52]. It turned out that, in order to bring the theoretical uncertainties on the running top quark mass at least in the range of the experimental precision, one needs even the three-loop corrections.…”