Resummation of terms enhanced by trilinear squark-Higgs couplings in the MSSM

TL;DR

This paper develops all-order resummation techniques for trilinear squark-Higgs couplings in the MSSM, improving the precision of Higgs sector calculations by summing dominant contributions.

Contribution

It introduces new resummation relations for $\Delta \lambda$ that incorporate $x_q$-enhanced terms across different orders, clarifying resummable and non-resummable contributions.

Findings

Derived all-order resummation formulas for $\Delta \lambda$ including $x_q$-enhanced terms.

Identified terms that cannot be resummed in the MSSM Higgs sector.

Provided constraints on maximal powers of $x_q$ in loop corrections.

Abstract

We analyze the appearance of the trilinear squark-Higgs couplings $x_q$ in Green functions in the Higgs sector of the MSSM and in threshold corrections to the SM. The results are constraints on maximal powers of $x_q$ in QCD-related loop corrections. In practice these often imply all-order resummations of leading or subleading $x_q$ contributions in SM-parametrized expressions. We present a variety of all-order resummation relations for $\Delta \lambda$ which include such $x_q$-enhanced terms and different orders in Yukawa and gauge couplings. We contrast which terms cannot be resummed.