Two-loop Higgs mass calculation from a diagrammatic approach

TL;DR

This paper develops a diagrammatic method to calculate two-loop corrections to the Higgs mass in theories with massless gauge bosons, providing analytic expressions and implementation in SARAH for efficient evaluation.

Contribution

It introduces a new diagrammatic approach for two-loop Higgs mass calculations and implements it in SARAH for broad applicability in generic theories.

Findings

Analytic expressions for two-loop tadpole diagrams

Implementation in SARAH for efficient calculations

Extension to massive gauge boson cases in appendix

Abstract

We calculate the corrections to the Higgs mass in general theories restricted to the case of massless gauge bosons (the gaugeless limit). We present analytic expressions for the two-loop tadpole diagrams, and corresponding expressions for the zero-momentum limit of the Higgs self energies, equivalent to the second derivative of the two-loop effective potential. We describe the implementation in SARAH, which allows an efficient, accurate and rapid evaluation for generic theories. In the appendix, we provide the expressions for tadpole diagrams in the case of massive gauge bosons.