All two-loop scalar self-energies and tadpoles in general renormalisable field theories

Mark D Goodsell,Sebastian Paßehr

doi:10.1140/epjc/s10052-020-7657-8

Abstract

We calculate the complete tadpoles and self-energies at the two-loop order for scalars in general renormalisable theories, a crucial component for calculating two-loop electroweak corrections to Higgs-boson masses or for any scalar beyond the Standard Model. We renormalise the amplitudes using mass-independent renormalisation schemes, based on both dimensional regularisation and dimensional reduction. The results are presented here in Feynman gauge, with expressions for all 121 self-energy and 25 tadpole diagrams given in terms of scalar and tensor integrals with the complete set of rules to reduce them to a minimal basis of scalar integrals for any physical kinematic configuration. In addition, we simplify the results to a set of only 16 tadpole and 58 self-energy topologies using relations in order to substitute the ghost and Goldstone-boson couplings that we derive. To facilitate their application, we also provide our results in electronic form as a new code TLDR. We test our results by applying them to the Standard Model and compare with analytic expressions in the literature.

Highlights

The Higgs boson mass has been measured to an accuracy of about O(100) MeV, making it an electroweak precision parameter
After carrying out the integral reduction and extracting all UV divergences via the relations in Appendix A, polynomials in the regulator 1/ will remain, which correspond to the genuine two-loop counterterm of the diagram; but we may find additional divergent and finite parts corresponding to any infra-red divergences: we do not introduce infra-red counterterms
The renormalised expressions for all of the basic classes of diagrams are given in Appendix B.1 for the tadpoles and Appendix B.2 for the self-energies, since they are rather long; initially, there are 25 tadpole and 121 self-energy classes which is a much larger set than in the gaugeless limit

Summary

Introduction

The Higgs boson mass has been measured to an accuracy of about O(100) MeV, making it an electroweak precision parameter. An enormous amount of effort has gone into refining the calculation of the Higgs-boson mass from a given set of physical or top-down inputs, in both generic and specific theories. This has typically been driven by the need for accurate predictions of the Higgs mass in supersymmetric models, where the Higgs quartic coupling is predicted from the gauge couplings (and other top–down parameters in extended models)

Objectives

Methods

Results

Conclusion