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

TL;DR

This paper provides a comprehensive calculation of two-loop scalar self-energies and tadpoles in general renormalisable theories, essential for precise Higgs mass predictions and beyond Standard Model physics, with detailed formulas and a new computational tool.

Contribution

It introduces complete two-loop scalar self-energy and tadpole calculations in general theories, including a new code TLDR for practical application and simplified topologies for easier use.

Findings

Validated results with Standard Model comparisons

Provided a new code TLDR for calculations

Simplified expressions for practical use

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.