Eur. Phys. J. C (2020) 80: 417
https://doi.org/10.1140/epjc/s10052-020-7657-8

Regular Article - Theoretical Physics

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

¹ Laboratoire de Physique Théorique et Hautes Energies (LPTHE), UMR 7589, Sorbonne Université et CNRS, 4 Place Jussieu, 75252, Paris Cedex 05, France
² Institute for Theoretical Particle Physics and Cosmology, RWTH Aachen University, Sommerfeldstraße 16, 52074, Aachen, Germany

^* e-mail: passehr@physik.rwth-aachen.de

Received: 26 November 2019
Accepted: 15 January 2020
Published online: 13 May 2020

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.