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

• Main Authors: Mark D. Goodsell, Sebastian Paßehr
• Format: Article
• Language: English
• Published: SpringerOpen 2020-05-01
• Series: European Physical Journal C: Particles and Fields
• Online Access: http://link.springer.com/article/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.