Matching renormalisable couplings: simple schemes and a plot

TL;DR

This paper explores various methods for matching high-energy theories to effective field theories at one loop, focusing on scalar and Yukawa couplings, and compares different schemes including pole mass matching.

Contribution

It generalizes the counterterm scheme for matching without heavy gauge bosons, compares it with pole mass methods, and applies it to models like the MSSM and Dirac gaugino models.

Findings

Different scheme choices significantly affect threshold corrections.

Matching pole masses is equivalent to a specific scheme choice.

Proposed methods improve efficiency of extracting quartic couplings.

Abstract

We discuss different choices that can be made when matching a general high-energy theory -- with the restriction that it should not contain heavy gauge bosons -- onto a general renormalisable effective field theory at one loop, with particular attention to the quartic scalar couplings and Yukawa couplings. This includes a generalisation of the counterterm scheme that was found to be useful in the case of high-scale/split supersymmetry, but we show the important differences when there are new heavy scalar fields in singlet or triplet representations of $SU(2)$. We also analytically compare our methods and choices with the approach of matching pole masses, proving the equivalence with one of our choices. We outline how to make the extraction of quartic couplings using pole masses more efficient, an approach that we hope will generalise beyond one loop. We give examples of the impact of different scheme choices in a toy model; we also discuss the MSSM and give the threshold corrections to the Higgs quartic coupling in Dirac gaugino models.