# Matching relations for decoupling in the Standard Model at two loops and beyond

## TL;DR

This paper derives two-loop order matching relations for the Standard Model parameters when heavy particles are decoupled, providing essential tools for precise low-energy effective theories.

## Contribution

It presents the complete two-loop matching relations for electromagnetic coupling and light fermion masses, extending existing results to include heavy particle decouplings in the Standard Model.

## Key findings

- Two-loop matching for electromagnetic coupling
- Two-loop matching for light fermion masses
- Sequential decoupling of lighter fermions

## Abstract

I discuss the matching relations for the running renormalizable parameters when the heavy particles (top quark, Higgs scalar, Z and W vector bosons) are simultaneously decoupled from the Standard Model. The complete two-loop order matching for the electromagnetic coupling and all light fermion masses are obtained, augmenting existing results at 4-loop order in pure QCD and complete two-loop order for the strong coupling. I also review the further sequential decouplings of the lighter fermions (bottom quark, tau lepton, and charm quark) from the low-energy effective theory.