Completely automated computation of the heavy-fermion corrections to the three-loop matching coefficient of the vector current

TL;DR

This paper presents a fully automated three-loop calculation of heavy-fermion corrections to the vector current matching coefficient between QCD and NRQCD, crucial for top and bottom quark threshold analyses.

Contribution

It introduces an automated framework for calculating three-loop heavy-fermion corrections, streamlining complex multi-step quantum field theory computations.

Findings

Computed three-loop heavy-fermion corrections for vector current matching

Automated the entire calculation process from diagram generation to numerical evaluation

Provides essential input for precise top and bottom quark threshold studies

Abstract

We evaluate the corrections to the matching coefficient of the vector current between Quantum Chromodynamics (QCD) and Non-Relativistic QCD (NRQCD) to three-loop order containing a closed heavy-fermion loop. The result constitutes a building block both for the bottom- and top-quark system at threshold. Strong emphasis is put on our completely automated approach of the calculation including the generation of the Feynman diagrams, the identification of the topologies, the reduction to master integrals and the automated numerical computation of the latter.