Yukawa coupling beta-functions in the Standard Model at three loops

TL;DR

This paper computes three-loop beta-functions for Yukawa couplings in the Standard Model, enhancing precision in understanding fermion interactions at high energies.

Contribution

It provides the first three-loop calculations of Yukawa beta-functions in the unbroken phase of the Standard Model, using advanced computational techniques.

Findings

Beta-functions are gauge-parameter independent.

Results are consistent with gauge anomaly cancellation.

Calculation confirms stability of Yukawa couplings at three loops.

Abstract

We present the results for three-loop beta-functions for Yukawa couplings of heavy Standard Model fermions calculated within the unbroken phase of the model. The calculation is carried out with the help of the MINCER program in a general linear gauge, and the final result is independent of the gauge-fixing parameters. In order to calculate three-point functions, we made use of infrared rearrangement (IRR) trick. Due to the chiral structure of the SM a careful treatment of loops with fermions is required to perform the calculation. It turns out that gauge anomaly cancellation in the SM allows us to obtain the result by means of the semi-naive treatment of gamma5.