Two-loop gauge coupling $\beta$-function in a four-dimensional framework: the Standard Model case

TL;DR

This paper applies Implicit Regularization, a physical dimension-preserving scheme, to compute the two-loop gauge coupling $eta$-function in the Standard Model, confirming previous results obtained via dimensional regularization.

Contribution

It demonstrates the use of Implicit Regularization for two-loop calculations in the Standard Model, providing an alternative to dimensional regularization.

Findings

Reproduces the known two-loop $eta$-function result.

Validates Implicit Regularization as a reliable scheme.

Shows consistency with dimensional regularization results.

Abstract

At present, the gauge coupling $\beta$-function in the Standard Model (SM) is known up to four-loop order. As most SM calculations, dimensional regularization was employed. Despite its striking success, other regularization schemes have emerged, which aim to stay in the physical dimension as far as possible. In this contribution, we apply Implicit Regularization, a scheme defined in momentum space that complies with BPHZ, to obtain the two-loop gauge coupling $\beta$-function in the Standard Model. We reproduce the same result obtained when applying dimensional regularization.