Two-loop gradient-flow renormalization of scalar QCD

TL;DR

This paper applies the gradient-flow formalism to scalar QCD, calculating renormalization constants and condensates up to three-loop level, demonstrating the method's consistency and advancing toward Standard Model applications.

Contribution

It extends the gradient-flow formalism to scalar QCD, providing two-loop renormalization constants and three-loop condensate calculations, a novel step in this theoretical framework.

Findings

Field renormalization for scalar quarks appears beyond one-loop.

Renormalization constants are computed at two-loop level.

Condensates are evaluated at three-loop level.

Abstract

The gradient-flow formalism is applied to a non-Abelian gauge theory with scalar and fermionic particles, dubbed "scalar QCD". It is shown that the flowed scalar quark requires a field renormalization, albeit only beyond the one-loop level. A pseudo-physical, t-dependent renormalization scheme is defined, and the corresponding renormalization constant is evaluated at the two-loop level. We also calculate the gluon action density as well as the condensate of the scalar and the fermionic quark at three-loop level in this theory. The results validate the consistency of the gradient-flow formalism in this theory and provide a further step towards applying the gradient-flow formalism to the full Standard Model.