# Gauge dependence and multiplicative renormalization of Yang-Mills theory with matter fields

## TL;DR

This paper investigates the gauge dependence and renormalization properties of an SU(2) Yang-Mills theory with matter fields using the background field method, proving multiplicative renormalizability and gauge independence of physical parameters.

## Contribution

It extends the BV-formalism with additional fields to demonstrate the multiplicative renormalizability and gauge independence in Yang-Mills theories with matter fields.

## Key findings

- Renormalization is gauge-independent.
- Multiplicative renormalizability is proven.
- The method extends the BV-formalism with extra fermionic fields.

## Abstract

In the paper, within the background field method, the renormalization and the gauge dependence is studied as for an SU(2) Yang-Mills theory with multiplets of spinor and scalar fields. By extending the quantum action of the BV-formalism with an extra fermion vector field and a constant fermion parameter, the multiplicative character of the renormalizability is proven. The renormalization of all the physical parameters of the theory under consideration is shown to be gauge-independent.