Renormalisability of the SU(2)$\times$U(1) Electroweak Theory with Massive W Z Fields and Massive Matter Fields

TL;DR

This paper proves the renormalisability of the SU(2)×U(1) electroweak theory incorporating massive W and Z bosons and matter fields, extending previous results to include mass terms while maintaining BRST invariance.

Contribution

It demonstrates that the electroweak theory with massive gauge and matter fields remains renormalizable using BRST symmetry and constraint conditions, extending prior massless results.

Findings

Renormalisability of the massive electroweak theory is established.

BRST invariance is preserved with mass terms.

The divergence structure of the theory is characterized.

Abstract

We extend the previous work and study the renormalisability of the SU$_L$(2) $\times$ U$_Y$(1) electroweak theory with massive W Z fields and massive matter fields. We expound that with the constraint conditions caused by the W Z mass term and the additional condition chosen by us we can still performed the quantization in the same way as before. We also show that when the $\delta-$ functions appearing in the path integral of the Green functions and representing the constraint conditions are rewritten as Fourier integrals with Lagrange multipliers $\lambda_a$ and $\lambda_y$, the total effective action consisting of the Lagrange multipliers, ghost fields and the original fields is BRST invariant. Furthermore, with the help of the the renormalisability of the theory without the the mass term of matter fields, we find the general form of the divergent part of the generating functional for the regular vertex functions and prove the renormalisability of the theory with the mass terms of the W Z fields and the matter fields.