UV asymptotically free QED as a broken YM theory in the unitary gauge

TL;DR

This paper demonstrates that a broken Yang-Mills theory in the unitary gauge exhibits asymptotic freedom similar to QED, with the physical charge decreasing logarithmically at high energies, by analyzing the coupling renormalization.

Contribution

It provides a novel calculation of the beta function in a broken YM theory using the unitary gauge, showing asymptotic freedom in a QED-like framework.

Findings

The coupling constant decreases logarithmically with the symmetry breaking scale.

Non-renormalizable divergences cancel in the physical amplitude.

The beta function indicates asymptotic freedom in the broken phase.

Abstract

We compute the $\beta$-function of a YM theory, broken to $U(1)$, by evaluating the coupling constant renormalization in the broken phase. We perform the calculation in the unitary gauge where only physical particles appear and the theory looks like a version of QED containing massive charged spin 1 particles. We consider an on-shell scattering process and after verifying that the non-renormalizable divergences which appear in the Green's functions cancel in the expression of the amplitude, we show that the coupling constant renormalization is entirely due to the photon self-energy as in QED. However we get the expected asymptotic freedom and the physical charge decreases logarithmically as a function of the symmetry breaking scale.