The strong couplings of massive Yang-Mills theory

TL;DR

This paper investigates the behavior of massive Yang-Mills theory with a mass term added explicitly, demonstrating that the apparent discontinuity in the massless limit is a perturbative artifact and that the limit is smooth.

Contribution

The study clarifies the smoothness of the massless limit in massive Yang-Mills theory, resolving longstanding perturbative issues and confirming the Vainshtein mechanism.

Findings

Longitudinal modes become strongly coupled at the Vainshtein scale.

Beyond this scale, these modes decouple, restoring the massless theory.

The discontinuity in the massless limit is a perturbative artifact.

Abstract

We study the massive Yang-Mills theory in which the mass term is added by hand. The standard perturbative approach suggests that the massless limit of this theory is not smooth. We confirm that this issue is related to the existence of additional degrees of freedom, which are absent in the massless theory. Nevertheless, we show that the longitudinal modes become strongly coupled at the Vainshtein scale, which coincides with the scale of the unitarity violation. Beyond this scale, they decouple from the remaining degrees of freedom, and the massless theory is restored up to small corrections. From here, it follows that the apparent discontinuity in the massless limit is only an artefact of the perturbation theory. The massless limit of massive Yang-Mills theory is smooth, as originally proposed by A. I. Vainshtein and I. B. Khriplovich.