Ultraviolet cutoffs and the photon mass

TL;DR

This paper examines the implications of treating the UV cutoff as a physical scale in quantum field theory, highlighting potential issues like a non-zero photon mass that conflicts with experimental bounds.

Contribution

It demonstrates that a physical UV cutoff at the Planck scale can lead to unacceptable predictions, such as a large photon mass, and discusses methods to restore gauge symmetry.

Findings

A physical UV cutoff can induce a photon mass exceeding experimental limits.

Naive cutoff approaches conflict with gauge invariance and physical observations.

Restoring gauge symmetry may be possible through order-by-order corrections.

Abstract

The momentum UV cutoff in Quantum Field Theory is usually treated as an auxiliary device allowing to obtain finite amplitudes satisfying all physical requirements. It is even absent (not explicit) in the most popular approach - the dimensional regularization. We point out that the momentum cutoff treated as a bona fide physical scale, presumably equal or related to the Planck scale, would lead to unacceptable predictions. One of the dangers is a non-zero mass of the photon. In the naive approach, even with the cutoff equal to the Planck scale, this mass would grossly exceed the existing experimental bounds. We present the actual calculation using a concrete realization of the physical cutoff and speculate about the way to restore gauge symmetry order by order in the inverse powers of the cutoff scale.