On the Observables of Renormalizable Interactions

TL;DR

This paper demonstrates that quantum corrections to physical observables in renormalizable theories are finite, scheme-independent, and insensitive to ultraviolet physics, with explicit calculations for QED and the Higgs mass correction.

Contribution

It shows that observable quantum corrections are scheme-independent and finite, challenging the view that quadratic divergences imply physical effects.

Findings

Quantum corrections to observables are scheme-independent.

Quadratic divergences cancel out in physical quantities.

Heavy fields have suppressed effects on scalar mass corrections.

Abstract

We reconsider the renormalization of scalar mass and point out that the quantum correction to the physical observable, as opposed to the bare parameter, of a renormalizable operator, is technically insensitive to ultraviolet physics and independent of the regularization scheme. It is expressed as the difference in the same quantities at different energy scales, maintaining the same asymptotics. Thus, any sensible regularization cancels out the divergences, including the quadratic ones, and yields the same finite corrections. To this end, we first show that the vacuum polarization of quantum electrodynamics is independent of the regularization scheme and a gauge-dependent quadratic divergence is canceled in the observable. We then calculate the quantum correction to the Higgs mass squared by the top-quark loop. It is again finite and regularization-scheme independent. For large external momentum, the correction of the pole mass-squared is dominated by power running, resulting in an order of 1 percent correction. In particular, the effect of heavy fields on the scalar mass correction is suppressed.