Regularization Dependence of Quadratic Divergence Cancellations, VPI-IHEP-92/10

TL;DR

This paper examines how the cancellation of quadratic divergences in quantum field theories depends on the choice of regularization method, showing that previous results are regulator-dependent and not universally valid.

Contribution

It demonstrates that quadratic divergence cancellations are strongly dependent on the regularization scheme, challenging previous claims of scale-independent cancellations.

Findings

Quadratic divergence cancellations depend on the regulator used.

Certain previously claimed cancellations do not hold under nonlocal regulators.

No specific top and Higgs mass values lead to divergence cancellation independent of scale.

Abstract

Certain results related to the cancellation of quadratic divergences, which had been obtained using dimensional reduction, are reconsidered using a nonlocal regulator. The results obtained are shown to depend strongly on the regulator. Specifically, it is shown that a certain result of Al-sarhi, Jack, and Jones no longer holds, even if a nontrivial measure factor is used; also that there are no values of the top and Higgs mass for which the one-loop quadratic divergence in the standard model cancels independently of the renormalization scale, whether or not strong interaction effects are ignored.