Gravity and the Higgs boson mass

TL;DR

This paper shows that when considering the path integral measure and gravitational background, the Higgs boson mass's dependence on high-energy cutoff is only logarithmic, challenging the usual quadratic sensitivity in quantum field theory.

Contribution

It demonstrates that the scalar mass's sensitivity to the UV cutoff is milder than previously thought, without requiring supersymmetry or special regularization schemes.

Findings

Mass squared shows only logarithmic sensitivity to the cutoff.

Results obtained without supersymmetry or special regularization.

Implications for the Higgs mass hierarchy problem.

Abstract

According to usual calculations in quantum field theory, both in flat and curved spacetime, the mass $m^2$ of a scalar particle is quadratically sensitive to the ultimate scale of the theory, the UV physical cutoff $\Lambda$. In the present work, paying attention to the path integral measure and to the way $\Lambda$ is introduced, we calculate the one-loop effective action $\Gamma^{1l}$ for a scalar field on a non-trivial gravitational background. We find that $m^2$ presents only a (mild) logarithmic sensitivity to $\Lambda$. This is obtained without resorting to a supersymmetric embedding of the theory, nor to regularization schemes (as dimensional or zeta-function regularization) where power-like divergences are absent by construction. In view of the results of the present work, we finally speculate on the way the Minkowski limit should be approached.