Meaning of the field dependence of the renormalization scale in Higgs inflation

TL;DR

This paper investigates how the choice of renormalization scale affects the Higgs effective potential in Higgs inflation, showing that prescription differences can be absorbed into potential redefinitions and proposing a mechanism to achieve a flat potential.

Contribution

It clarifies the prescription dependence of the Higgs effective potential and introduces a method to obtain a flat potential by controlling the running of the quartic coupling.

Findings

Effective action is identical in Jordan and Einstein frames when measure change is properly accounted for.

Differences between prescriptions are due to counter terms canceling divergences and can be absorbed into potential choices.

A mechanism is proposed to freeze the quartic coupling's running, aiding in flat potential realization.

Abstract

We consider the prescription dependence of the Higgs effective potential under the presence of general nonminimal couplings. We evaluate the fermion loop correction to the effective action in a simplified Higgs-Yukawa model whose path integral measure takes simple form either in the Jordan or Einstein frame. The resultant effective action becomes identical in both cases when we properly take into account the quartically divergent term coming from the change of measure. Working in the counterterm formalism, we clarify that the difference between the prescriptions I and II comes from the counter term to cancel the logarithmic divergence. This difference can be absorbed into the choice of tree-level potential from the infinitely many possibilities, including all the higher-dimensional terms. We also present another mechanism to obtain a flat potential by freezing the running of the effective quartic coupling for large field values, using the nonminimal coupling in the gauge kinetic function.