Positivity bounds at one-loop level: the Higgs sector

TL;DR

This paper extends the convex cone method to one-loop level in the Higgs sector, deriving new positivity bounds for four-Higgs scattering in the Standard Model effective field theory, and explores their validity and renormalization group effects.

Contribution

It introduces one-loop level positivity bounds in the Higgs sector using an extended convex cone method, applicable to the Standard Model effective field theory.

Findings

New positivity bounds at one-loop level for four-Higgs scattering.

Validation of bounds through specific ultraviolet models.

Renormalization group analysis showing bounds hold across scales.

Abstract

In this paper, we promote the convex cone method of positive bounds from tree level to loop level. This method is general and can be applied to obtain leading $s^2$ positivity bounds on the forward scattering process in the standard model effective field theory. To obtain the loop level bounds, the original tree level bounds are modified by loop corrections, which involve low dimensional coefficients. New positivity bounds being valid at one loop level on the four-Higgs scattering have been provided. We study some specific ultraviolet models to check the validity of the new bounds. In addition, the renormalisation group effect on positivity is explored. We point out that as long as the new bounds are satisfied at the cutoff scale $\Lambda$, they will also be satisfied at all scales.