Extremal Higgs couplings

TL;DR

This paper examines the validity of bounding Wilson coefficients of dimension-six operators in Higgs physics, introducing a well-defined observable, $c_H$, that provides a two-sided bound and clarifies its relation to the operator $O_H$.

Contribution

It establishes that the observable $c_H$ is well-defined, non-dispersive, and satisfies a two-sided bound, linking it to the dimension-six operator $O_H$ in Higgs scattering.

Findings

$c_H$ is a well-defined, non-dispersive observable.

A two-sided bound on $c_H$ is established.

Conditions are identified when the bound on $c_H$ equates to a bound on $O_H$.

Abstract

We critically assess to what extent it makes sense to bound the Wilson coefficients of dimension-six operators. In the context of Higgs physics, we establish that a closely related observable, $c_H$, is well-defined and satisfies a two-sided bound. $c_H$ is derived from the low momentum expansion of the scattering amplitude, or the derivative of the amplitude at the origin with respect to the Mandelstam variable $s$, expressed as $M(H_iH_i\rightarrow H_jH_j)=c_H s +O(g_\text{SM}, s^{-2})$ where $g_\text{SM}$ represents all Standard Model couplings. This observable is non-dispersive and, as a result, not sign-definite. We also determine the conditions under which the bound on $c_H$ is equivalent to a bound on the dimension-six operator $O_H=\partial| H|^2 \partial |H|^2$.