Constraining the Higgs self couplings at $e^+e^-$ colliders

TL;DR

This paper investigates how future electron-positron colliders can measure deviations in the Higgs potential, including cubic and quartic self-couplings, using effective field theory and various Higgs production processes.

Contribution

It provides a comprehensive analysis of Higgs self-coupling sensitivities at future colliders, considering higher-dimensional operators and combining multiple Higgs production channels.

Findings

Single Higgs measurements can determine cubic coupling deviations with ~10% accuracy.

Combining double and triple Higgs production improves constraints on self-couplings.

Higher energy colliders can set initial bounds on dimension-eight operator effects.

Abstract

We study the sensitivity to the shape of the Higgs potential of single, double, and triple Higgs production at future $e^+e^-$ colliders. Physics beyond the Standard Model is parameterised through the inclusion of higher-dimensional operators $(\Phi^\dagger \Phi- v^2/2)^n/\Lambda^{(2n-4)}$ with $n=3,4$, which allows a consistent treatment of independent deviations of the cubic and quartic self couplings beyond the tree level. We calculate the effects induced by a modified potential up to one loop in single and double Higgs production and at the tree level in triple Higgs production, for both $Z$ boson associated and $W$ boson fusion production mechanisms. We consider two different scenarios. First, the dimension six operator provides the dominant contribution (as expected, for instance, in a linear effective-field-theory(EFT)); we find in this case that the corresponding Wilson coefficient can be determined at $\mathcal{O}(10\%)$ accuracy by just combining accurate measurements of single Higgs cross sections at $\sqrt{\hat s}=$240-250 GeV and double Higgs production in $W$ boson fusion at higher energies. Second, both operators of dimension six and eight can give effects of similar order, i.e., independent quartic self coupling deviations are present. Constraints on Wilson coefficients can be best tested by combining measurements from single, double and triple Higgs production. Given that the sensitivity of single Higgs production to the dimension eight operator is presently unknown, we consider double and triple Higgs production and show that combining their information colliders at higher energies will provide first coarse constraints on the corresponding Wilson coefficient.