An Indirect Model-Dependent Probe of the Higgs Self-Coupling

The Higgs associated production cross section at an $e^+ e^-$ collider is indirectly sensitive to the Higgs self-coupling, $h^3$, at next-to-leading order (NLO). Utilizing this, a new indirect method is proposed for constraining deviations in the self-coupling below the di-Higgs production threshold in certain models. Although this indirect constraint is model-dependent, making it valid only under specific assumptions, meaningful indirect constraints on the self-coupling may be realized. Specific realistic scenarios where the indirect constraint applies are discussed and in particular it is shown that in the well-motivated class of two Higgs-doublet models there exist regions of parameter space in which the NLO effects from a modified self-coupling dominate over the LO modifications, demonstrating a concrete scenario in which large modifications of the Higgs self-coupling may be indirectly constrained using the proposed method. Other models, such as strongly coupled scenarios, are also discussed. The indirect method would give valuable constraints on deviations in the Higgs self-coupling, and would be complementary to the direct measurements possible with di-Higgs production at other colliders, providing precious additional information in the effort to unravel the properties of the Higgs boson.