Accidental Suppression of Wilson Coefficients in Higgs Coupling

Higgs couplings are essential probes for physics beyond the Standard Model (BSM) since they can be modified by new physics, such as through the Higgs portal interaction $\mathrm{\mid }H{\mathrm{\mid }}^2\mathcal{O}$. These modifications influence Higgs interactions via dimension-6 operators of the form ${\left(\mathrm{\partial }\mathrm{\mid }H{\mathrm{\mid }}^2\right)}^2$ and $\mathrm{\mid }H{\mathrm{\mid }}^6$, which are generally expected to be of comparable size. This paper discusses a phenomenon of accidental suppression, where the $\mathrm{\mid }H{\mathrm{\mid }}^6$ coupling is significantly smaller than ${\left(\mathrm{\partial }\mathrm{\mid }H{\mathrm{\mid }}^2\right)}^2$. This suppression, arising from the truncation of the tree-level effective potential, lacks a clear symmetry explanation but persists in portal models. This paper aims to inspire further studies on additional instances of accidental suppression without symmetry explanations or a general framework to characterize such suppression. We also discuss constraints, at the HL-LHC and future colliders, on the Wilson coefficients of the two dimension-6 operators for various benchmark scenarios of the concrete model.