CP violating hW+W− coupling in the Standard Model and beyond

Inspired by the recent development in determining the property of the observed Higgs boson, we explore the CP-violating (CPV) $$ -{c}_{\mathrm{CPV}}{hW}^{+\mu \nu}{\tilde{W}}_{\mu \nu}^{-}/\upsilon $$ − c CPV hW + μν W ˜ μν − / υ coupling in the Standard Model (SM) and beyond, where W±μν and $$ {\tilde{W}}^{\pm \mu \nu} $$ W ˜ ± μν denote the W-boson field strength and its dual. To begin with, we show that the leading-order SM contribution to this CPV vertex appears at two-loop level. By summing over the quark flavor indices in the two loop integrals analytically, we can estimate the order of the corresponding Wilson coefficient to be $$ {c}_{\mathrm{CPV}}^{\mathrm{SM}}\sim \mathcal{O}\left({10}^{-23}\right) $$ c CPV SM ∼ O 10 − 23 , which is obviously too small to be probed at the LHC and planned future colliders. Then we investigate this CPV hW+W− interaction in two Beyond the Standard Model benchmark models: the left-right model and the complex 2-Higgs doublet model (C2HDM). Unlike what happens for the SM, the dominant contributions in both models arise at the one-loop level, and the corresponding Wilson coefficient can be as large as of $$ \mathcal{O} $$ O (10−9) in the former model and of $$ \mathcal{O} $$ O (10−3) for the latter. In light of such a large CPV effect in the hW+W− coupling, we also give the formulae for the leading one-loop contribution to the related CPV hZZ effective operator in the complex 2-Higgs doublet model. The order of magnitude of the Wilson coefficients in the C2HDM may be within reach of the high-luminosity LHC or planned future colliders.