CP Violating $hW^+W^-$ Coupling in the Standard Model and Beyond

TL;DR

This paper investigates the CP-violating $hW^+W^-$ coupling in the Standard Model and beyond, finding it negligible in the SM but potentially detectable in certain BSM models like the C2HDM at future colliders.

Contribution

It provides the first detailed estimate of the CPV $hW^+W^-$ coupling in the SM and explores its enhancement in BSM models, with explicit calculations of Wilson coefficients.

Findings

SM contribution to CPV coupling is extremely small (~10^{-23})

BSM models like C2HDM can produce larger CPV effects (~10^{-3})

Potential detectability of CPV effects at future colliders in BSM scenarios

Abstract

Inspired by the recent development in determining the property of the observed Higgs boson, we explore the $CP$-violating (CPV) $- c_{\rm CPV} h W^{+\, \mu\nu}\tilde{W}^{-}_{\mu\nu}/v$ coupling in the Standard Model (SM) and beyond, where $W^{\pm \, \mu \nu}$ and $\tilde{W}^{\pm\,\mu\nu}$ 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 $c^{\rm SM}_{\rm CPV} \sim {\cal O}(10^{-23})$, 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 ${\cal O}(10^{-9})$ in the former model and of ${\cal O}(10^{-3})$ 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 C2HDM. The order of magnitude of the Wilson coefficients in the C2HDM may be within reach of the high-luminosity LHC or planned future colliders.