CPasymmetry in charged Higgs decays to chargino-neutralino pairs

Abstract

We analyze the charge-parity ($CP$) asymmetry in the charged Higgs boson decays to chargino-neutralino pairs, ${H}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}{\ensuremath{\chi}}_{i}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\chi}}_{j}^{0}$, $i=1$, 2, $j=1,\dots{},4$. We show first that these modes have a large branching ratio for ${m}_{{H}^{\ifmmode\pm\else\textpm\fi{}}}\ensuremath{\gtrsim}600\text{ }\text{ }\mathrm{GeV}$. We use Cutkosky rules to obtain the analytical formulas needed for the evaluation of the asymmetry under consideration. We then calculate the $CP$ asymmetry in chargino-neutralino decays by including supersymmetric mass bounds, as well as constraints from $b\ensuremath{\rightarrow}s\ensuremath{\gamma}$, $(g\ensuremath{-}2{)}_{\ensuremath{\mu}}$, $\ensuremath{\Delta}\ensuremath{\rho}$ and electric dipole moments. Finally, we discuss observability of the asymmetry at the LHC by calculating the number of required charged Higgs events to observe the asymmetry for each decay channel. We show that the inclusion of constraints considerably reduces the projected $CP$ asymmetry, and that the optimal channel for observing the asymmetry is ${H}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}{\ensuremath{\chi}}_{1}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\chi}}_{2}^{0}$.