Exclusive rare Higgs decays into lepton pair and light mesons

Exclusive rare Higgs decays into lepton pair plus one light hadron, such as $h\to \rho^0(\omega)\ell\bar{\ell}$, $h\to \pi^0\ell\bar{\ell}$, $h\to \pi^+ (K^+)\ell^-\bar{\nu}_\ell$, and $h\to \rho^+(K^{*+})\ell^-\bar{\nu}_\ell$, have been explored in the standard model. Decay amplitudes are dominantly from the Higgs couplings to gauge bosons and to charged leptons, and their branching ratios are predicted in the range of $10^{-8}\sim 10^{-5}$. We have also analyzed the differential dilepton invariant mass and angular distributions of $h\to \rho^0 \ell^+\ell^-$ decays. It will be challenging to search for these rare processes. Nevertheless, experimental studies of them, in particular, $h\to \rho^0\ell^+\ell^-$ with $\ell=e,\mu$, might be interesting both to help deepen our understanding of the standard model and to probe new physics beyond the standard model in the future high-precision experiments.