Radiative Higgs decay to $ψ\left(4230\right)$

Abstract

We calculate the decay rate for the radiative Higgs decay $H \to ψ(4230) + γ$ within and beyond the SM. The vector state $ψ(4230)$ is a candidate exotic tetraquark state and has the quantum numbers $I^G(J^{PC})=0^-(1^{--})$, having a mass $m_{ψ(4230)}=4221.7 \pm 2.5$ MeV and a decay width $Γ_{ψ(4230)}=51 \pm 7$ MeV. We propose a practical parametrization of the so-called {\it direct amplitude}, using the leptonic coupling of the $ψ(4230)$ to estimate the short-distance overlap relevant to the Higgs decay amplitude. We find ${\cal B}_{\rm SM}( H \to ψ(4230) γ)=4.88^{+4.71}_{-4.52}\times 10^{-7}$, where the uncertainties are dominated by the experimental uncertainty in the leptonic decay width of the $ψ(4230)$. The branching ratio increases to about $10^{-6}$ for $y_c=-3 $, where $y_c$ is the Higgs-Yukawa coupling of the charm quark.