Dalitz decays of vector heavy quarkonia into $χ_{QJ}(1P)$ in the Bethe-Salpeter approach

Abstract

We systematically investigate the Dalitz decays of vector heavy quarkonia into $χ_{QJ}(1P)\ell^+\ell^-$ ($Q=c,b$; $J=0,1,2$; $\ell=e,μ$) within the instantaneous Bethe--Salpeter framework. The study covers $ψ(2S)$, $ψ(1D)$, $Υ(2S)$, and the so-far unobserved $Υ(1D)$ states. For $ψ(2S)$ electron channels, our predictions are in excellent agreement with BESIII data. We further provide the first relativistic predictions for $ψ(1D)$ decays, with branching ratios for several electron channels reaching the $10^{-5}$ level, which is accessible at current BESIII statistics. For bottomonium, $Υ(2S)\toχ_{bJ}e^+e^-$ decays yield branching fractions of $\mathcal{O}(10^{-4})$, suggesting potential observability at Belle~II. Muonic channels are also discussed, with kinematic constraints carefully addressed. Our results establish a coherent theoretical basis for future experimental searches for heavy quarkonium Dalitz decays.