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

Abstract

We systematically investigate the Dalitz decays of vector heavy quarkonia into ${\chi }_{QJ}(1P){\ell }^{+}{\ell }^{-}$ ($Q=c,b$; $J=0,1,2$; $\ell =e,\mu$) within the instantaneous Bethe--Salpeter framework. The study covers $\psi (2S)$, $\psi (1D)$, ${\rm Y}(2S)$, and the so-far unobserved ${\rm Y}(1D)$ states. For $\psi (2S)$ electron channels, our predictions are in excellent agreement with BESIII data. We further provide the first relativistic predictions for $\psi (1D)$ decays, with branching ratios for several electron channels reaching the $10^{-5}$ level, which is accessible at current BESIII statistics. For bottomonium, ${\rm Y}(2S)\to {\chi }_{bJ}{e}^{+}{e}^{-}$ 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.

22 pages, 5 figures