Rare Radiative Decays of Z boson into S- and P-wave Charmonium within the Bethe-Salpeter Model

Abstract

We employ the Bethe-Salpeter (BS) model to investigate radiative decays of the Z boson into charmonium. Within the instantaneous approximation of the BS equation, we analyze the relevant decay channels for S-wave charmonium states ($\psi (nS)$, ${\eta }_c(nS)$, $n=1,2,3$) and P-wave charmonium states (${\chi }_{c0}(mP)$, ${\chi }_{c1}(mP)$, $h_c(mP)$, $m=1,2$). We compute all branching fractions using leading-order Feynman diagrams. For the $J/\psi$ channel, our BS calculations suggest that prior theoretical results were likely underestimated, making our prediction more promising for future experimental measurements.

29 pages, 6 figures, 3 tables