Hidden charmonium decays of $$\psi (nS)$$ through charmed meson loops

Abstract

AbstractWe calculated transitions of the higher radial excited charmonia $$ \psi (nS) ~ ( n=3,4,5 )$$ ψ ( n S ) ( n = 3 , 4 , 5 ) to the orbital excited charmonium $$ h_c(1P) $$ h c ( 1 P ) with emission of one pion or eta meson. In calculations, the intermediate S- and P-wave charmed meson loops were considered in terms of the nonrelativistic effective field theory. The results indicate that the transitions of interest are dominated by the loops involving the $$ s_l^P=(1/2)^+ $$ s l P = ( 1 / 2 ) + charmed mesons, whereas the $$ s_l^P=(1/2)^- $$ s l P = ( 1 / 2 ) - charmed meson loops are of minor contributions. The partial decay widths of $$ \psi (nS) \rightarrow h_c \pi ^0 $$ ψ ( n S ) → h c π 0 are of the order of 0.01–1 keV. For the case of $$ \psi (nS) \rightarrow h_c \eta $$ ψ ( n S ) → h c η , the partial decay widths are from 0.1 to 100 keV, implying the branching ratios from $$ 10^{-5} $$ 10 - 5 to $$ 10^{-3} $$ 10 - 3 . Moreover, the partial decay widths for $$ \psi (nS) \rightarrow h_c \eta $$ ψ ( n S ) → h c η are found to decrease as the $$ \eta $$ η -$$ \eta ' $$ η ′ mixing angle increases. It is hoped that the present calculated results would be observed in the future experiments.