Vector- and tensor-meson resonance contributions to ${\chi }_{cJ}\to PPV$ decays

Abstract

Light vector- and tensor-meson resonance contributions to the three-body decays ${\chi }_{cJ}\to P_1{P}_{2}V$ are studied in a quasi-two-body framework combined with SU(3) flavor relations for the two-body subprocesses, covering both the ${\chi }_{c0,1,2}\to VV\to P_1{P}_{2}V$ and ${\chi }_{c1,2}\to TP\to P_1{P}_{2}V$. Both the narrow-width approximation (NWA) and the finite-width effects (FWE) treatment are considered, the latter being essential for tensor subdecays that are kinematically closed at the nominal mass and contribute only through the high-mass tail of the resonance. The predicted resonance bands span several orders of magnitude, with the largest ones in the $\pi \pi \rho$, $\pi K{\bar{K}}^{\ast }$, and $K\bar{K}\varphi$ final states, whereas the $K\bar{K}\omega$ and ${\eta }^{\prime }K{K}^{\ast }$ channels are dominated by the tensor band and thus provide a clean window onto the $T\to PV$ tensor resonances. The band-by-band strengths and their ordering are intended as priors and channel priorities for future invariant-mass and amplitude analyses, and can be compared with the measured totals of several channels.

arXiv comment16 pages,0 figures,7 tables