Pion radiative decays of excited hidden-charm pentaquark molecules: from ${\mathrm{\Sigma }}_c^{(\ast )}{\bar{D}}^{(\ast )}(2S)$ molecules to the reported $P_c$ states

The discovery of the hidden-charm pentaquarks $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$ by the LHCb collaboration are very likely to identify as the ${\mathrm{\Sigma }}_c^{(\ast )}{\bar{D}}^{(\ast )}$ molecules. A natural and crucial extension is the existence of excited molecular partners built from a ground-state charmed baryon and a radially excited anti-charmed meson, namely ${\mathrm{\Sigma }}_c^{(\ast )}{\bar{D}}^{(\ast )}(2S)$ molecules. In a framework of chiral quark model, we systematic study pion-emission decays of such excited molecules into the known ground-state $P_c$ molecules. Our results show that the decay widths are sensitive to the spin structures and the coupled-channel interferences, i.e., the ${\mathrm{\Sigma }}_c\bar{D}(2S)\mathrm{/}{\mathrm{\Sigma }}_c{\bar{D}}^{\ast }(2S)\mathrm{/}{\mathrm{\Sigma }}_c^{\ast }{\bar{D}}^{\ast }(2S)[1\mathrm{/}2(1\mathrm{/}{2}^{-})]$ state decays to $P_c(4440)$ with a width of several MeV, while the width to $P_c(4457)$ is suppressed below $0.3$ MeV due to destructive interference. The pion-emission decay can be the key to unveiling the excited molecular spectrum of hidden-charm pentaquarks and provides decisive experimental signatures. We expect the future experiments such as the LHCb and PANDA can verify our predictions.