Study on the rare decays of $Y(4630)$ induced by final state interactions

A resonance $Y(4630)$ at the invariant mass spectrum of $\Lambda_c \bar\Lambda_c$ observed by the Belle Collaboration triggers a hot discussion about its inner structure. Since it preferably decays into two charmed baryons $\Lambda_c\bar\Lambda_c$, it is tempted to conjecture it as a tetraquark. Because the dominant decay portal $Y(4630)\to \Lambda_c \bar\Lambda_c$ is close to the energy threshold, the final state interactions may be significant and result in other baryonic and/or mesonic final states whose branching fractions are sizable to be measured in the future experiments. In this work we calculate the branching ratios of the $Y(4630)$ decays into $p\bar p$, $D^{(*)+} D^{(*)-}$, $\pi^+\pi^-$, and $K^+K^-$ which are induced by the $\Lambda_c \bar\Lambda_c$ re-scattering. The resultant decay patterns will be tested by the future experiments and the consistency degree with the data composes a valuable probe for the tetraquark conjecture.