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

Abstract

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 $p\bar{p}$, $D^{(\ast )+}{D}^{(\ast )-}$, ${\pi }^{+}{\pi }^{-}$, 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.

Comments: 6 pages, 2 figures, and 1 table. More discussions added and typos corrected. Accepted by PRD