Phenomenological study on the decay widths of ${\rm Y}(nS)\to {\bar{d}}^{\ast }(2380)+X$

Abstract

The decay widths of ${\rm Y}(nS)$ $\to$ ${\bar{d}}^{\ast }(2380)+X$ with $n=1,2,3$ are studied in a phenomenological way. With the help of crossing symmetry, the decay widths are obtained by investigating the imaginary part of the forward scattering amplitudes between $d^{\ast }$ and ${\rm Y}(nS)$. The wave functions of $d^{\ast }$ and deuteron obtained in previous studies are used for calculating the amplitude. The interaction between $d^{\ast }$ ($d$) and ${\rm Y}$ is governed by the quark-meson interaction where the coupling constant is determined by fitting the observed widths of ${\rm Y}(nS)$ $\to$ $\bar{d}+X$. The numerical results show that the decay widths of ${\rm Y}(nS)$ $\to$ ${\bar{d}}^{\ast }+X$ are about $2-10$ times smaller than that of $\bar{d}+X$. The calculated momentum of $\overline{d^{\ast }}$ is in the range $0.3-0.8$ GeV. Therefore, it is very likely that one can find ${\bar{d}}^{\ast }(2380)$ in these semi-inclusive decay processes.