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

The decay widths of $\Upsilon(nS)$ $\rightarrow$ $\bar{d}^{\ast}(2380)+X$ 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 $\Upsilon(nS)$. 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 $\Upsilon$ is governed by the quark-meson interaction where the coupling constant is determined by fitting the observed widths of $\Upsilon(nS)$ $\rightarrow$ $\bar{d}+X$. The numerical results show that the decay widths of $\Upsilon(nS)$ $\rightarrow$ $\bar{d}^{\ast}+X$ are about $2 - 10$ times smaller than that of $\bar{d}+X$. The calculated momentum of $\bar{d^*}$ 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.