First characterization of the scattering length distribution of vector meson interaction with deuteron

Abstract: Under the framework of the vector meson dominance model (VMD), the absolute scattering lengths of light vector mesons ($\phi$, $\omega$, and $\rho$) with the deuteron are calculated from the cross sections of vector meson photoproduction off a deuteron. Additionally, a fitting function is used to predict the scattering lengths of the heavy vector mesons $J/\psi$-$d$ and $% \Upsilon$-$d$. Based on these results, the distribution of the scattering lengths $|\alpha_{V d}|$ between vector mesons and the deuteron is presented for the first time and compared with the scattering lengths $|\alpha_{V p}|$ between vector mesons and the proton. It is found that as the mass of the vector meson increases, the scattering lengths $|\alpha_{V d}|$ become closer to $|\alpha_{V p}|$. In addition, the correlation analysis indicates a strong positive relationship between the scattering length and the vector meson radius, with a high correlation coefficient. The implications of results are essential for improving our understanding of the interaction between hadron and nucleus.