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Under the framework of the vector meson dominance model (VMD), the absolutescattering lengths of light vector mesons ($\phi$, $\omega$, and $\rho$) withthe deuteron are calculated from the cross sections of vector mesonphotoproduction off a deuteron. Additionally, a fitting function is used topredict the scattering lengths of the heavy vector mesons $J/\psi$-$d$ and$\Upsilon$-$d$. Based on these results, the distribution of the scatteringlengths $|\alpha_{V d}|$ between vector mesons and the deuteron is presentedfor 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 thevector meson increases, the scattering lengths $|\alpha_{V d}|$ become closerto $|\alpha_{V p}|$. Finally, a preliminary analysis and interpretation ofthese novel findings are provided based on the hadron size and the embeddednessof mesons in the nucleus.

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