QCD sum rules for rho, ω, φ meson-nucleon scattering lengths and the mass shifts in nuclear medium

A new QCD sum rule analysis on the spin-isospin averaged $\rho$, $\omega$ and $\phi$ meson-nucleon scattering lengths is presented. By introducing the constraint relation on the the low energy limit of the vector-current nucleon forward scattering amplitude, we get $a_\rho=-0.47\pm 0.05$ fm, $a_\omega=-0.41\pm 0.05$ fm and $a_\phi=-0.15\pm 0.02$ fm, which suggests that these V-N interactions are attractive. It is also proved that the previous studies on the mass shift of these vector mesons in the nuclear medium are essentially the ones obtained from these scattering lengths in the linear density approximation.