rho, omega, phi-Nucleon Scattering Lengths from QCD Sum Rules

The QCD sum rule method is applied to derive a formula for the rho, omega, phi meson-nucleon spin-isospin-averaged scattering lengths $a_{\rho ,\omega ,\varphi }$. We found that the crucial matrix elements are $⟨\bar{q}{\gamma }_{\mu }{D}_{\nu }q{⟩}_N$ ($q=u,d$) (twist-2 nucleon matrix element) for $a_{\rho ,\omega }$ and $m_s⟨\bar{s}s{⟩}_N$ for $a_{\varphi }$, and obtained $a_{\rho }=0.14\pm 0.07$ fm, $a_{\omega }=0.11\pm 0.06$ fm and $a_\phi =0.035\pm 0.020$fm\mathrm{.}Thesesmallnumbersoriginatefromacommonfactor$1/(m_N+m_{\rho,\omega,\phi})$\mathrm{.}Ourresultsuggestsaslightincrease($< 60$MeVfor$\rho$,$\omega$,and$<15$MeVfor$\phi$) of the effective mass of these vector mesons in the nuclear matter (in the {\it dilute} nucleon gas approximation). The origin of the discrepancy with the previous study was clarified.