ρ, ω, and φ meson-nucleon scattering lengths from QCD sum rules

The QCD sum rule method is applied to derive a formula for the {ρ}, {ω}, and {φ} meson-nucleon spin-isospin--averaged scattering lengths a_ρ,ω,φ. We found that the crucial matrix elements are 〈q{}γ_μ{D}_{{ν}}q{〉}N$ (q=ud) (twist-2 nucleon matrix element) for ${a}_{{{ρ}},{{ω}}}$ and ${m}ₛ〈ss{〉}N$ for ${a}_{{{φ}}}$, and obtained ${a}_{{{ρ}}}=0.14±0.07 fm,{a}_{{{ω}}}=0.11±0.06 fm, and{a}_{{{φ}}}=0.035±0.020 fm. These small numbers originate from a common factor 1/({m}N$+${m}_{{{ρ}},{{ω}},{{φ}}}$). Our result suggests a slight increase (60 MeV for {ρ} and {ω}, and 15 MeV for {φ}) of the effective mass of these vector mesons in nuclear matter (in the dilute nucleon-gas approximation). The origin of the discrepancy with Hatsuda-Lee was clarified.