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 aρ,ω,φ. We found that the crucial matrix elements are left-angle bar qγμDνq right-angle N (q=ud) (twist-2 nucleon matrix element) for aρ,ω and ms left-angle bar ss right-angle N for aφ, and obtained aρ=0.14±0.07 fm, aω=0.11±0.06 fm, and aφ=0.035±0.020 fm. These small numbers originate from a common factor 1/(mN+mρ,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