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

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Abstract
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 〈q¯γμDνq〉N (q=ud) (twist-2 nucleon matrix element) for aρ,ω and ms〈s¯s〉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 (dilute nucleon-gas approximation). The origin of the discrepancy with Hatsuda-Lee was clarified.