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

Abstract

The QCD sum rule method is applied to derive a formula for the rho, omega, phi meson-nucleon spin-isospin-averaged scattering lengths $a_{ρ,ω,ϕ}$. We found that the crucial matrix elements are $\langle\bar{q}γ_μD_νq\rangle_N$ ($q=u,d$) (twist-2 nucleon matrix element) for $a_{ρ,ω}$ and $m_s\langle\bar{s}s\rangle_N$ for $a_ϕ$, and obtained $a_ρ=0.14\pm 0.07$ fm, $a_ω=0.11\pm 0.06$ fm and $a_ϕ=0.035\pm 0.020$ 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 $ρ$, $ω$, and $<15$ MeV for $ϕ$) 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.