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.

Latex file. 12 pages. One figure not modified. More expanded discussion which clarify the origin of the discrepancy with Hatsuda-Lee is added. Phys.Rev.C in press