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 $a_{\rho ,\omega ,\varphi }$. We found that the crucial matrix elements are $⟨\bar{q}{\gamma }_{\mu }{D}_{\nu }q{⟩}_N$ ($q=u,d$) (twist-2 nucleon matrix element) for $a_{\rho ,\omega }$ and $m_s⟨\bar{s}s{⟩}_N$ for $a_{\varphi }$, and obtained $a_{\rho }=0.14\pm 0.07$ fm, $a_{\omega }=0.11\pm 0.06$ fm and $a_{\varphi }=0.035\pm 0.020$ fm. These small numbers originate from a common factor $1/(m_N+m_{\rho ,\omega ,\varphi })$. Our result suggests a slight increase ($<60$ MeV for $\rho$, $\omega$, and $<15$ MeV for $\varphi$) 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.

Comments: 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