The $F/D$ ratio and meson-baryon couplings from QCD sum rules-II

Abstract

Using QCD sum rules, we compute the diagonal meson-baryon couplings, $\pi NN$, $\eta NN$, $\pi \Xi \Xi$, $\eta \Xi \Xi$, $\pi \Sigma \Sigma$ and $\eta \Sigma \Sigma$, from the baryon-baryon correlation function with a meson, $i\int d^{4}x{e}^{iq\cdot x}<0|T{J}_B(x){\bar{J}}_B(0)|M(p)>$. The calculations are performed to leading order in $p_{\mu }$ by considering the two separate Dirac structures, $i{\gamma }_5{\gamma }_{\mu }{p}^{\mu }$ and ${\gamma }_5{\sigma }_{\mu \nu }{q}^{\mu }{p}^{\nu }$ separately. We first improve the previous sum rule calculations on these Dirac structures for the $\pi NN$ coupling by including three-particle pion wave functions of twist 4 and then extend the formalism to calculate the other couplings, $\eta NN$, $\pi \Xi \Xi$, $\eta \Xi \Xi$, $\pi \Sigma \Sigma$ and $\eta \Sigma \Sigma$. In the SU(3) symmetric limit, we identify the terms responsible for the $F/D$ ratio in the OPE by matching the obtained couplings with their SU(3) relations. Depending on the Dirac structure considered, we find different identifications for the $F/D$ ratio. The couplings including the SU(3) breaking effects are also discussed within our approach.

Comments: 28 pages including 4 figures. slightly revised. accepted for publication in Nuclear Physics A