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, $πNN$, $ηNN$, $πΞΞ$, $ηΞΞ$, $πΣΣ$ and $ηΣΣ$, from the baryon-baryon correlation function with a meson, $i\int d^4x e^{iq\cdot x} < 0| T J_B(x) {\bar J}_B(0)|M(p)>$. The calculations are performed to leading order in $p_μ$ by considering the two separate Dirac structures, $i γ_5 γ_μp^μ$ and $γ_5 σ_{μν} {q^μp^ν}$ separately. We first improve the previous sum rule calculations on these Dirac structures for the $πNN$ coupling by including three-particle pion wave functions of twist 4 and then extend the formalism to calculate the other couplings, $ηNN$, $πΞΞ$, $ηΞΞ$, $πΣΣ$ and $ηΣΣ$. 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.