Pertinent Dirac structure for QCD sum rules of meson-baryon coupling constants

Abstract

Using general baryon interpolating fields $J_B$ for $B= N, \Xi, \Sigma, $ without derivative, we study QCD sum rules for meson-baryon couplings and their dependence on Dirac structures for the two-point correlation function with a meson $i\int d^4x e^{iqx} \bra 0|{\rm T}[J_B(x)\bar{J}_B(0)] |{\cal M}(p)\ket$. Three distinct Dirac structures are compared: $i\gamma_5$, $i\gamma_5\fslash{p}$, and $\gamma_5\sigma_{\mu\nu}q^\mu p^\nu$ structures. From the dependence of the OPE on general baryon interpolating fields, we propose criteria for choosing an appropriate Dirac structure for the coupling sum rules. The $\gamma_5\sigma_{\mu\nu}q^\mu p^\nu$ sum rules satisfy the criteria while the $i\gamma_5$ sum rules beyond the chiral limit do not. For the $i\gamma_5\fslash{p}$ sum rules, the large continuum contributions prohibit reliable prediction for the couplings. Thus, the $\gamma_5\sigma_{\mu\nu}q^\mu p^\nu$ structure seems pertinent for realistic predictions. In the SU(3) limit, we identify the OPE terms responsible for the $F/D$ ratio. We then study the dependence of the ratio on the baryon interpolating fields. We conclude the ratio $F/D \sim 0.6-0.8$ for appropriate choice of the interpolating fields.