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: $i{\gamma }_5$, $i{\gamma }_5\text{fslash}p$, 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 $i{\gamma }_5\text{fslash}p$ 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.

Comments: To be published in Phys.Rev.C ; 21 pages,8 figures, revtex ; references are added