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: $i{\gamma }_5$, $iγ_5\fslash{p}$, 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 $iγ_5\fslash{p}$ 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.

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

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• A projected correlation function approach to the pi NN coupling constant in QCD sum rules
• Eta-nucleon coupling constant in QCD with SU(3) symmetry breaking
• The F/D Ratio and Meson-Baryon Couplings from QCD Sum Rules