Calculation ofgπNS11andgηNS11couplings in QCD sum rules

Abstract

We calculate the coupling constants ${g}_{\ensuremath{\pi}{\mathrm{NS}}_{11}}$ and ${g}_{\ensuremath{\eta}{\mathrm{NS}}_{11}}$ using QCD sum rules in the presence of an external meson field. A covariant derivative is introduced within the ${S}_{11}$ interpolating field so that in the nonrelativistic limit the field dominantly reduces to two quarks in the $s$-wave state and one quark in the $p$-wave state. Our result for the couplings obtained by further making use of the soft-meson theorem qualitatively agrees with its phenomenological value extracted from the ${S}_{11}$(1535) decay width. The prediction for the couplings, however, depends on the value of the quark-gluon condensate $〈\overline{q}{g}_{s}\ensuremath{\sigma}\ensuremath{\cdot}\mathcal{G}q〉,$ which is also important in the calculation of the ${S}_{11}$(1535) mass itself within the sum rule approach.