Abstract
The pion-nucleon and kaon-nucleon scattering lengths are studied in the QCD sum rule. We show that the leading and next-to-leading order terms of the operator product expansion (OPE) give rise to the Tomozawa-Weinberg and \ensuremath{\sigma} terms, respectively in the pion-nucleon and kaon-nucleon scattering lengths. We discuss phenomenological contributions which should be added to the experimental scattering lengths to be compared with the theoretical calculation by the OPE: we estimate the \ensuremath{\Lambda}(1405) contribution in the kaon-nucleon channel by using the effective coupling strength determined by the analysis of the scattering data. We also estimate the continuum contribution above the threshold in the pion-nucleon channel by using the nonlinear \ensuremath{\sigma} model. It turns out that the results of the QCD sum rule for the pion-nucleon scattering lengths are consistent with those of the low energy theorem and therefore with experiments and those for the kaon-nucleon scattering lengths differ from the results of naive partial conservation of axial-vector current--plus-current-algebra approach by the contribution from \ensuremath{\Lambda}(1405). \textcopyright{} 1996 The American Physical Society.
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