Pion-nucleon and kaon-nucleon scattering lengths in QCD sum rules

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 σ 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 Λ(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 σ 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 Λ(1405). © 1996 The American Physical Society.