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 OPE give rise to the Tomozawa-Weinberg and sigma terms, respectively. We also show that in the kaon-nucleon system the Λ(1405) contribution has to be subtracted from the OPE side in order to obtain the scattering length. The odd components of the T-matrices are in agreement with the experimental values not only in the pion-nucleon channel but also in the kaon-nucleon channel after the Λ(1405) contribution subtracted. The even components disagree with the experimental values in the pion-nucleon channel, which is similar to the situation in the PCAC-plus-current-algebra approach at the Weinberg point. We speculate that this discrepancy should be explained by the continuum contribution in the spectral function above the pion-nucleon threshold. (author)