Pion-Nucleon and Kaon-Nucleon Scattering Lengths in QCD Sum Rules

Details Pion-Nucleon and Kaon-Nucleon Scattering Lengths in QCD Sum Rules Pion-Nucleon and Kaon-Nucleon Scattering Lengths in QCD Sum Rules

1994-09-13

arxiv.org/abs/nucl-th/9409012v1

Phys.Rev.C53:1927-1935,1996

Physics

Nuclear Physics

Nuclear Theory

14 pages, INS-Rep.-1059, RCNP Preprint 073

Scientific paper

10.1103/PhysRevC.53.1927

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 OPE give rise to the Tomozawa-Weinberg and sigma terms, respectively. We also show that in the kaon-nucleon system the $\Lambda(1405)$ 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 $\Lambda(1405)$ 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.

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