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Axial vector coupling renormalization and the meson baryon scattering lengths

Aug, 1966
11 pages
Published in:
  • Nuovo Cim.A 46 (1966) 707-717
DOI:
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Abstract: (Springer)
Assuming that the current algebra of Gell-Mann and the PCAC (partially conserved axial-vector current) are valid approximations, and that aspecific form of the LSZ reduction formula for pion-nucleon scattering amplitude has a small variation for the change of pion 4-momentumkμ from (0, 0, 0, iμπ) tokμ=0, we derive two simple relations between the axial-vector coupling constant renormalizationgA and the pion-nucleon scattering lengths. (Equations (7) and (8) in the text.) Both are satisfied quite well by the experimental values, and are shown to be intimately related with the Adler-Weisberger relation and the consistency condition of Adler. In a similar way, the scattering lengths of pion-baryon, pion-kaon and kaon-nucleon systems are predicted. The assumption of the generalized form of PCAC in theSU3 context leads to the prediction of the meson-baryon scattering lengths. They are identical to those which are calculated by the model of the vector-meson exchange with the universalF-type coupling.
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