Determination of the pion-nucleon coupling constant

A method for determining the pion-nucleon coupling constant $f^2$ by the application of an interior dispersion relation to the $B^{\mathrm{}(+)\mathrm{}}\pi N$ scattering amplitude is presented and its advantages over other dispersion relation techniques are discussed. The method is used to calculate $f^2$ for two sets of phase shifts: CERN 71 of Almehed and Lovelace and a modified version of the Carter, Bugg, and Carter solution, to obtain $f^2=(81.5\mathrm{}\pm 1.5)\times {10}^{-3\mathrm{}}$ and $f^2=(79.5\mathrm{}\pm 1.0)\times {10}^{-3\mathrm{}}$, respectively.