Determination of the Pion-Nucleon Coupling Constant from Photoproduction Angular Distribution

Abstract

The pion-nucleon coupling constant is determined from the pion photoproduction angular distribution. The method is based upon a certain conjecture concerning the analyticity of the photoproduction amplitude, and does not depend on the validity of any specific theory of photoproduction. It consists of an extrapolation of the angular distribution at any given fixed energy to $cos\ensuremath{\theta}={{V}_{\ensuremath{\pi}}}^{\ensuremath{-}1}$, where ${V}_{\ensuremath{\pi}}$ is the pion velocity divided by the velocity of light. The amplitude at this nonphysical angle has a pole, and the pion-nucleon coupling constant is simply related to the residue of the amplitude. The quartic representation of photoproduction angular distributions is used as the functional form of the extrapolating curve. The most important feature of the new method is in the fact that it measures, at least in principle, the pion-nucleon coupling constant at any given fixed energy, while previous determinations in general measure the coupling constant in the low-energy limit, or require assumptions concerning the behavior of the cross section at all energies.In addition, the new method does not depend on the assumption of charge independence, and in fact measures explicitly the interaction of positive pions with nucleons. The scheme cannot be used for photoproduction of neutral pions. The method is applied to available data at 230, 260, 265, and 290 Mev photon energy in the laboratory system, and an over-all value of ${f}^{2}=0.064\ifmmode\pm\else\textpm\fi{}0.041$ is obtained. In view of the large error, a detailed discussion is given of possible improvements in experiments which could give a more accurate value. Also discussed is the sensitivity of the value of the coupling constant to various features of the experiment, such as the energy of the photons, the relative importance of the various angles, the relative importance of the relative and absolute normalizations, and the statistical errors on the individual pieces of data. Finally, numerical illustrations are given of the accuracy obtainable for certain given conditions on the factors listed above.