Low Energy Limits of Photon-Nucleon and Pion-Nucleon Collisions

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Low energy limits of photon-nucleon and pion-nucleon collisions are investigated on the basis of the approximation which neglects higher order terms with respect to the pion-nucleon mass ratio but includes the radiative corrections to an arbitrary order in the coupling constants. It is shown that, near threshold, all the radiative corrections to the processes, π+N→N+2π and γ+N→N+3π, can be concealed into the nucleon mass, the electric charge, the mesic charge and the Matthews' constant renormalized in accordance with the conventional prescription, provided that the renormalized Matthews' constant is of the same order of magnitude as or larger than the renormalized coupling constant for the pion-nucleon interaction (§§3 and 4). It is suggested that these processes may serve the experimental determination of the Matthews' constant and the test of validity of the PS(PS)theory(§5). As preliminaries for these arguments, Thirring's and Kroll and Ruderman's theorems on the low energy Compton scattering and the threshold photomeson production are reviewed, taking accout of those terms which have been omitted in the original works, and effective charges are introduced for pion-nucleon scattering and two-gamma decay of a neutral pion(§2). It is noted that the results are unaffected by virtual processes caused by heavy mesons obeying the "even-odd" rule proposed by Pais(§5).
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