Production of Charged  -Meson by  -Ray: Higher Order Corrections

The effective cross section for the production of charged π-meson by γ-ray is calculated by the Lorentz-covariant perturbation method, including the effects of order e2f4 (e2g4). The pseudoscalar meson field with both pseudoscalar and pseudovector coupling has been employed. Virtual mesons in intermediate states can be either charged or neutral. The procedure of the renormalization of mass and mesic charge (f, g) is sufficient to determine unambiguously the finite fourth order matrix element except only one term to be interpreted as “electric charge of neutron,” which we have struck out. The general requirement of gauge invariance restricts the possible interaction of nucleon and meson with photon to only four types; consequently we have divided numerious Dyson diagrams into certain gauge invariant classes and then reduced them according to Dyson's general program, to obtain ultimately those four types. In our second approximation the anomalous magnetic moment of the nucleon plays an essential part; consequently the lack of any correct analysis for the latter complicates our results considerably. Moreover, in our γ-π process the behaviour of the magnetic corrections, dependent on the incident energy of photon, are comparable with the static effects. Three provisional measures have been taken with regard to the anomalous moments and the resulting values for the various combinations and couplings of meson fields are compared and discussed. Though the results depend upon the choice of these possibilities, it is shown, in general, that the fourth order contributions turn out for the energy region of the present experiments (incident X-ray being about 330 Mev.), not so large compared with the second order in the case of the symmetrical combination, while they are of the same order of magnitude with the second order in the case of the “charged plus pure neutral” combination. Finally some qualitative aspects of the γ-π process are discussed, which might be valid independently of the order of approximation.