Threshold π0 photo- and electro-production in a meson-exchange model

Abstract

We show that, within a meson-exchange dynamical model describing well most of the existing pion electromagnetic production data up to the second resonance region, one is also able to obtain a good agreement with the π 0 photo-and electroproduction data near threshold. In the case of π 0 production, the effects of final state interaction in the threshold region are nearly saturated by single charge exchange rescattering. This indicates that in ChPT, it might be sufficient to carry out the calculation just up to one-loop diagrams for threshold neutral pion production.Photo-and electroproduction of π 0 near threshold have been a subject of many experimental and theoretical studies in the last decade. It was prompted by the discrepancy between the "old" low-energy-theorem (LET) prediction of E 0 + = −2.4 × 10 −3 /m π and the "new" experimental measurements [ 1,2], which yielded E 0 + ∼ −1.3 × 10 −3 /m π . The discrepancy between LET and the experimental data was eventually resolved by the chiral perturbation theory (ChPT) calculation [ 3] which showed that the loop corrections gave rise to nonanalytical terms in m π . Since then precise measurements on the π 0 electromagnetic (EM) production near threshold have been performed [ 4] and the ChPT calculations to one loop O(p 3 ) (O(p 4 ) in the case of photoproduction) have been carried out in the heavy baryon formulation [ 5]. Nice agreement between theory and experiment was reached not only for the S-wave multipoles but also for the P -wave amplitudes.Meson-exchange models (MEM's), as in ChPT, also start from an effective chiral Lagrangian. However, they differ from ChPT in the approach to calculate the scattering amplitudes. In ChPT, crossing symmetry is maintained in the perturbative field-theoretic calculation, and the agreement between its predictions and the data is expected as long as the series converges. In MEM's, the effective Lagrangian is used in the construction of potential for use in the scattering equation. The solutions of the scattering equation include rescattering effects to all orders and hence unitarity is ensured, while crossing symmetry is violated. Such models [ 6,7,8,9,10,11,12] have been able to provide a good description of πN scattering lengths and phase shifts in S-, P -, and D-waves up to 600 MeV pion laboratory kinetic energy.MEM's have been constructed for pion EM production as well [ 10,13] and good