Neutral Meson Photoproduction in $S{U}_f(3)$ $\chi$PT

Abstract

We present the results for the electric dipole amplitude for $\gamma N\to {\pi }^{0}N$ at threshold at the $O(p^2)$ level in SU${}_f$(3) chiral perturbation theory. We find that the SU${}_f$(3) results differ only slightly from the SU${}_f$(2) results. At the $O(p^3)$ level one encounters new, unknown counterterms to fix which one is likely to need the threshold photoproduction data themselves, thus losing predictive power. We suggest, instead, that the {\it difference} between the proton and neutron ${\pi }^0$ photoproduction amplitudes may provide a test of the convergence properties of the $\chi$PT in the present context. We urge that the neutron's electric dipole amplitude be measured.

Comments: Revised version with corrected value of the Kaon loop contribution