An experiment on the radiative π + -meson photoproduction from the proton (γp → γπ + n) was carried out at the Mainz Microtron MAMI in the kinematic region 537 MeV < E γ < 817 MeV, 140 • ≤ θ cm γγ ′ ≤ 180 • . The π + -meson polarizabilities have been determined from a comparison of the data with the predictions of two different theoretical models, the first one being based on an effective pole model with pseudoscalar coupling while the second one is based on diagrams describing both resonant and nonresonant contributions. The validity of the models has been verified by comparing the predictions with the present experimental data in the kinematic region where the pion polarizability contribution is negligible (s 1 < 5m 2 π ) and where the difference between the predictions of the two models does not exceed 3%. In the region, where the pion polarizability contribution is substantial (5 < s 1 /m 2 π < 15, −12 < t/m 2 π < −2), the difference (α − β) π + of the electric (α) and the magnetic (β) polarizabilities has been determined. As a result we find: (α − β) π + = (11.6 ± 1.5 stat ± 3.0 syst ± 0.5 mod ) × 10 −4 fm 3 . This result is at variance with recent calculations in the framework of chiral perturbation theory.

We present a phenomenological discussion of spin-independent, generalized dipole polarizabilities of hadrons entering the virtual Compton scattering process γ * h → γh. We introduce a new method of obtaining a tensor basis with appropriate Lorentz-invariant amplitudes which are free from kinematical singularities and constraints. The result is summarized in terms of a compact effective Lagrangian. We then motivate a gauge-invariant separation into a generalized Born term containing ground-state properties only, and a residual contribution describing the model-dependent internal structure. The generalized dipole polarizabilities are defined in terms of Lorentz-invariant residual amplitudes. Particular emphasis is laid on a physical interpretation of these quantities as characterizing the spatial distributions of the induced electric polarization and magnetization of hadrons. It is argued that three dipole polarizabilities, namely the longitudinal electric α L (q 2 ), the transverse electric α T (q 2 ), and the magnetic β(q 2 ) ones are required in order to fully reconstruct local polarizations induced by soft external fields in a hadron. One of these polarizabilities, α T (q 2 ), describes an effect of higher order in the soft final-photon momentum q ′ . We argue that the associated spatial distributions obtained via the Fourier transforms in the Breit frame are meaningful even for such a light particle as the pion. The spatial distributions are determined at large distances r ∼ 1/m π for pions, kaons, and octet baryons by use of ChPT.

The differential cross sections for $\pi^- p \to \gamma n$ and $\pi^+ n \to \gamma p$ are computed up to $O(p^3)$ in heavy baryon chiral perturbation theory (HBChPT). The expressions at $O(p)$ and $O(p^2)$ have no free parameters. There are three unknown parameters at $O(p^3)$, low energy constants of the HBChPT Lagrangian, which are determined by fitting to experimental data. Two acceptable fits are obtained, which can be separated by comparing with earlier dispersion relation calculations of the inverse process. Expressions for the multipoles, with emphasis on the p-wave multipoles, are obtained and evaluated at threshold. Generally the results obtained from the best of the two fits are in good agreement with the dispersion relation predictions.Comment: 24 pages, Latex, using RevTe

We present a calculation of the virtual Compton scattering amplitude for γ * + π → γ + π in the framework of chiral perturbation theory at O(p 4 ). We explicitly derive expressions for generalized electromagnetic polarizabilities and discuss alternative definitions of these quantities.

We present a calculation of the cross section and the event generator of the reaction πe → πeγ. This reaction is sensitive to the pion generalized dipole polarizabilities, namely, the longitudinal electric α L (q 2 ), the transverse electric α T (q 2 ), and the magnetic β(q 2 ) which, in the real-photon limit, reduce to the ordinary electric and magnetic polarizabilitiesᾱ andβ, respectively. The calculation of the cross section is done in the framework of chiral perturbation theory at O(p 4 ). A pion VCS event generator has been written which is ready for implementation in GEANT simulation codes or for independent use. 13.60.Fz,14.40.Aq