Measurement of the πmeson polarizabilities via the γp → γπ+n reaction

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 537MeV < E_γ < 817MeV, 140^°≤$ \theta_{{\gamma \gamma ^{\prime }}}^{{{{\rm cm}}}}$≤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 ( s₁ < 5m_π²) 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 < s₁/m_π² < 15, -12 < t/m_π² < - 2), the difference $\ensuremath{(\alpha -\beta )_{\pi^{+}}}$ of the electric (α) and the magnetic (β) polarizabilities has been determined. As a result we find $\ensuremath{(\alpha -\beta )_{\pi^{+}}=(11.6\pm 1.5_{{\rm stat}}\pm 3.0_{{\rm syst}}\pm 0.5_{{\rm mod}})\times 10^{-4}{}{\rm fm^{3}}}$. This result is at variance with recent calculations in the framework of chiral perturbation theory.