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

Abstract

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.

Revisiting at low energies

“…In the same figure, we also show the result of the recent measurement at MAMI [8] of this quantity. It is seen that the chiral expansion is in conflict with that measurement, independent of any reasonable value chosen for a r 1 .…”

“…The width of the ChPT band is calculated in the manner described in the text. "MAMI data" refers to the recent MAMI experiment [8]. We have added the errors quoted there in quadrature.…”

“…In view of the large scatter of the results, which are partly inconsistent among each other, it is interesting to note that the COMPASS collaboration at CERN is presently remeasuring pion and kaon polarizabilities with high statistics, using the Primakoff effect [42]. It is also worth mentioning that a reanalysis of the MAMI data [8], using a chiral invariant framework, is underway [43].…”

“…The MAMI Collaboration [8] has recently reported the experimental result (α 1 − β 1 ) π ± = (11.6 ± 1.5 stat ± 3.0 syst ± 0.5 mod ) × 10 −4 fm 3 .…”

“…Section 5 contains a concise representation of the two Lorentz invariant amplitudes that describe the scattering matrix element. Section 6 contains explicit expressions for the dipole and quadrupole polarizabilities valid at next-to-next-to-leading order in the chiral expansion, together with a detailed numerical analysis and a comparison with the recent MAMI data [8], and with an evaluation from data on γγ → π + π − [10]. The summary and an outlook are given in Section 7.…”