Radiative charged pion photoproduction and pion polarizabilities: An analysis within heavy baryon chiral perturbation theory

Abstract

We analyze the amplitude of radiative charged pion photoproduction in the framework of heavy baron chiral perturbation theory and discuss the best kinematic conditions for the extraction of pion polarizabilities from the total cross section.Electric (α) and magnetic (β) polarizabilities characterize the global deformation response of a composite system in static uniform external electric and magnetic fields. They provide precious information about the underlying dynamics of the composite system. As a result, a precise measurement of the pion polarizabilities is of great importance to understand the inner structure of the pion. Chiral symmetry allows one to predict the electromagnetic polarizabilities of charged pion in terms of the radiative decay π + → e + ν e γ [1] ,where l r 6 − l r 5 is a linear combination of scale-independent parameters of the Gasser and Leutwyler Lagrangian [2].is the axial vector coupling constant. The next-to-leading-order result has been calculated at O(p 6 ) in Chiral Perturbation Theory(ChPT), and the correction to (1) is small: [4,5]:Therefore the measurement of pion polarizabilities becomes an excellent test of chiral dynamics. Compton scattering of real photons(RCS) is one of the simplest reactions to determine the polarizabilities. When expanded in the energy of final photon, the leading order term of the low-energy scattering amplitudes is specified by the Thomson limit in terms of the charge and the mass of the target. Genuine structure effects first appear at second order parametrized as polarizabilities.where ǫ 1 ( ǫ 2 ), ω(ω ′ ) and k( k ′ ) are the polarization vector, energy and momentum of the initial (final) photon, respectively. T B is the Born amplitude. Because pion targets are unavailable, RCS of pions was done by using indirect ways, such as high-energy pion-nucleus bremsstrahlung π − Z → π − Zγ [6] or radiative pion photoproduction off the proton γp → γπ + n [7] and the cross channel two-photon reaction γγ → ππ [8,9]. Recently the new radiative charged pion photoproduction experiment at Mainz Microtron MAMI [10] reported their result which is far away from the prediction of ChPT,In this letter, we investigate the relation between the charged pion polarizabilities and the radiative charged pion photoproduction in the framework of heavy baryon chiral perturbation theory(HBChPT). (see [11] for a review of HBChPT.) So far, the extractions of charged pion polarizabilities α π ± and β π ± from radiative charged pion photoproduction have relied on two different ways. The method of extrapolation [12,13] is similar to the one suggested by Chew and Low [14] in the late fifties. This method has been successfully employed to determine the pion-nucleon coupling constant through γp → π + p. It is also used in the determination of ππ → ππ scattering from πN → ππN reaction. However, in order to do extrapolation, one has to obtain the experimental data with small error over a sufficiently wide region of t, particularly when very close to t=0. The authors of [10] also point out tha...

Cross sections for low-energy $π^-γ$ reactions

“…The result α π − β π = (4.4 ± 3.2) • 10 −4 fm 3 [10] extracted from the MARK II data [11] is consistent with the chiral prediction, but the corresponding low-energy cross sections for γγ → π + π − are (within their errorbars) rather insensitive to even sizeable changes of the pion polarizabilities [13]. We also note that radiative pion photoproduction γp → γπ + n has recently been considered in the framework of heavy baryon chiral perturbation theory [14]. It has been argued in ref.…”

“…It has been argued in ref. [14] that additional contributions from γγπNN vertices in the chiral Lagrangian L…”

Chiral perturbation theory: Introduction and recent results in the one-nucleon sector

“…In Ref. [Kao et al, 2007] radiative pion photoproduction was studied in the framework of heavy-baryon chiral perturbation theory at the one-loop level. Unfortunately, the kinematical conditions of the MAMI experiment were not explicitly considered.…”