Charged pion polarizability in the nonlocal quark model of Nambu–Jona-Lasinio type

The polarizability of a charged pion is estimated in the framework of the nonlocal chiral quark model of the Nambu–Jona-Lasinio type. Nonlocality is described by quark form factors of the Gaussian type. It is shown that the polarizability in this model is very sensitive to the form of nonlocality and choice of the model parameters. Recently, the interest to direct determination of the pion polarizability in Primakoff scattering has been renewed. Now the new experiment at CERN is prepared by the collaboration COMPASS where it is expected to obtain the statistics factor 6000 higher than in the previous experiment performed by the IHEP and JINR group in Protvino [1] at the beginning of the 80s. However, the technical possibilities of this experiment allow one to obtain only very rough estimations of the pion polarizability with large error bars απ = −βπ = 8.54± 1.76± 1.51, (1) where απ and βπ are electric and magnetic polarizabilities of the charged pion. Hereafter we express the polarizability in the units of 10cm. The new experiment gives an opportunity to obtain a value of the pion polarizability with good accuracy [2]. What concerns the theoretical aspect of this problem for the past years, there are a lot of estimations of this quantity made by many authors in different theoretical models, in particular, one of the authors of this article (MKV) together with V. N. Pervushin obtained estimations of the pion polarizability in the framework of the nonlinear chiral model in 1975 [3]. After that, analogous calculations were performed by him in the quark linear sigma model of Nambu–Jona-Lasinio(NJL) type [4, 5]. The estimation obtained in the above-mentioned works corresponds to the experimental result (1). In this short note, we want to return to this question and estimate the pion polarizability in the nonlocal model of the NJL type [6], where nonlocality described by quark form factors of the Gaussian type. As it is shown in [5], in the local NJL model the main contribution to the pion polarizability in the leading order of 1/Nc expansion stems from two types of diagrams: the diagrams with light intermediate σ-meson, and the box diagrams (see fig.1). The contribution from the diagrams with other resonances (heavier scalars, vectors and axialvectors) is smaller than 3% and can be neglected in the present consideration. The contribution of the box diagrams to the structure part of the Compton effect takes the form A (a) = α 9πf 2 π (g(q1 · q2)− q μ 2 q ν 1 ),