First radial excitations of the scalar and pseudoscalar meson nonets as well as their ground states are described as quark–antiquark bound systems in the framework of a nonlocal chiral quark model of the NJL type. Glueball states and their possible mixing with members of the [Formula: see text] multiplets are not considered. Radial excitations are described by means of simple polynomial form factors in the momentum–space which are introduced into the four-quark vertices of the quark Lagrangian. The form factors are chosen in the regime of spontaneous chiral symmetry breaking so that the gap equations do not change their standard form, which provides fulfillment of the low energy theorems. All free parameters of the form factors are fixed by experimentally observed masses of pseudoscalar mesons. All masses of the scalar mesons are predicted. The local six-quark 't Hooft interaction is introduced to solve the so-called UA(1)-problem. The (four particle) singlet–octet mixing for the ground and radially excited states of scalar and pseudoscalar mesons is taken into account. The widths of the main strong decays of the first radial excitation of the scalar meson nonet are calculatedin satisfactory agreement with experimental data. Classification of the considered meson nonets is given. It is shown that the meson states a0(1450), f0(1370), fJ(1710) and [Formula: see text] are the first radial excitations of a0(980), f0(400-1200), f0(980), [Formula: see text].
Pion-to-photon transition distribution amplitudes and related form factors in the non-local chiral quark model
