First radial excitations of scalar meson nonet

Abstract

First radial excitations of 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 Nambu-Jona-Lasinio (NJL) type. Glueball states and their possible mixing with members of the qq 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. The masses of scalar mesons are predicted. The local six-quark ’t Hooft interaction is introduced to solve the so-called UA(1)-problem. The singlet-octet mixing for the ground and radially excited states of scalar...