First radial excitations of the scalar and pseudoscalar meson nonets as wel
l 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 st
ates and their possible mixing with members of the (q) over bar q multiplet
s 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 spontan
eous 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 ma
sses of pseudoscalar mesons. All masses of the scalar mesons are predicted.
The local six-quark 't Hooft interaction is introduced to solve the so-call
ed U-A(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 excitati
on of the scalar meson nonet are calculated in satisfactory agreement with
experimental data.
Classification of the considered meson nonets is given. It is shown that th
e meson states a(0)(1450), f(0)(1370), f(J)(1710) and K-0*(1430) are the fi
rst radial excitations of a(0)(980), f(0)(400 - 1200), f(0)(980), K-0*(960)
.