Interplays among the masses, mixing parameters, and couplings of the 1++ and 1+- q bar q-meson system

Despite the old prediction mA1= √2 mρ from the spectral function sum rules, the mass of the isovector L++ meson A1 [now a1(1270)] is indicated to be close to that of the isovector L+- meson b1(1235). In this paper, we address the question ''Is there any dynamical reason to expect the approximate degeneracy of the masses of a1(1270) and b1(1235)?'' From the theoretical framework of ''asymptotic flavor symmetry plus hadron constraining algebras involving the generators of underlying symmetry groups of QCD,'' we present an argument which shows that the answer is yes. Interesting intimate interplays among the masses, mixing parameters, and the coupling constants of the 1++ and 1+- nonet systems are demonstrated. The mass degeneracy is closely related to the presence of dynamical selection rules observed