Low-Energy Interactions of Mesons with Participation of the First Radially Excited States in U(3) × U(3) NJL Model

Abstract

The U(3)×U(3) chiral symmetric NJL model describing pseudoscalar, vector, and axial-vector mesons in both the ground state and first radially excited states is shortly presented in this review. In this model, it is possible to describe a large number of low-energy interactions of mesons, τ lepton decays into mesons, and processes of meson production in electron–positron annihilations in satisfactory agreement with the experiments. In describing a number of processes, it turned out to be necessary to take into account the interactions of mesons in the final state.

Semileptonic decays of $ρ$, $ω$, $ϕ$, $η$ and $η'$ mesons in ground and first radially excited states in the $U(3)\times U(3)$ NJL model

“…The U(3) × U(3) chirally symmetric NJL model will be used to describe semileptonic decays. The quark-meson Lagrangian for the strong interaction of ρ, ω, φ , η and η ′ mesons in the ground and first radially excited states in the NJL model takes the form [16,17,34,35]…”

“…For the η mesons, the factor A takes a slightly different form. This is due to the fact that in the case of the η meson four states are mixed [17]:…”

“…The values of the mixing (a q i ) parameters are shown in Table I [17]. The η ′ meson corresponds to the physical state η ′ (958) and the η, η′ mesons correspond to the first radial excitation mesons η and η ′ .…”

“…Therefore, one has to use various phenomenological theories based on internal symmetries of strong interactions. The most frequently used models in specific calculations are the Chiral Perturbation Theory [1, 2] and Nambu-Jona-Lasinio type chiral symmetric models [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17].…”

“…Among the mesons of a pseudoscalar nonet described in the U(3) ×U(3) NJL model, η and η ′ mesons are of special interest [17,18]. Indeed, unlike pions and kaons, singlet-octet mixing occurs in η and η ′ mesons.…”