EXCITED PIONS, ρ- AND ω-MESONS AND THEIR DECAYS IN A CHIRAL SU(2) × SU(2) LAGRANGIAN

Abstract

A chiral SU (2) × SU (2) Lagrangian containing, besides the usual meson fields, their first radial excitations is considered. The Lagrangian is derived by bosonization of the NambuJona-Lasinio quark model with separable non-local interactions, with form factors corresponding to 3-dimensional ground and excited state wave functions. The spontaneous breaking of chiral symmetry is governed by the NJL gap equation. The first radial excitations of the pions, ρ-and ω-mesons are described with the help of two form factors. The weak decay constant F π ′ is calculated. The values for the decay widths of the processes ρ → 2π, π ′ → ρπ, ρ ′ → 2π, ρ ′ → ωπ and ω ′ → ρπ are obtained in agreement with the experimental data.

Decayτ→πωνin the extended NJL model

“…[6,7,15]. Therefore, in present work we give only the expression for the amplitude describing the decay τ → πων: one given by the vector meson dominance model: …”

“…[15] 2 Using the same set of parameters and the approach to loop integral computation, we re-calculated the energy dependence of the e + + e − → ω + π 0 process cross-section. Here we get a better description of the experimental data with respect to our earlier result [6] obtained within the same model (but with another treatment of the loop integrals and other parameter values).…”

“…On the other hand the similar processes e − e + → π 0 γ, π 0 ρ 0 , π 0 ω, π + π − in the extended Nambu-Jona-Lasinio (NJL) model [13][14][15][16] were described [6][7][8][9].…”

Processese+e−→ππ(π′)in the extended Nambu–Jona-Lasinio model

“…For description of the radial excited mesons interactions we use the extended version of the NJL Lagrangian [3,22,23]:…”

“…On the other hand, for the description of the amplitude of this process with the intermediate ρ ′ (1450) meson the extended NJL model [20][21][22][23][24] should be used.…”