Separable Nonlocal Interactions Research Articles

Excited strange mesons and their decays in a chiral U(3)×U(3) Lagrangian

We bosonize the Nambu-Jona-Lasinio quark model with separable nonlocal interactions in order to derive a chiral U(3)×U(3) Lagrangian, containing, besides the usual meson fields, their first radial excitations. The spontaneous breaking of chiral symmetry is governed by the Nambu-Jona-Lasinio gap equation. The first radial excitations of the kaon, K*, and ϕ are described with the help of two form factors. The decays K*′ → ρK, K*′ → K*π, K*′ → Kπ, ϕ′ → K*K, ϕ′ → \(\bar KK\)K, K′ → Kρ, K′ → K*π, and K′ → K2π are considered, and a qualitative agreement of our results with the experimental data is found.

Decays of excited strange mesons in the extended NJL model

A chiral U(3) × U(3) Lagrangian, containing besides the usual meson fields their first radial excitations, is considered. The Lagrangian is derived by bosonization of the Nambu-Jona-Lasinio (NJL) quark model with separable nonlocal interactions. The spontaneous breaking of chiral symmetry is governed by the NJL gap equation. The first radial excitations of the kaon, K* and are described with the help of three form factors. The values for the decay widths of the processes K*´ K,K*´ K*, K*´ K, ´ K*K, ´K, K´ K, K´ K* and K´ K2 are obtained in qualitative agreement with the experimental data.

Decays of excited pseudoscalar and vector mesons in the chiralU(3) ×U(3) model

A chiralU(3) ×U(3) Lagrangian containing, besides the usual meson fields, their first radial excitations is considered. The Lagrangian is derived by bosonization of the Nambu-Jona-Lasinio (NJL) quark model with separable nonlocal interactions. The spontaneous breaking of chiral symmetry is governed by the NJL gap equation. The first radial excitations of the pion, ρ, ω, kaon, K* and ϕ are described with the help of form factors. The values for the decay widths for the processes π′ → ρπ, ρ′ → 2π, ρ′ → ωπ, ω′ → ρπ, K*′ → ρK, K*′ → K*π, K*′ → Kπ, K′ → K*K, K′ → K, K′ → Kρ, K′ → K*π and K′ → K2π are obtained in satisfactory agreement with the experimental data.

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

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 Nambu–Jona-Lasinio (NJL) quark model with separable nonlocal interactions, with form factors corresponding to three-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 Fπ′ 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.

Chiral Lagrangian for excited pions

We construct a chiral Lagrangian containing, in addition to the usual pion field $(\ensuremath{\pi})$, also its first radial excitation $({\ensuremath{\pi}}^{\ensuremath{'}})$. The Lagrangian is derived in the large-${N}_{c}$ limit from a Nambu--Jona-Lasinio (NJL) quark model with separable nonlocal interactions, with form factors corresponding to three-dimensional ground- and excited-state wave functions. Chiral symmetry breaking is governed by the NJL gap equation. The effective Lagrangian for $\ensuremath{\pi}$ and ${\ensuremath{\pi}}^{\ensuremath{'}}$ mesons shows the decoupling of the Goldstone pion and the vanishing of the ${\ensuremath{\pi}}^{\ensuremath{'}}$ leptonic decay constant ${f}_{{\ensuremath{\pi}}^{\ensuremath{'}}}$ in the chiral limit, as required by axial-vector current conservation. We derive the excited-state contribution to the axial-vector current of the model using Noether's theorem. For a finite pion mass and ${\ensuremath{\pi}}^{\ensuremath{'}}$ masses in the range of 750--1300 MeV, ${f}_{{\ensuremath{\pi}}^{\ensuremath{'}}}{/f}_{\ensuremath{\pi}}$ is found to be of the order of 1%.

Scattering by separable non-local interactions

The Schwinger variational principle, together with arbitrary trial functions, is used to derive exact expressions for the scattering amplitudes arising in multichannel scattering by separable non-local interactions.

Separable non-local interactions in nuclei

The lowest six even parity states of Li 6 are calculated in the L- S coupling scheme with the use of separable non-local potentials proposed by Mitra et al. It is shown that the non-central terms of the potential give very small contributions to the energies of these states. The reaction matrix evaluated with the central terms of the interaction does give matrix elements in these states that are in good agreement with experiment.