Alex H. Blin

Pion Observables in the Extended NJL Model with Vector and Axial-Vector Mesons☆

Abstract The momentum-space bosonization method of a Nambu and Jona-Lasinio type model with vector and axial-vector mesons is applied to ππ scattering. Unlike the case in earlier published papers, we obtain the ππ scattering amplitude using the linear and nonlinear realizations of chiral symmetry and fully taking into account the momentum dependence of meson vertices. We show the full physical equivalence between these two approaches. The chiral expansion procedure in this model is discussed in detail. Chiral expansions of the quark mass, pion mass and constant f π are obtained. The low-energy ππ phase shifts are compared to the available data. We also study the scalar form factor of the pion.

Effects of eight-quark interactions on the hadronic vacuum and mass spectra of light mesons

Abstract The combined effective low energy QCD Lagrangians of Nambu–Jona-Lasinio (NJL) and ’t Hooft are supplemented with eight-quark interactions. This work is a follow-up of recent findings, namely (i) the six quark flavour determinant ’t Hooft term destabilizes the NJL vacuum, (ii) the addition of a chiral invariant eight-fermion contact term renders the ground state of the theory globally stable; (iii) stability constrains the values of coupling constants of the model, meaning that even in the presence of eight-quark forces the system can be unstable in a certain parameter region. In the present work we study a phenomenological output of eight-quark interactions considering the mass spectra of pseudoscalar and scalar mesons. Mixing angles are obtained and their equivalence to the two angle approach is derived. We show that the masses of pseudoscalars are almost neutral to the eight-quark forces. The only marked effect of the second order in the SU(3) breaking is found in the η – η ′ system. The scalars are more sensitive to the eight-quark interactions. A strong repulsion between the singlet and octet members is the reason for the obtained low mass of the σ state within the model considered.

Four-point functions in quark flavor dynamics: meson-meson scattering

Abstract We study pion-pion scattering in an extended version of the three-flavor Nambu-Jona-Lasinio model. We show that the leading order contributions of the ππ scattering amplitude agree with the standard current algebra results. We evaluate the various scattering lengths and amplitudes. For the regime of “barely broken” chiral symmetry, which is characterized by substantial non-linearities under the introduction of the current quark masses, we find a00=0.26 in agreement with the data. The threshold parameters in the other channels are also satisfactorily described.

Strong and radiative meson decays in a generalized Nambu-Jona-Lasinio model☆

Abstract We investigate strong and radiative meson decays in a generalized Nambu-Jona-Lasinio model. The one loop order calculation provides a satisfactory agreement with the data for the mesonic spectrum and for radiative decays. Higher order effects for strong decays of ϱ and K ∗ are estimated to be large. We also discuss the role of the flavour mixing determinantal interaction.

Medium effects on meson properties

Abstract A coupled meson field is extracted from a quark system by means of a technique based on the time-dependent Hartree-Fock formalism. The model hamiltonian is of the Nambu-Jona-Lasinio type. Meson properties are studied, namely the ρππ coupling constant, the ρ decay width and the low-energy ππ scattering lengths, respectively, at zero and finite baryonic densities.

Mesonic excitations in the Nambu-Jona-Lasinio quark-antiquark continuum

Abstract The strength distribution of mesonic modes of the original Nambu-Jona-Lasinio lagrangian is investigated for energies above twice the consistuent quark mass.

Stationary phase corrections in the process of bosonization of multi-quark interactions

The functional integration over the auxiliary bosonic variables of cubic order related with the effective action of the Nambu–Jona–Lasinio model with ’t Hooft term has recently been obtained in the form of a loop expansion. Even numbers of loops contribute to the action, while odd numbers of loops are assigned to the measure. We consider the two-loop corrections and analyse their effect on the low-lying pseudoscalar and scalar mass spectra, quark condensates and weak decay constants. The results are compared to the leading order calculations and other approaches.

The phase diagram in the SU(3) Nambu-Jona-Lasinio model with 't Hooft and eight-quark interactions

It is shown that the endpoint of the first order transition line which merges into a crossover regime in the phase diagram of the Nambu—Jona‐Lasinio model, extended to include the six‐quark ’t Hooft and eight‐quark interaction Lagrangians, is pushed towards vanishing chemical potential and higher temperatures with increasing strength of the OZI‐violating eight‐quark interactions. We clarify a connection between the location of the endpoint in the phase diagram and the mechanism of chiral symmetry breaking at the quark level. Constraints on the coupling strengths based on groundstate stability and physical considerations are explained.

Quark-antiquark resonances in the NJL model

Abstract The problem of the ϱ meson resonance solution in the extended NJL model is studied. It has been shown previously that the solution for the ϱ meson changes smoothly from a bound state to a “virtual state” when the vector channel attraction becomes too weak to support bound state solutions. We have found that together with these solutions a separate resonance branch appears which is not connected smoothly with the bound state solutions. At small values of constituent quark mass, m ∼ 200 MeV, it corresponds to the physical vector meson resonance solution in the quark-continuum region. The a 1 and σ resonances are also discussed.

The temperature dependence of the optical model potential and of the nucleon mean free path

Abstract The complex nuclear self energy is calculated in nuclear matter at full and half density semiclassically at higher temperatures including Pauli blocking. From this the nucleon mean free path λ mf is obtained in a wide energy region. For excitation energies per particle E ∗ /A ⪡ 8 MeV , λ mf decreases drastically with higher temperature, whereas for E ∗ /A ≫ 8 MeV it decreases only weakly from the value of λ mf ≈ 5 fm at T = 0.