Meson properties in an extended non-local NJL model

Abstract

We consider a nonlocal version of the NJL model, based on a separable quark-quark interaction. The interaction is extended to include terms that bind vector and axial-vector mesons. The nonlocality means that no further regulator is required. Moreover the model is able to confine the quarks by generating a quark propagator without poles at real energies. Working in the ladder approximation, we calculate amplitudes in Euclidean space and discuss features of their continuation to Minkowski energies. Conserved currents are constructed and we demonstrate their consistency with various Ward identities. Various meson masses are calculated, along with their strong and electromagnetic decay amplitudes. We also calculate the electromagnetic form factor of the pion, as well as form factors associated with the processes γγ * → π 0and ω → π 0 γ * . The results are found to lead to a satisfactory phenomenology and lend some dynamical support to the idea of vector-meson dominance.

Pion pole light-by-light contribution tog−2of the muon in a nonlocal chiral quark model

“…In NχQM one finds the contribution of the triangle diagram to the invariant amplitude as where q = q 1 − q 2 , k ± = k ± q 3 /2, k 3 = k − q/2. In the chiral limit q 2 3 = m 2 π = 0 with both photons real q 2 i = 0 one finds the normalization by the axial anomaly (within the nonlocal models it was proven in [35])…”

Light pseudoscalar mesons in a nonlocalSU(3)chiral quark model

“…In the case of the Gaussian (Lorentzian) regulator, we find that for m above a critical value m crit ≃ 8.3 MeV (3.9 MeV) the quark propagators have only complex poles in Minkowski space. This can be understood as a sort of quark confinement [12,13]. In contrast, for m m crit one finds that u and d quark Euclidean propagators do have at least two doublets of purely imaginary poles (i.e.…”

“…However, since in the present case we are dealing with nonlocal fields, an extra replacement has to be performed in the regulator r(x − y) [12,13,17]. One has…”

“…In the nonlocal model under consideration the coefficients g P γγ are given by quark loop integrals. Besides the usual "triangle" diagram, given by a closed quark loop with one meson and two photon vertices, in the present nonlocal scheme one has a second diagram [13] in which one of the quark-photon vertices arises from the gauge contribution to the regulator, see Eq. (37).…”

Hadronic corrections to muon anomalous magnetic moment within the instanton liquid model

“…The quark-pion coupling, g πq , and the pion decay constant, f π , are connected by the Goldberger-Treiman relation, g π = M q /f π , which is verified to be valid in the nonlocal model [39], as requested by the chiral symmetry. The vector vertex following from the model (26) is (Fig.…”