Meson properties in a renormalizable version of the NJL model

Abstract

In the present paper we implement a non-trivial and renormalizable extension of the NJL model. We discuss the advantages and shortcomings of this extended model compared to a usual effective Pauli-Villars regularized version. We show that both versions become equivalent in the case of a large cutoff. Various relevant mesonic observables are calculated and compared.

Symmetries and Ambiguities in the Linear Sigma Model With Light Quarks

“…In this contribution we extended the work presented in [8] in a way as to leave open until the end of the calculations all arbitrary finite constants related with differences of divergent integrals of the same degree of divergence. This is possible using the implicit regularization technique, in which the divergent content of any amplitude is rendered strictly independent of the external (physical) momenta.…”

“…We start with the following generating functional of the SU(2)×SU(2) linear sigma model with fermions [7] and follow closely [8] …”

“…The index 0 stands for bare quantities, the scalar σ 0 is a SU(2) flavor singulet and the pseudoscalar π 0 = π 0i τ i is a flavor SU(2) triplet with τ i being the usual Pauli matrices. The explicit symmetry breaking term is introduced through the term linear in the scalar field, with a factor which would correspond to the symmetry breaking pattern of the NJL Lagrangian [8];m 0 is a diagonal matrix with current quark massesm 0u =m 0d . To finish bosonization one integrates over the quadratic fermionic Lagrangian…”

“…Finally we use the gap equation (22) in order to eliminate the quadratic divergencies in the expressions for the renormalized masses µ 2 σ,π (m, λ 2 ), eq.(27). It is possible to define a renormalized coupling (physical) related with the current quark mass as in [8] …”

Neutrino photoproduction on pseudo Nambu–Goldstone bosons

“…Within a renormalized version of the NJL model [30], in the chiral limit, one arrives at the well known result [31,32,33] Γ π 0 →γγ (T ) = m 3 π (T ) 64π…”