Strangeness content of the pion in the U(3) Nambu–Jona–Lasinio model

Abstract

The Nambu-Jona-Lasinio model is considered with flavor-dependent coupling constants $G_{ij} \left[ ( \bar{\psi} \lambda_i \psi ) ( \bar{\psi} \lambda_j \psi ) + ( \bar{\psi} i\gamma_5 \lambda_i \psi ) ( \bar{\psi} i \gamma_5\lambda_j \psi ) \right]$ for $i,j=0,1..N_f^2-1$, and $N_f=3$. A self consistent calculation of quark effective masses and coupling constants is performed making the strange quark effective mass to vary considerably. Quantum mechanical mixings between up, down and strange constituent quarks yields a strangeness content of the light u and d quarks constituent and of the pion. Different types of estimates for the strangeness contribution for the pion mass are provided. Mixing type interactions, $G_{i\neq j}$, induce the light mesons mixings and estimates for the $\pi^0-\eta$ and $\eta-\eta'$ mixings are provided. The $\eta-\pi^0$ mixing is argued to be an indication of the strangeness content of the pion.

Magnetic field induced corrections to the NJL model coupling constant from vacuum polarization

“…Finally estimates for the magnetic field dependence of the η − η mixing angle were provided by considering the mixing type interaction G 08 (B) according to Refs. [34,35]. As shown in the Appendix (B) G 08 (B) ∼ G uu + G dd − 2G ss that is proportional to the up/down -strange quark effective mass non-degeneracy.…”

“…The mixing type interactions G 08 (B) give rise to the eta-eta' mesons mixings. This mixing emerges already by considering the contribution of non degenerate quark masses M u = M s [34,35] and we we'll present exclusively the effect of the magnetic field on the mixing angle.…”

“…The vacuum contributions for the flavor symmetric model were analyzed in [32,68] and for non degenerate quark masses in [34,35]. By making the change of variables…”

“…Among the successful QCD effective models, the Nambu-Jona-Lasinio (NJL) model is known to reproduce, and eventually to predict, many observables for the hadron structure and dynamics under different conditions [23,24,25,26,19]. Several approaches have been already employed to describe how the NJL model coupling constant might be obtained in terms of QCD degrees of freedom in the vacuum [27,28,29,30,31,32] or to understand further how those degrees of freedom contribute for the NJL-model parameters [33,34,35]. Lately, lattice QCD provided results for hadron observables in a finite strong magnetic field were also used to test the predictions of NJL model in such conditions and, eventually, this type of comparison may favor an improvement of its the predictive power [36,37,38].…”

“…This work extends the more restricted calculation for weak magnetic field and SU (N f = 2) presented in [53] and, besides that, estimations for its effects on the neutral pion and kaon masses are presented. The dependencies of the u, d and s quark condensates and of the η − η mixing angle [54,55,34,35] on the magnetic field are also calculated. The auxiliary field method (AFM) will be considered, as usually, being that the scalar field allows for the DChSB although a chiral rotation is performed to eliminate the corresponding meson degree of freedom which seems absent in the light hadron spectrum.…”