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 $i,j=0,\mathrm{1..}{N}_f^2-1$, 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, $G_{i\ne j}$, induce the light mesons mixings and estimates for the ${\pi }^0-\eta$ and $\eta -{\eta }^{\prime }$ mixings are provided. The $\eta -{\pi }^0$ mixing is argued to be an indication of the strangeness content of the pion.

30 pages, 8 figures, new comments, discussions and estimates for the strangeness content of the pion, including an estimate based on the pi-eta mixing. Few misprints/mistakes corrected

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Cited by in corpus (6)

• Magnetic field induced corrections to the NJL model coupling constant from vacuum polarization
• Quark-antiquark states of the lightest scalar mesons within the Nambu-Jona-Lasinio model with flavor-dependent coupling constants
• U(5) Nambu-Jona-Lasinio model with flavor dependent coupling constants: pseudoscalar and scalar mesons masses
• $U_A(1)$ symmetry breaking quark interactions from vacuum polarization
• Charged pions asymmetry from the decay of light neutral axial mesons due to interference
• Symmetry breaking effects in pion couplings to constituent quark currents