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.

arXiv comment30 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

References in corpus (68)

• QCD Phenomenology based on a Chiral Effective Lagrangian
• FLAG Review 2019
• Mixing and Decay Constants of Pseudoscalar Mesons
• Collective perspective on advances in Dyson-Schwinger Equation QCD
• Explanation and Prediction of Observables using Continuum Strong QCD
• Bridging a gap between continuum-QCD and ab initio predictions of hadron observables
• Constituent Quarks from QCD
• Precision measurement and interpretation of inclusive $W^{+}$, $W^{-}$ and $Z/{\gamma }^{\ast }$ production cross sections with the ATLAS detector
• Flavour-symmetry breaking of the quark condensate and chiral corrections to the Gell-Mann-Oakes-Renner relation
• Proton Mass Decomposition from the QCD Energy Momentum Tensor
• A new measurement of K+(e4) decay and the s-wave pi-pi-scattering length a00
• Precise determination of the strangeness magnetic moment of the nucleon
• Essence of the vacuum quark condensate
• The quark condensate from K_{e_4} decays
• Sigma term and strangeness content of octet baryons
• Extracting nucleon strange and anapole form factors from world data
• High statistics measurement of Ke4 decay properties
• $\pi$N and strangeness sigma terms at the physical point with chiral fermions
• Running Gluon Mass from Landau Gauge Lattice QCD Propagator
• Strange Electric Form Factor of the Proton
• The Asymmetry of Antimatter in the Proton
• Direct determinations of the nucleon and pion $\sigma$ terms at nearly physical quark masses
• Leading isospin-breaking corrections to pion, kaon and charmed-meson masses with Twisted-Mass fermions
• Toward a first-principle derivation of confinement and chiral-symmetry-breaking crossover transitions in QCD
• Multi-quark interactions with a globally stable vacuum
• Effects of eight-quark interactions on the hadronic vacuum and mass spectra of light mesons
• Parity-Violating Electron Scattering and the Electric and Magnetic Strange Form Factors of the Nucleon
• Masses and decay constants of the $\eta$ and ${\eta }^{\prime }$ mesons from lattice QCD
• The Electromagnetic Mass Differences of Pions and Kaons
• Masses of positive- and negative-parity hadron ground-states, including those with heavy quarks
• Charmed mesons with a symmetry-preserving contact interaction
• Meson-loop contributions to the rho-omega mass splitting & rho charge radius
• Lattice computation of the electromagnetic contributions to kaon and pion masses
• Scalar Form Factors in SU(3) Chiral Perturbation Theory
• Entropy, confinement, and chiral symmetry breaking
• Strong and Radiative Meson Decays in a Generalized Nambu--Jona-Lasinio Model
• Parameter fitting in three-flavor Nambu--Jona-Lasinio model with various regularizations
• The Sea of Quarks and Antiquarks in the Nucleon: a Review
• Meson Mass Decomposition from Lattice QCD
• Determination of the quark condensate from heavy-light current-current correlators in full lattice QCD
• U_A(1) symmetry breaking, scalar mesons and the nucleon spin problem in an effective chiral field theory
• Mixing of pseudoscalar mesons and isospin symmetry breaking
• The Neutral Decay Modes of the Eta-Meson
• What Does Low Energy Physics Tell Us About The Zero Momentum Gluon Propagator
• Low energy constituent quark and pion effective couplings in a weak external magnetic field
• Vacuum polarization corrections to low energy quark effective couplings
• The expansion by regions in pi K scattering
• The Constituent Chiral Quark Model Revisited
• On the two-loop contributions to the pion mass
• Pion constituent quarks couplings strong form factors: a dynamical approach
• On light vector mesons and chiral SU(3) extrapolations
• An Analytic Analysis of the Pion Decay Constant in Three-Flavoured Chiral Perturbation Theory
• SU(2) higher-order effective quark interactions from polarization
• Flavor-dependent U(3) Nambu Jona Lasinio coupling constant
• SU(2) low energy quark effective couplings in weak external magnetic field
• Form Factors and Dyson-Schwinger Equations
• Form factors for pions couplings to constituent quarks under weak magnetic field
• Polyakov loop effects on the phase diagram in strong-coupling lattice QCD
• The ${\pi }^0-\eta -{\eta }^{\prime }$ mixing in a generalized multi-quark interaction scheme
• A Nambu-Jona-Lasinio like model from QCD at low energies
• A lattice study of the strangeness content of the nucleon
• Note on Strange Quarks in the Nucleon
• Calculation of the nucleon sigma term and strange quark content with two flavors of dynamical overlap fermions
• Correlations between the strange quark condensate, strange quark mass, and kaon PCAC relation
• Factorization breaking of four-quark condensates in the Nambu Jona Lasinio model
• Weak magnetic field corrections to light vector or axial mesons mixings and vector meson dominance
• On pion and kaon decay constants and chiral SU(3) extrapolations
• Effects of charge symmetry breaking on form factors of the pion and kaon

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