Aspects of U_A(1) breaking in the Nambu and Jona-Lasinio model

Abstract

The six-quark instanton induced 't Hooft interaction, which breaks the unwanted U_A (1) symmetry of QCD, is a source of perturbative corrections to the leading order result formed by the four-quark forces with the U_L(3)X U_R(3) chiral symmetry. A detailed quantitative calculation is carried out to bosonize the model by the functional integral method. We concentrate our efforts on finding ways to integrate out the auxiliary bosonic variables. The functional integral over these variables cannot be evaluated exactly. We show that the modified stationary phase approach leads to a resummation within the perturbative series and calculate the integral in the ``two-loop'' approximation. The result is a correction to the effective mesonic Lagrangian which may be important for the low-energy spectrum and dynamics of the scalar and pseudoscalar nonets.

arXiv comment42 pages, 3 figures; concluding section and references added

References in corpus (13)

• QCD Phenomenology based on a Chiral Effective Lagrangian
• QCD forces and heavy quark bound states
• Instantons at work
• Nambu Jona-Lasinio Like Models and the Low Energy Effective Action of QCD
• Chiral Lagrangians and Nambu-Jona-Lasinio like models
• Multi-quark interactions with a globally stable vacuum
• Pion Observables in the Extended NJL Model with Vector and Axial-Vector Mesons
• The Momentum--Space Bosonization of the Nambu--Jona-Lasinio Model with Vector and Axial-Vector Mesons
• Long distance expansion for the NJL model with SU(3) and U_A(1) breaking
• Effective quark Lagrangian in the instanton-gas model
• Effective Chiral Meson Lagrangian For The Extended Nambu-Jona-Lasinio Model
• Path Integral Bosonization of the 't Hooft Determinant: Quasiclassical Corrections
• Path integral bosonization of the 't Hooft determinant: fluctuations and multiple vacua

Cited by in corpus (20)

• Susceptibilities with multi-quark interactions in PNJL model
• Correlation between conserved charges in PNJL Model with multi-quark interactions
• Dynamical chiral symmetry breaking by a magnetic field and multi-quark interactions
• Lowering the critical temperature with eight-quark interactions
• Thermodynamic potential with correct asymptotics for PNJL model
• Strange quark matter in the presence of explicit symmetry breaking interactions
• The large degeneracy of excited hadrons and quark models
• Vacuum polarization corrections to low energy quark effective couplings
• Determination of $U(1{)}_{\mathrm{A}}$ restoration from pion and $a_0$-meson screening masses: Toward the chiral regime
• The strange critical endpoint and isentropic trajectories in an Extended PNJL Model with Eight Quark Interactions
• Effects of Quark Interactions on Dynamical Chiral Symmetry Breaking by a Magnetic Field
• Factorization breaking of four-quark condensates in the Nambu Jona Lasinio model
• Thermomagnetic effects on light pseudo-scalar meson masses within the SU(3) Nambu-Jona--Lasinio model
• Thermodynamical properties of strongly interacting matter in a model with explicit chiral symmetry breaking interactions
• $U_A(1)$ symmetry breaking quark interactions from vacuum polarization
• Charged pions asymmetry from the decay of light neutral axial mesons due to interference
• Functional Integral Approaches to the Bosonization of Effective Multi-Quark Interactions with $U_\A(1)$ Breaking
• Study of net-baryon higher moments in PNJL model and their expectation for net-proton using the Subensemble Acceptance Method for the search of QCD critical point
• Eight-quark interactions as a chiral thermometer
• Nonuniform phases in the 't Hooft extended Nambu--Jona-Lasinio Model