SU(2) higher-order effective quark interactions from polarization

Abstract

Higher order quark effective interactions are found for SU(2) flavor by departing from a non local quark-quark interaction. By integrating out a component of the quark field, the determinant is expanded in chirally symmetric and symmetry breaking effective interactions up to the fifh order in the quark bilinears. The resulting coupling constants are resolved in the leading order of the longwavelength limit and exact numerical ratios between several of these coupling constants are obtained in the large quark mass limit. In this level, chiral invariant interactions only show up in even powers of the quark bilinears, i.e. $\mathcal{O}(\bar{\psi }\psi {)}^{2n}$ ($n=1,2,3,..$), whereas (explicit) chiral symmetry breaking terms emerge as $\mathcal{O}(\bar{\psi }\psi {)}^n$ being always proportional to some power of the Lagrangian quark mass.

11 pages, revised version, submitted to publication

References in corpus (13)

• Susceptibilities and the Phase Structure of a Chiral Model with Polyakov Loops
• Bridging a gap between continuum-QCD and ab initio predictions of hadron observables
• Critical endpoint in the Polyakov-loop extended NJL model
• Effects of eight-quark interactions on the hadronic vacuum and mass spectra of light mesons
• Chiral phase transition in an extended NJL model with higher-order multi-quark interactions
• Repulsive Vector Interaction in Three Flavor Magnetized Quark and Stellar Matter
• Entropy, confinement, and chiral symmetry breaking
• Effects of a multi-quark interaction on color superconducting phase transition in an extended NJL model
• Determination of the strength of the vector-type four-quark interaction in the entanglement Polyakov-extended Nambu-Jona-Lasino model
• OZI violating eight-quark interactions as a thermometer for chiral transitions
• What Does Low Energy Physics Tell Us About The Zero Momentum Gluon Propagator
• Vacuum polarization corrections to low energy quark effective couplings
• Neutral quark matter in a Nambu-Jona Lasinio model with vector interaction

Cited by in corpus (12)

• Low energy constituent quark and pion effective couplings in a weak external magnetic field
• Flavor-dependent U(3) Nambu Jona Lasinio coupling constant
• Magnetic field induced corrections to the NJL model coupling constant from vacuum polarization
• SU(2) low energy quark effective couplings in weak external magnetic field
• Strangeness content of the pion in the U(3) Nambu-Jona-Lasinio model
• Light vector and axial mesons effective couplings to constituent quarks
• Many-quark interactions: Large-$N$ scaling and contribution to baryon masses
• U(5) Nambu-Jona-Lasinio model with flavor dependent coupling constants: pseudoscalar and scalar mesons masses
• Masses of the lowest spin-0 and spin-1 meson nonets: explicit symmetry breaking effects
• $U_A(1)$ 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