Low energy constituent quark and pion effective couplings in a weak external magnetic field

Abstract

An effective model with pions and constituent quarks in the presence of a weak external background electromagnetic field is derived by starting from a dressed one gluon exchange quark-quark interaction.By applying the auxiliary field and background field methods, the structureless pion limit is considered to extract effective pion and constituent quark couplings in the presence of a weak magnetic field. The leading terms of a large quark and gluon masses expansion are obtained by resolving effective coupling constants which turn out to depend on a weak magnetic field. Two pion field definitions are considered for that. Several relations between the effective coupling constants and parameters can be derived exactly or in the limit of very large quark mass at zero and weak constant magnetic field. Among these ratios, the Gell Mann Oakes Renner and the quark level Goldberger Treiman relations are obtained. In addition to that, in the pion sector, the leading terms of Chiral Perturbation Theory coupled to the electromagnetic field is recovered. Some numerical estimates are provided for the effective coupling constants and parameters.

26 pages, revised and improved version with numerical estimates. To be published in Eur.Phys. Journ. A (2018)

References in corpus (18)

• The Chiral Magnetic Effect
• Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals
• Bridging a gap between continuum-QCD and ab initio predictions of hadron observables
• The Importance of Asymptotic Freedom for the Pseudocritical Temperature in Magnetized Quark Matter
• Mesonic low-energy constants
• Spontaneous electromagnetic superconductivity of vacuum in strong magnetic field: evidence from the Nambu--Jona-Lasinio model
• Quark Antiscreening at Strong Magnetic Field and Inverse Magnetic Catalysis
• Maximum Wavelength of Confined Quarks and Gluons and Properties of Quantum Chromodynamics
• Spontaneous generation of local CP violation and inverse magnetic catalysis
• Pions in Large-$N$ Quantum Chromodynamics
• Entropy, confinement, and chiral symmetry breaking
• Chiral asymmetry and axial anomaly in magnetized relativistic matter
• CP violation and chiral symmetry breaking in hot and dense quark matter in presence of magnetic field
• Vacuum polarization corrections to low energy quark effective couplings
• SU(2) higher-order effective quark interactions from polarization
• SU(2) low energy quark effective couplings in weak external magnetic field
• Chiral asymmetry in cold QED plasma in a strong magnetic field
• Derivation of the effective Chiral Lagrangian for pseudoscalar, scalar, vector and axial-vector mesons from QCD

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• Strangeness content of the pion in the U(3) Nambu-Jona-Lasinio model
• Form factors for pions couplings to constituent quarks under weak magnetic field
• Thermoelectric response of a weakly magnetized thermal QCD medium
• Weak magnetic field corrections to light vector or axial mesons mixings and vector meson dominance
• Pion Pressure in a Magnetic Field
• Constituent quark axial current couplings to light vector mesons in the vacuum and with a weak magnetic field
• U(5) Nambu-Jona-Lasinio model with flavor dependent coupling constants: pseudoscalar and scalar mesons masses
• Strongly interacting matter in extreme magnetic fields
• $U_A(1)$ symmetry breaking quark interactions from vacuum polarization
• Symmetry breaking effects in pion couplings to constituent quark currents