Weak magnetic field corrections to light vector or axial mesons mixings and vector meson dominance

Abstract

Weak magnetic field induced corrections to effective coupling constants describing light vector mesons mixings and vector meson dominance (VMD) are derived. The magnetic field must be weak with respect to an effective quark mass $M^{\ast }$ such that: $e{B}_0/{M^{\ast }}^2<1$ or $e{B}_0/{M^{\ast }}^2<<1$.For that, a flavor SU(2) quark-quark interaction due to non perturbative one gluon exchange is considered. By means of methods usually applied to the Nambu Jona Lasinio (NJL) and Global Color Models (GCM), leading light vector/axial mesons couplings to a background electromagnetic field are derived. The corresponding effective coupling constants are resolved in the structureless mesons and longwavelength limits. Some of the resulting coupling constants are redefined such as to become magnetic field induced corrections to vector or axial mesons couplings. Due to the approximated chiral symmetry of the model, light axial mesons mixings induced by the magnetic field are also obtained. Some numerical estimates are presented for the coupling constants and for some of the corresponding momentum dependent vertices. The contributions of the induced VMD and vector mesons mixing couplings for the low momentum pion electromagnetic form factor and for the (off shell) charge symmetry violation potential at the constituent quark level are estimated. The relative overall weak magnetic field-induced anisotropic corrections are of the order of $(e{B}_0/{M^{\ast }}^2{)}^n$, where $n=2$ or $n=1$ respectively.

27 pages, 6 figures

References in corpus (5)

• Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals
• Vector meson form factors and their quark-mass dependence
• Pions in Large-$N$ Quantum Chromodynamics
• A study of $\rho -\omega$ mixing in resonance chiral theory
• $\rho$-$\omega$ mixing and spin dependent CSV potential

Cited by in corpus (7)

• One-loop constituent quark contributions to the vector and axial-vector meson curvature mass
• Magnetic field induced corrections to the NJL model coupling constant from vacuum polarization
• Strangeness content of the pion in the U(3) Nambu-Jona-Lasinio model
• Constituent quark axial current couplings to light vector mesons in the vacuum and with a weak magnetic field
• $U_A(1)$ symmetry breaking quark interactions from vacuum polarization
• Momentum-dependence of $\rho -\omega$ mixing in the pion vector form factor and its effect on $(g-2{)}_{\mu }$
• Charged pions asymmetry from the decay of light neutral axial mesons due to interference