Weak magnetic field corrections to pion and constituent quarks form factors

Abstract

A quark–quark interaction due to nonperturbative one gluon exchange is considered for the derivation of leading weak magnetic field induced anisotropic corrections to usual pion—constituent quarks form factors. Besides that, few chiral and isospin symmetry breaking effective couplings which emerge only due to the weak magnetic field are also found. Numerical estimations for these magnetic field corrections are presented. All of these corrections are ultraviolet finite and their relative values are found to be of order of being n = 1 for the vector and axial pion couplings and n = 2 for the pseudoscalar and scalar ones. The corresponding anisotropic corrections to the constituent quark and pion strong averaged quadratic radii in the plane perpendicular to the magnetic field are also calculated as functions of the quark effective mass.

Strangeness content of the pion in the U(3) Nambu–Jona–Lasinio model

“…By considering the quark propagator with the electromagnetic quark coupling, the relations (3) are preserved. This gauge invariance has the same roots of the description in terms of the auxiliary fields to describe electromagnetic couplings of charged mesons and their resulting couplings with (background) constituent quarks analyzed in [44,[50][51][52]. In the limit of degenerate quark effective masses, M u = M d = M s , the coupling constants reduce to a single constant that, as discussed below, will be normalized to be the coupling constant of reference G 0 such that G i j → G 0 δ i j , and the standard treatment of the model can be done.…”