Abstract
Form factors for pions interactions with constituent quarks are investigated as the leading effective couplings obtained from a one loop background field method applied to a global color model. Two pion field definitions are considered and the resulting eleven form factors are expressed in terms of components of the quark and gluon propagators that compose only two momentum dependent functions. A momentum dependent Goldberger Treiman relation is also obtained as one of the ratios between the form factors. The resulting form factors with pion momenta up to 1.5 GeV are exhibited for different quark effective masses and two different non-perturbative gluon propagators and they present similar behavior to fittings of experimental data from nucleons form factors. The corresponding pseudoscalar averaged quadratic radii (a.q.r.) and correction to the axial a.q.r. are presented as functions of the sea quark effective mass, being equal respectively to the scalar and vector ones at the present level of calculation.
Highlights
The strong, electromagnetic and weak content of hadrons has been under continuous intense theoretical and experimental scrutiny
Pion-constituent quark momentum-dependent form factors were investigated from the one-loop background field method for the one nonperturbative gluon exchange quark interaction from the QCD effective action
Different values for the sea quark effective mass MÃ were considered and it mostly contributes for the overall normalization of the form factors
Summary
The strong, electromagnetic and weak content of hadrons has been under continuous intense theoretical and experimental scrutiny. Four further pion derivative couplings with scalar and pseudoscalar constituent quark currents that emerge at the same leading terms of the determinant expansion are presented They might contribute to the vector and axial channels. Besides that the corresponding strong quadratic radii of constituent quarks (scalar, pseudoscalar, vector, and axial) are presented as functions of the quark effective mass. By keeping the full momentum dependence of the resulting constituent quark—pion couplings the corresponding form factors are presented for the two definitions of the pion field . The corresponding contributions for the pseudoscalar and axial strong constituent quark quadratic radii are investigated as a functions of the quark effective mass for the different gluon propagators. Α 1⁄4 2=9 from the Fierz transformation, Rðx − yÞ was given in (4) and
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