Quark tensor charge and electric dipole moment within the Schwinger-Dyson formalism

Abstract

We calculate the tensor charge of the quark in the QCD-like theory in the Landau gauge using the Schwinger-Dyson formalism. It is found that the dressed tensor charge of the quark is significantly suppressed against the bare quark contribution, and the result agrees qualitatively with the analyses in the collinear factorization approach and lattice QCD. We also analyze the quark confinement effect with the phenomenological strong coupling given by Richardson, and find that this contribution is small. We show that the suppression of the quark tensor charge is due to the superposition of the spin flip of the quark arising from the successive emission of gluons which dress the tensor vertex. We also consider the relation between the quark and the nucleon electric dipole moments by combining with the simple constituent quark model.

Quark scalar, axial, and pseudoscalar charges in the Schwinger-Dyson formalism

“…This means that the gluon-dressed axial vertex is decomposed into terms which alternate in sign in the perturbative expansion. The calculation of the quark tensor charge exhibits a similar behavior [39]. This result shows that the reversal of the quark spin is preferred in gluon emission/absorption.…”

“…We have tested the contribution of the S 1 and S 2 functions through a fictitious manipulation by setting S 2 (p 2 ) = 0 when solving the SDE (13) and (14). This approximation was tested previously in the analysis of the quark tensor charge, and the reduction of the SDE was successful within a few percent [39]. The result is plotted in Fig.…”

“…One of the main candidates is the spin-dependent interactions of the quarks. The explanation of the suppression of the single quenched (isovector) quark axial charge is similar to the mechanism of the suppression of the single quark tensor charge [39]. We now look at the quark axial charge obtained after a few iterations.…”

“…This manipulation has also been used for the estimation of the quark tensor charge [39]. Qualitatively, the result of Eq.…”

“…We use the Schwinger-Dyson (SD) formalism as a powerful nonperturbative way to investigate the dynamics of quantum field theory and in particular low energy QCD; many quantities have been investigated using this technique, such as the dynamical quark mass, the meson masses, etc [28][29][30][31][32][33][34][35][36][37][38][39]. In a previous work, we calculated the effect of the gluon dressing on the single quark tensor charge and showed that the gluon dressing suppresses the tensor charge of the bare quark, due to the superposition of states with spin-flipped quarks.…”