Non-perturbative Analysis of Various Mass Generation by Gluonic Dressing Effect with the Schwinger-Dyson Formalism in QCD

As a topic of "quantum color dynamics", we study various mass generation of colored particles and gluonic dressing effect in a non-perturbative manner, using the Schwinger-Dyson (SD) formalism in (scalar) QCD. First, we review dynamical quark-mass generation in QCD in the SD approach as a typical fermion-mass generation via spontaneous chiral-symmetry breaking. Second, using the SD formalism for scalar QCD, we investigate the scalar diquark, a bound-state-like object of two quarks, and its mass generation, which is clearly non-chiral-origin. Here, the scalar diquark is treated as an extended colored scalar field, like a meson in effective hadron models, and its effective size $R$ is introduced as a form factor. As a diagrammatical difference, the SD equation for the scalar diquark has an additional 4-point interaction term, in comparison with the single quark case. The diquark size $R$ is taken to be smaller than a hadron, $R\sim 1$ fm, and larger than a constituent quark, $R\sim 0.3$ fm. We find that the compact diquark with $R\simeq 0.3$ fm has a large effective mass of about 900 MeV, and therefore such a compact diquark is not acceptable in effective models for hadrons. We also consider the artificial removal of 3- and 4-point interaction, respectively, to see the role of each term, and find that the 4-point interaction plays the dominant role of the diquark self-energy. From the above two different cases, quarks and diquarks, we guess that the mass generation of colored particles is a general result of non-perturbative gluonic dressing effect.Comment: 17 pages, 15 figure

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

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.Comment: 16 pages, 11 figures. arXiv admin note: text overlap with arXiv:1401.285

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

We calculate the scalar, axial, and pseudoscalar charges of the quark in the Schwinger-Dyson formalism of Landau gauge QCD. It is found that the dressed quark scalar density of the valence quark is significantly enhanced against the bare quark contribution, and the result explains qualitatively the phenomenologically known value of the pion-nucleon sigma term and also that given by lattice QCD. Moreover, we show that the Richardson's interquark potential suppresses the quark scalar density in the Higashjima-Miransky approximation. This fact suggests that the quark scalar density is an observable that is sensitive to quark confinement. For the quark axial charge, we find that it is suppressed due to the gluon dynamics. The result of the quenched analysis agrees qualitatively with the experimental data of the isovector axial coupling constant $g_A$. We show that the suppression of the quenched axial charge is due to a mechanism similar to that of the quark tensor charge. In the Schwinger-Dyson equation with the leading unquenching quark-loop contribution the quark axial charge is more suppressed, due to the anomaly effect. The quark pseudoscalar density is found to be large, and is divergent as the bare quark becomes massless. This result is in agreement with the phenomenological current algebraic analysis, and explains well the dominance of the pion-pole contribution.Comment: 28 pages, 22 figure

A Numerical Method for Distinction between Blow-up and Global Solutions of the Nonlinear Heat Equation

The famous one-dimensional nonlinear heat equation is considered. To this equation a numerical method for distinction between blow-up and global solutions is proposed. Difficulty is in the treatment of the global solution which is defined in the infinite interval. The bounding transform is used to overcome this difficulty. Numerical experiments show the validity of our method