Abstract
To study meson properties, one needs to solve the gap equation for the quark propagator and the Bethe-Salpeter (BS) equation for the meson wavefunction, self-consistently. The gluon propagator, the quark-gluon vertex, and the quark--anti-quark scattering kernel are key pieces to solve those equations. Predicted by lattice-QCD and Dyson-Schwinger analyses of QCD's gauge sector, gluons are non-perturbatively massive. In the matter sector, the modeled gluon propagator which can produce a veracious description of meson properties needs to possess a mass scale, accordingly. Solving the well-known longitudinal Ward-Green-Takahashi identities (WGTIs) and the less-known transverse counterparts together, one obtains a nontrivial solution which can shed light on the structure of the quark-gluon vertex. It is highlighted that the phenomenologically proposed anomalous chromomagnetic moment (ACM) vertex originates from the QCD Lagrangian symmetries and its strength is proportional to the magnitude of dynamical chiral symmetry breaking (DCSB). The color-singlet vector and axial-vector WGTIs can relate the BS kernel and the dressed quark-gluon vertex to each other. Using the relation, one can truncate the gap equation and the BS equation, systematically, without violating crucial symmetries, e.g., gauge symmetry and chiral symmetry.
Highlights
The visible mass of the universe is mainly contributed by hadrons – bound states of fundamental blocks, i.e., quarks and gluons. Their dynamics is described by quantum chromodynamics (QCD) – the strong interaction sector of the Standard Model
It is believed that dynamical chiral symmetry breaking (DCSB) is responsible for the generation of mass from nothing, and the Higgs mechanism has almost nothing to do with the origin of the mass of the visible matter
Putting the non-perturbatively massive gluon into consideration, we proposed a realistic interaction model [5] as g2Dμν(k) = k2G(k2)Dfμrνee(k) = [k2GIR(k2) + αpQCD(k2)]Dfμrνee(k), (4)
Summary
The visible mass of the universe is mainly contributed by hadrons – bound states of fundamental blocks, i.e., quarks and gluons. Their dynamics is described by quantum chromodynamics (QCD) – the strong interaction sector of the Standard Model. QCD has two fascinating features: dynamical chiral symmetry breaking (DCSB) and confinement, which are not apparent in its Lagrangian. The fundamental degree of freedoms, i.e., quarks and gluons, are confined and cannot directly be detected. Neither DCSB nor confinement is understood perturbatively. The quark-gluon vertex, and the scattering kernel are specified, the two equations can be solved, and meson properties can be studied
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