The impact of transverse Slavnov-Taylor identities on dynamical chiral symmetry breaking
arXiv:2108.06204 · doi:10.1007/JHEP11(2021)196
Abstract
We extend earlier studies of transverse Ward-Fradkin-Green-Takahashi identities in QED, their usefulness to constrain the transverse fermion-boson vertex and their importance for multiplicative renormalizability, to the equivalent gauge identities in QCD. To this end, we consider transverse Slavnov-Taylor identities that constrain the transverse quark-gluon vertex and derive its eight associated scalar form factors. The complete vertex can be expressed in terms of the quark's mass and wave-renormalization functions, the ghost-dressing function, the quark-ghost scattering amplitude and a set of eight form factors. The latter parametrize the hitherto unknown nonlocal tensor structure in the transverse Slavnov-Taylor identity which arises from the Fourier transform of a four-point function involving a Wilson line in coordinate space. We determine the functional form of these eight form factors with the constraints provided by the Bashir-Bermudez vertex and study the effects of this novel vertex on the quark in the Dyson-Schwinger equation using lattice QCD input for the gluon and ghost propagators. We observe significant dynamical chiral symmetry breaking and a mass gap that leads to a constituent mass of the order of 500 MeV for the light quarks. The flavor dependence of the mass and wave-renormalization functions as well as their analytic behavior on the complex momentum plane is studied and as an application we calculate the quark condensate and the pion's weak decay constant in the chiral limit. Both are in very good agreement with their reference values.
Published version in JHEP which includes the chiral limit case in figure 6, typos corrected, improved discussion about transverse form factor ( and ) contributions on pages 21-22; 36 pages, 8 figures, 1 table
References in corpus (30)
- A refinement of the Gribov-Zwanziger approach in the Landau gauge: infrared propagators in harmony with the lattice results
- Gluon and ghost propagators in the Landau gauge: Deriving lattice results from Schwinger-Dyson equations
- Lattice gluodynamics computation of Landau-gauge Green's functions in the deep infrared
- Baryons as relativistic three-quark bound states
- Constraints on the IR behavior of the gluon propagator in Yang-Mills theories
- The quark-gluon vertex in Landau gauge QCD: Its role in dynamical chiral symmetry breaking and quark confinement
- Direct determination of the strange and light quark condensates from full lattice QCD
- Chiral symmetry breaking with lattice propagators
- Natural constraints on the gluon-quark vertex
- The quark-gluon vertex in Landau gauge bound-state studies
- Spectra of heavy mesons in the Bethe-Salpeter approach
- Correlation functions of Landau gauge Yang-Mills theory
- Building the Full Fermion-Photon Vertex of QED by Imposing Multiplicative Renormalizability of the Schwinger-Dyson Equations for the Fermion and Photon Propagators
- On light baryons and their excitations
- A new method for determining the quark-gluon vertex
- On gluon and ghost propagators in linear covariant gauges
- Does The Lattice Zero Momentum Gluon Propagator for Pure Gauge SU(3) Yang-Mills Theory Vanish in the Infinite Volume Limit?
- Quark-gluon vertex in general kinematics
- Exciting flavored bound states
- Landau gauge Yang-Mills propagators in the complex momentum plane
- Distribution Amplitudes of Heavy Mesons and Quarkonia on the Light Front
- The analytic structure of the lattice Landau gauge gluon and ghost propagators
- Quark-gluon vertex from Nf=2 lattice QCD
- The soft-gluon limit and the infrared enhancement of the quark-gluon vertex
- Transverse Symmetry Transformations and the Quark-Gluon Vertex Function in QCD
- Transverse Ward-Takahashi Relation for the Fermion-Boson Vertex Function in 4-dimensional QED
- How gauge covariance of the fermion and boson propagators in QED constrain the effective fermion-boson vertex
- The Podolsky propagator in gap and bound-state equations
- Gauge Symmetry and its Implications for the Schwinger-Dyson Equations
- Intrinsic Glue and Wilson lines within Dressed Quarks