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Register a new userTriple-gluon and quark-gluon vertex from lattice QCD in Landau gauge
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We report on preliminary results for the triple-gluon and the quark-gluon vertex in Landau gauge. Our results are based on two-flavor and quenched lattice QCD calculations for different quark masses, lattice spacings and volumes. We discuss the momentum dependence of some of the verticess form factors and the deviations from the tree-level form.
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In lattice QCD the computation of one-particle irreducible (1PI) Greens functions with a large number (> 2) of legs is a challenging task. Besides tuning the lattice spacing and volume to reduce finite size effects, the problems associated with the estimation of higher order moments via Monte Carlo methods and the extraction of 1PI from complete Greens functions are limitations of the method. Herein, we address these problems revisiting the calculation of the three gluon 1PI Greens function.
We address the interpretation of the Landau gauge gluon propagator at finite temperature as a massive type bosonic propagator. Using pure gauge SU(3) lattice simulations at a fixed lattice volume $sim(6.5fm)^3$, we compute the electric and magnetic form factors, extract a gluon mass from Yukawa-like fits, and study its temperature dependence. This is relevant both for the Debye screening at high temperature $T$ and for confinement at low $T$.
We study the quark-gluon vertex in the limit of vanishing gluon momentum using lattice QCD with 2 flavors of O(a) improved Wilson fermions, for several lattice spacings and quark masses. We find that all three form factors in this kinematics have a significant infrared strength, and that both the leading form factor $lambda_1$, multiplying the tree-level vertex structure, and the scalar, chiral symmetry breaking form factor $lambda_3$ are significantly enhanced in the infrared compared to the quenched (Nf=0) case. These enhancements are orders of magnitude larger than predicted by one-loop perturbation theory. We find only a weak dependence on the lattice spacing and quark mass.
We study the nonperturbative structure of the quark-photon vertex in Landau gauge. To this end, we utilize lattice QCD data for the vector current for two mass-degenerate quark flavours and extract all longitudinal and transverse form factors of the underlying vertex for two off-shell kinematics. The momentum dependence of the form factors is compared to the solution of the inhomogeneous Bethe-Salpeter equation for the vertex in the rainbow-ladder approximation. Differences but also similarities are seen between our lattice and the truncated continuum results.
The infrared behavior of the quark-gluon vertex of quenched Landau gauge QCD is studied by analyzing its Dyson-Schwinger equation. Building on previously obtained results for Green functions in the Yang-Mills sector we analytically derive the existence of power-law infrared singularities for this vertex. We establish that dynamical chiral symmetry breaking leads to the self-consistent generation of components of the quark-gluon vertex forbidden when chiral symmetry is forced to stay in the Wigner-Weyl mode. In the latter case the running strong coupling assumes an infrared fixed point. If chiral symmetry is broken, either dynamically or explicitely, the running coupling is infrared divergent. Based on a truncation for the quark-gluon vertex Dyson-Schwinger equation which respects the analytically determined infrared behavior numerical results for the coupled system of the quark propagator and vertex Dyson-Schwinger equation are presented. The resulting quark mass function as well as the vertex function show only a very weak dependence on the current quark mass in the deep infrared. From this we infer by an analysis of the quark-quark scattering kernel a linearly rising quark potential with an almost mass independent string tension in the case of broken chiral symmetry. Enforcing chiral symmetry does lead to a Coulomb type potential. Therefore we conclude that chiral symmetry breaking and confinement are closely related. Furthermore we discuss aspects of confinement as the absence of long-range van-der-Waals forces and Casimir scaling. An examination of experimental data for quarkonia provides further evidence for the viability of the presented mechanism for quark confinement in the Landau gauge.
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