Ayse Kizilersu

Quark-gluon vertex from lattice QCD

The quark-gluon vertex in Landau gauge is studied in the quenched approximation using the Sheikholeslami-Wohlert (SW) fermion action with mean-field improvement coefficients in the action and for the quark fields. We see that the form factor that includes the running coupling is substantially enhanced in the infrared, over and above the enhancement arising from the infrared suppression of the quark propagator alone. We define two different momentum subtraction renormalisation schemes — MOM-tilde (asymmetric) and MOM-bar (symmetric) — and determine the running coupling in both schemes. We find ΛMS-barNf = 0 = 300+150−180 ± 55 ± 30 MeV from the asymmetric scheme. This is somewhat higher than other determinations of this quantity, but the uncertainties — both statistical and systematic — are large. In the symmetric scheme, statistical noise prevents us from obtaining a meaningful estimate for ΛMS-bar

One-loop QED vertex in any covariant gauge: Its complete analytic form

The one-loop vertex in QED is calculated in arbitrary covariant gauges as an analytic function of its momenta. The vertex is decomposed into a longitudinal part, which is fully responsible for ensuring that the Ward and Ward-Takahashi identities are satisfied, and a transverse part. The transverse part is decomposed into 8 independent components each being separately free of kinematic singularities in {ital any} covariant gauge in a basis that modifies that proposed by Ball and Chiu. Analytic expressions for all 11 components of the {ital O}({alpha}) vertex are given explicitly in terms of elementary functions and one Spence function. These results greatly simplify in particular kinematic regimes.

Building the Full Fermion-Photon Vertex of QED by Imposing Multiplicative Renormalizability of the Schwinger-Dyson Equations for the Fermion and Photon Propagators

In principle, calculation of a full Greens function in any field theory requires knowledge of the infinite set of multipoint Greens functions, unless one can find some way of truncating the corresponding Schwinger-Dyson equations. For the fermion and boson propagators in QED this requires an ansatz for the full 3-point vertex. Here we illustrate how the properties of gauge invariance, gauge covariance and multiplicative renormalizability impose severe constraints on this fermion-boson interaction, allowing a consistent truncation of the propagator equations. We demonstrate how these conditions imply that the 3-point vertex in the propagator equations is largely determined by the behavior of the fermion propagator itself and not by knowledge of the many higher-point functions. We give an explicit form for the fermion-photon vertex, which in the fermion and photon propagator fulfills these constraints to all orders in leading logarithms for massless QED, and accords with the weak coupling limit in perturbation theory at O({alpha}). This provides the first attempt to deduce nonperturbative Feynman rules for strong physics calculations of propagators in massless QED that ensure a more consistent truncation of the 2-point Schwinger-Dyson equations. The generalization to next-to-leading order and masses will be described in a longer publication.

Nonperturbative three-point vertex in massless quenched QED and perturbation theory constraints

Dong, Munczek, and Roberts have shown how the full 3-point vertex that appears in the Schwinger-Dyson equation for the fermion propagator can be expressed in terms of a constrained function

Instanton and eigenmodes in a two-dimensional theory of gravity with torsion☆

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Quark–gluon vertex in general kinematics

in massless quenched QED. However, this analysis involved two key assumptions: that the fermion anomalous dimension vanishes in the Landau gauge and that the transverse vertex has a simplified dependence on momenta. Here we remove these assumptions and find the general form for a new constrained function

Quark-gluon vertex in arbitrary kinematics

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Fractional Poisson processes and their representation by infinite systems of ordinary differential equations

that ensures the multiplicative renormalizability of the fermion propagator nonperturbatively. We then study the restriction imposed on

Does the weak coupling limit of the Burden-Tjiang deconstruction of the massless quenched three-dimensional QED vertex agree with perturbation theory?

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Lattice Landau gauge quark propagator and the quark-gluon vertex

by recent perturbative calculations of the vertex and compute its leading logarithmic expansion. Since