Gluon Vertex Research Articles

E +e − annihilation in QCD - two specific problems

Two contributions are summarized. The first is on a QCD calculation of the triple energy correlation near the phase space limit. The second / author Z. Fodor/ is on methods for finding the triple gluon vertex already at 44 GeV.

The fate of the gluon in two dimensional space-time

The gluon propagator of QCD 2 with N f flavors of massless quarks in the light-cone is examined in the large N f limit. It is obtained from a set of identities for the gluon vertices based on the axial anomaly. The first and second order terms of a 1/ N f expansion of the two-point gluon vertex indicate that to each order the Fourier transform of the propagator has a branch point coinciding with its pole at the Schwinger mass. In contrast with QED 2, the gluon field has no massive component corresponding to a well-defined mass. A conjecture on the singularity structure of the full propagator us presented.

Studies of jet production rates ine + e ? annihilation atE cm=29 GeV

Production rates of multijet hadronic final states are studied ine + e − annihilation at 29 GeV center of mass energy. QCD shower model calculations with exact first order matrix element weighting at the first gluon vertex are capable of reproducing the observed multijet event rates over a large range of jet pair masses. The method used to reconstruct jets is well suited for directly comparing experimental jet rates with parton rates calculated in perturbative QCD. Evidence for the energy dependene of α s is obtained by comparing the observed production rates of 3-jet events with results of similar studies performed at higher center of mass energies.

Quantum Chromodynamics in 1+3 Dimensions at High Temperature: Dimensional Reduction Revisited

The gluon sector of QCD in 1+3 dimensions in analyzed at high temperature (much larger than the critical ones) thereby generalizing previous results by other authors. The imaginary time formalism is used. The analysis is carried out to all orders in an improved perturbation theory which includes all second-order internal quark loops in the “free” gluon propagators. General results are given for the leading high temperature contributions to all renormalized connected gluon Green's functions (for fixed external threemomenta, much smaller than the temperature). The latter are generated by a new (dimensionally reduced) high-temperature partition function ZHT, which corresponds to: i) the Yang-Mills (“magnetic”) gluon field coupled to a massive scalar (“electric”) gluon field, all in 3 spatial dimensions and at zero imaginary time, ii) the quark field, which continues to depend on imaginary time, coupled to the above gluon fields ZHT also depends on the renormalized quark masses and gauge coupling constant at zero temperature, the second order quark-loop contributions to the zero-temperature renormalization constants for the gluon field and the three and four gluon vertices and on new gluon mass terms. The latter correspond to a finite number of diagrams in the improved perturbation theory at high temperature. ZHT could be useful as the starting point for further non-perturbative studies. For the pure Yang-Mills plus ghosts theory (no quarks), it is conjectured that contributions to Green's functions depending on external momenta due to internal electric gluons could be regarded, as subdominant. Arguments are given in order to justify that conjecture. Then, the above ZHT can be simplified and another high-temperature generating functional depending only on magnetic gluon fields is given. For the full theory including quarks, the possibility of neglecting contributions due to internal quark loops is discussed: certain infrared divergences beyond the oneloop level appear to imply that such a simplification, although not discarded, is rather hard to establish.

Infrared asymptotics of gluon Green's functions in covariant gauge

It is considered whether the singular infrared behavior D(k) ∼ M2/k4 of the gluon propagator and the corresponding asymptotic behavior of the gluon vertices are compatible with the Schwinger-Dyson equation in a covariant gauge. For the investigated asymptotic behaviors, the two-loop terms most singular in the infrared region are calculated. It is shown that there exists a distinguished covariant gauge in which one can find a self-consistent description of the lowest gluon and ghost Green's functions in the infrared region of QCD.

New Coulomb-like gauge for massive gauge fields

The gauge independent renormalization prescription obtained from on-shell scattering of superheavy test particles is extended to the case of spontaneously broken gauge theories. We are led to a generalized Coulomb gauge for massive gauge fields implying the same simple Ward identity for the Coulomb gluon vertex as in the case of massless vector bosons. The derivation of this Ward identity will be simplified considerably by observing a parallel to the method of background field gauges. Gauge independent threshold effects of the β-function are illustrated in an SU(2) model.

One-loopN-point functions in the light-cone gauge

We consider, in the light-cone gauge, the possible structure of the counterterms arising in the solution to the renormalization equation. Using the structure of these counterterms and the noncovariant formalism of the integrals as guidelines, we also examine to one-loop order the divergence and nonlocality of theN-point gluon vertex functions forN≧5.

A Selective Experimental Review of the Standard Modela

Before disussing experimental comparisons with the Standard Model, (S-M) it is probably wise to define more completely what is commonly meant by this popular term. This model is a gauge theory of SU(3)/sub f/ x SU(2)/sub L/ x U(1) with 18 parameters. The parameters are ..cap alpha../sub s/, ..cap alpha../sub qed/, theta/sub W/, M/sub W/ (M/sub Z/ = M/sub W//cos theta/sub W/, and thus is not an independent parameter), M/sub Higgs/; the lepton masses, M/sub e/, M..mu.., M/sub r/; the quark masses, M/sub d/, M/sub s/, M/sub b/, and M/sub u/, M/sub c/, M/sub t/; and finally, the quark mixing angles, theta/sub 1/, theta/sub 2/, theta/sub 3/, and the CP violating phase delta. The latter four parameters appear in the quark mixing matrix for the Kobayashi-Maskawa and Maiani forms. Clearly, the present S-M covers an enormous range of physics topics, and the author can only lightly cover a few such topics in this report. The measurement of R/sub hadron/ is fundamental as a test of the running coupling constant ..cap alpha../sub s/ in QCD. The author will discuss a selection of recent precision measurements of R/sub hadron/, as well as some other techniques for measuring ..cap alpha../sub s/. QCD alsomore » requires the self interaction of gluons. The search for the three gluon vertex may be practically realized in the clear identification of gluonic mesons. The author will present a limited review of recent progress in the attempt to untangle such mesons from the plethora q anti q states of the same quantum numbers which exist in the same mass range. The electroweak interactions provide some of the strongest evidence supporting the S-M that exists. Given the recent progress in this subfield, and particularly with the discovery of the W and Z bosons at CERN, many recent reviews obviate the need for further discussion in this report. In attempting to validate a theory, one frequently searches for new phenomena which would clearly invalidate it. 49 references, 28 figures.« less

Efficient numerical techniques for perturbative lattice gauge theory computations

We discuss a set of methods and numerical tools, which are useful for a computer based approach to perturbative calculations in lattice gauge theory. The topics considered include the automatic generation of gluon vertex programs, a derivation of the Faddeev-Popov determinant on lattices with boundary, the use of a partially finite lattice with twisted boundary conditions as an infrared cutoff without zero modes, and finally the numerical extrapolation of lattice Feynman diagrams to the continuum limit. As an illustration of the methods we describe their implementation in the computation of the on-shell improved lattice action at weak coupling.

Solution of the renormalization group equation and ultraviolet asymptotics of gauge-dependent propagators in QCD

The general solution of the RGE for gluon vertices in massless QCD is obtained for arbitrary α. It is shown that, contrary to the view prevailing in the literature, the ultraviolet behaviour of gluon vertices is discontinuous both in the gauge-fixing parameter α and in the number of flavours.

Infrared properties of the glue propagator in non-abelian gauge theories

In a pure Yang-Mills theory, the Dyson equation for the gluon propagator is studied in the infrared regime, under the assumption that, as in QED, only those parts of the proper gluon vertex functions determined by the Ward identities are relevant. The calculations are all carried out in the axial gauge. With a number of simplifying assumptions the resulting integral equation for the gluon propagator can be solved in the IR regime. The solution displays a power singularity in the IR for the renormalized coupling constant g( q 2).

Second-class currents and very light quarks

We consider induced second-class nucleon currents in a light-quark model generated by unequal u and d quark masses. The effect produced by gluon vertex corrections is strikingly large without confinement effects. Restricting the quarks to the limited spatial region of a physical nucleon changes the energy scale from the quark mass to the quark bound-state energy and thereby reduces the second-class form factors well below their first-class counterparts. (AIP)