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Register a new userMaximum Wavelength of Confined Quarks and Gluons and Properties of Quantum Chromodynamics
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Because quarks and gluons are confined within hadrons, they have a maximum wavelength of order the confinement scale. Propagators, normally calculated for free quarks and gluons using Dyson-Schwinger equations, are modified by bound-state effects in close analogy to the calculation of the Lamb shift in atomic physics. Because of confinement, the effective quantum chromodynamic coupling stays finite in the infrared. The quark condensate which arises from spontaneous chiral symmetry breaking in the bound state Dyson-Schwinger equation is the expectation value of the operator $bar q q$ evaluated in the background of the fields of the other hadronic constituents, in contrast to a true vacuum expectation value. Thus quark and gluon condensates reside within hadrons. The effects of instantons are also modified. We discuss the implications of the maximum quark and gluon wavelength for phenomena such as deep inelastic scattering and annihilation, the decay of heavy quarkonia, jets, and dimensional counting rules for exclusive reactions. We also discuss implications for the zero-temperature phase structure of a vectorial SU($N$) gauge theory with a variable number $N_f$ of massless fermions.
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The variational Hamiltonian approach to Quantum Chromodynamics in Coulomb gauge is investigated within the framework of the canonical recursive Dyson--Schwinger equations. The dressing of the quark propagator arising from the variationally determined non-perturbative kernels is expanded and renormalized at one-loop order, yielding a chiral condensate compatible with the observations.
Asymptotic freedom of gluons in QCD is obtained in the leading terms of their renormalized Hamiltonian in the Fock space, instead of considering virtual Greens functions or scattering amplitudes. Namely, we calculate the three-gluon interaction term in the front-form Hamiltonian for effective gluons in the Minkowski space-time using the renormalization group procedure for effective particles (RGPEP), with a new generator. The resulting three-gluon vertex is a function of the scale parameter, $s$, that has an interpretation of the size of effective gluons. The corresponding Hamiltonian running coupling constant, $g_lambda$, depending on the associated momentum scale $lambda = 1/s$, is calculated in the series expansion in powers of $g_0 = g_{lambda_0}$ up to the terms of third order, assuming some small value for $g_0$ at some large $lambda_0$. The result exhibits the same finite sensitivity to small-$x$ regularization as the one obtained in an earlier RGPEP calculation, but the new calculation is simpler than the earlier one because of a simpler generator. This result establishes a degree of universality for pure-gauge QCD in the RGPEP.
We use perturbation theory to construct perfect lattice actions for quarks and gluons. The renormalized trajectory for free massive quarks is identified by blocking directly from the continuum. We tune a parameter in the renormalization group transformation such that for 1-d configurations the perfect action reduces to the nearest neighbor Wilson fermion action. The fixed point action for free gluons is also obtained by blocking from the continuum. For 2-d configurations it reduces to the standard plaquette action. Classically perfect quark and gluon fields, quark-gluon composite operators and vector and axial vector currents are constructed as well. Also the quark-antiquark potential is derived from the classically perfect Polyakov loop. The quark-gluon and 3-gluon perfect vertex functions are determined to leading order in the gauge coupling. We also construct a new block factor $n$ renormalization group transformation for QCD that allows to extend our results beyond perturbation theory. For weak fields it leads to the same perfect action as blocking from the continuum. For arbitrarily strong 2-d Abelian gauge fields the Manton plaquette action is classically perfect for this transformation.
The course begins with an introduction to the Standard Model, viewed as an effective field theory. Experimental and theoretical limits on the energy scales at which New Physics can appear, as well as current constraints on quark flavor parameters, are reviewed. The role of lattice QCD in obtaining these constraints is described. A second section is devoted to explaining the Cabibbo-Kobayashi-Maskawa mechanism for quark flavor mixing and CP violation, and to detailing its most salient features. The third section is dedicated to the study of K -> pi pi decays. It comprises discussions of indirect CP violation through K^0-bar K^0 mixing, of the Delta I=1/2 rule and of direct CP violation. It presents some of the lattice QCD tools required to describe these phenomena ab initio.
In this review article, we develop the perturbative framework for the calculation of hard scattering processes. We undertake to provide both a reasonably rigorous development of the formalism of hard scattering of quarks and gluons as well as an intuitive understanding of the physics behind the scattering. We emphasize the importance of logarithmic corrections as well as power counting of the strong coupling constant in order to understand the behavior of hard scattering processes. We include rules of thumb as well as official recommendations, and where possible seek to dispel some myths. Experiences that have been gained at the Fermilab Tevatron are recounted and, where appropriate, extrapolated to the LHC.
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