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Register a new userQuantum Chromodynamics (CERN-2014-001)
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Scientific Information Service CERN
Publication date
2014
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and research's language is
English
Authors
Hsiang-nan Li
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I review the basics of perturbative QCD, including infrared divergences and safety, collinear and $k_T$ factorization theorems, and various evolution equations and resummation techniques for single- and double-logarithmic corrections. I then elaborate its applications to studies of jet substructures and hadronic two-body heavy-quark decays.
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Starting with the usual definitions of octonions, an attempt has been made to establish the relations between octonion basis elements and Gell-Mann lambda matrices of SU(3)symmetry on comparing the multiplication tables for Gell-Mann lambda matrices of SU(3)symmetry and octonion basis elements. Consequently, the quantum chromo dynamics (QCD) has been reformulated and it is shown that the theory of strong interactions could be explained better in terms of non-associative octonion algebra. Further, the octonion automorphism group SU(3) has been suitably handled with split basis of octonion algebra showing that the SU(3)_{C}gauge theory of colored quarks carries two real gauge fields which are responsible for the existence of two gauge potentials respectively associated with electric charge and magnetic monopole and supports well the idea that the colored quarks are dyons.
In the high density, low temperature limit, Quantum Chromodynamics exhibits a transition to phases characterized by color superconductivity and energy gaps in the fermion spectra. We review some fundamental results obtained in this area and in particular we describe the low energy effective lagrangian describing the motion of the quasi-particles in the high density medium (High Density Effective Theory).
Single-scale quantities, like the QCD anomalous dimensions and Wilson coefficients, obey difference equations. Therefore their analytic form can be determined from a finite number of moments. We demonstrate this in an explicit calculation by establishing and solving large scale recursions by means of computer algebra for the anomalous dimensions and Wilson coefficients in unpolarized deeply inelastic scattering from their Mellin moments to 3-loop order.
Using a technique devised by Bender, Milton and Savage, we derive the Dyson-Schwinger equations for quantum chromodynamics in differential form. We stop our analysis to the two-point functions. The t~Hooft limit of color number going to infinity is derived showing how these equations can be cast into a treatable even if approximate form. It is seen how this limit gives a sound description of the low-energy behavior of quantum chromodynamics by discussing the dynamical breaking of chiral symmetry and confinement, providing a condition for the latter. This approach exploits a background field technique in quantum field theory.
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