The Gluon Emission Model for Vector Meson Decay

Abstract

Quantum Chromodynamics (QCD), the heart of the so-called Standard Model, was developed along the lines of the most successful theoretical structure in all of physics, namely, Quantum Electrodynamics (QED), which represents the interactions between the electron and the electromagnetic field, photons serving as the mediator between the two entities. QCD, therefore, contains many objects which are analogous to those within QED. There are the quarks, for example, which come in six “flavors” (up, down, strange, charm, bottom, top), serving as the analogous construct to the electron and its cousins, the muon and the tauon. Plexiformation, of course, always accompanies the proceeding by analogy to any theory, and so we find that quarks must come not only in flavors, but also in “colors” (three total), and they must be fractionally charged (one or two thirds of the electron charge in absolute value). What mediates the quark and the strong field, analogous to the photon in QED, is the gluon. In QED all quantum events are described by a coupling between the electron and the photon, called the fine structure constant of magnitude approximately 0.007. Regarding the coupling between quarks and the strong field responsible for hadronization ... the production of hadron pairs in a colliding beams experiment, for example ... the situation in QCD is quite different. Work continues at present in the field of high-energy physics to determine the precise nature of the quark-gluon coupling, but one overarching behavior pattern of such coupling, called the strong coupling, is that it is not a constant. Rather, it varies generally as the reciprocal of the natural logarithm of the energy wrapped up in the colliding beams. In the work which follows we will have occasion to investigate the phenomenon of vector meson formation and decay in accord with a QCD model, called the Gluon Emission Model (GEM), first developed by F. E. Close in the 1970s. The GEM follows rigorously the precepts of QED proper, the only QCD quantity entering into the calculations being the strong coupling parameter, which replaces the fine structure constant in the relevant places. The GEM thus provides for a self-contained formalism that follows the constructs of QED essentially as closely as is possible at the present time. As we will see, even the precise form for the strong coupling parameter may be determined within the GEM, the valid range