On the properties of the color dipoles in QCD

Abstract

In this paper I will undertake a detailed investigation of the local properties of the color dipoles, i.e. two color connected neighbours, in a QCD cascade. It is known that it is a good approximation (which incorporates in particular “the strong angular ordering conditions” corresponding to coherence) to treat the cascade as proceeding through repeated emission of gluons from such dipoles. The dipole motion reflects basically the motion of a Lund String, in which the gluons are treated as internal kink excitations on the string. Therefore a description of the local properties of the dipoles is basically a description of the behaviour of the String before fragmentation. My major findings are that the dipoles have a (logarithmic) size distribution which settles into a gaussian-like shape, that they show short-range correlations and that they have a multiplicity distribution similar to the blackbody radiation in QED. The dipoles in this description are not color neutral objects. The size of a dipole as used in this paper does, however, reflect the phase space region (at the given virtuality) inside which a color produced in the cascade is neutralised. It is interesting to note that the dipoles in a nonabelian field theory like QCD, which are close to “neutrality”, also behave very similar to the (neutral) photon field quanta in the abelian QED. The relative simplicity to describe the rather complex QCD cascades indicates that it may be worthwhile to try to quantise the theory in terms of such objects. I will use classical gain-loss considerations leading to first-order partial differential equations with simple solutions. I show the close relationship to the corresponding renormalisation group treatment in terms of Callan-Symanzik equations.