Finite Nc Research Articles

Non-global jet evolution at finite Nc

Resummations of soft gluon emissions play an important role in many applications of QCD, among them jet observables and small x saturation effects. For the case of non-global observables, Banfi, Marchesini, and Smye have cast the problem in terms of an evolution equation that exhibits a remarkable analogy with the BK equation used in the small x context. Here, this analogy is used to generalize the former beyond the leading N c approximation. The result shows striking analogy with the JIMWLK equation describing the small x evolution of the color glass condensate. A Langevin description allows numerical implementation and provides clues for the formulation of closed forms for amplitudes at finite N c . The proof of the new equation is based on amplitudes with ordered soft emission. It is fully independent of the derivation of the JIMWLK equation and thus sheds new light also on this topic.

Cutoff Dependence of Self-Consistent Solutions in Unquenched QED3

In the leading order of the 1/N expansion for the vacuum polarization, we obtain the chiral-symmetry-breaking solutions of the Schwinger-Dyson equation in three-dimensional QED with N four-component Dirac fermions. Special attention is paid on the critical number of the fermion flavor Nc and the scaling law for the dynamical fermion mass. In this framework we introduce the infrared cutoff as well as the ultraviolet one. We show the relation between the vertex ansatz and the scaling law which is consistent with our numerical results that the scaling law is affected by the infrared cutoff. Especially in the case of the Pennington and Webb's vertex ansatz, the mean-field type scaling law and cutoff-dependent finite Nc are obtained in the large infrared cutoff, while the exponential type scaling and infinite Nc are given in the sufficiently small infrared cutoff. The connection with the Monte Carlo simulation is discussed.

Cutoff Dependence of Self-Consistent Solutions in Unquenched QED3

In the leading order of the liN expansion for the vacuum polarization, we obtain the chiral­ symmetry-breaking solutions of the Schwinger-Dyson equation in three-dimensional QED with N four-component Dirac fermions. Special attention is paid on the critical number of the fermion flavor Nc and the scaling law for the dynamical fermion mass. In this framework we introduce the infrared cutoff as well as the ultraviolet one. We show the relation between the vertex ansatz and the scaling law which is consistent with our numerical results that the scaling law is affected by the infrared cutoff. Especially in the case of the Pennington and Webb's vertex ansatz, the mean-field type scaling law and cutoff-dependent finite Nc are obtained in the large infrared cutoff, while the exponential type scaling and infinite Nc are given in the sufficiently small infrared cutoff. The connection with the Monte Carlo simulation is discussed.