Power Counting Rules Research Articles

High-energy scattering in a two-dimensional gauge theory

We study high-energy scattering in two-dimensional quantum chromodynamics in the 1/ N colour expansion. To first order, high-energy forward scattering amplitudes are power-behaved with the factorization, signature and exchange degeneracy properties found in dual Regge models. Backward scattering has deviations from naive quark power-counting rules which are related to the form factor and “Regge” behaviours. In the second order of 1/ N colour vacuum exchange diagrams do not give a new Pomeron singularity, but do break exchange degeneracy.

New approach to the singularities of Feynman amplitudes in the zero-mass limit

We present an improved method for studying the behavior of Feynman amplitudes in the limit in which some or all of the masses of the internal lines vanish. Feynman amplitudes develop singularities in such a limit for certain configurations of external momenta. Our method enables us to determine these configurations, be they Euclidean or Minkowskian, on or off the mass shell. They are worked out explicitly in a few relatively simple cases which include most of the physically interesting singularities. Power-counting rules for these singularities are briefly discussed.

Perturbation calculations for the scalar multiplet in a superfield formulation

Based on the superfield propagators for the scalar multiplet, we investigate the occurence of divergence cancellations in supersymmetric models. This cancellation mechanism is governed by the Ward identity which has an integral form in the present formulation. The power counting rules for the actual divergence of diagrams in the models with a φ 3 and a φ 4 self-interaction are given. Finally we present a systematic treatment of the φ 4 model up to the two-loop level. The structure of the necessary counter terms is specified and the appearance of negative norm states is indicated.