Extended hadrons, scaling variables and the poincaré group

Abstract

A convenient description of hadron states is presented by means of minimum-uncertainty wave packets in transverse internal position or momentum operators which can be defined in the infinite-momentum frame (IMF) basis for the Poincare group. The center of mass of the hadron is described either by its momentum or its IMF position operator, while its internal structure is fixed by taking coherent states symmetrical in the internal co-ordinates. The resulting physical picture of hadrons as extended objects with a stable structure agrees with Yang’s model of droplets with optimum universal size. The reduction of products of states in the infinite-momentum frame with respect to our basis introduces Clebsch-Gordan coefficients which asymptotically depend only on certain scaling variables, thus allowing us to trace their emergence to a general framework. These are precisely the scaling variables connected with different high-energy regions where limiting behavior patterns for hadronic cross-sections, like diffraction, Bjorken scaling, Feynman scaling and limiting fragmentation are known to occur.