Fragmentation in aφ3-Theory Ladder Model

Abstract

We study the inclusive reaction a + b -c + (anything), where all the particles belong to a single scalar field @ ( x ) interacting through a g @~~( x ) term. We do this in a ladder model for the forward a b c -abE process, whose amplitude is intimately related to the inclusive distribution. The choice of the infinite sequence of ladder diagrams as well as the assumptions involved are natural extensions of analogous work in the literature for four-point functions.In the fragmentation limit, the model yields the expected Regge behavior as the initial energy tends to infinity. An expression is derived for the limiting distribution function E , do/ d& for fixed 6, as s + m. The results are derived both in the "leading-term approximation" as well as by an exact Mellin-transform method.

Effective kink-kink interaction in a one-dimensional model mediated by phonon exchange

“…In comparison to this interaction the direct interaction which decays exponential [12] can be neglected. We stress that the leading asymptotic term of the x dependence of u(x) is determined by the quartic anharmonicity only.…”

“…In case of one dimension all analytical results concerning the dynamics of the domain walls (multikink dynamics) were obtained in the framework of an ideal-gas phenomenology [2][3][4]6,9]. There, the direct interaction between kinks does not play a crucial role due to its exponential decay [12]. Furthermore it was shown that the kink-phonon interaction results in a renormalization of either the phonon density of states [3] or the kink density [6].…”