Finite S matrix

Abstract

When massless particles are involved, the traditional scattering matrix (S matrix) does not exist: It has no rigorous nonperturbative definition and has infrared divergences in its perturbative expansion. The problem can be traced to the impossibility of isolating single-particle states at asymptotic times. On the other hand, the troublesome nonseparable interactions are often universal: In gauge theories, they factorize so that the asymptotic evolution is independent of the hard scattering. Exploiting this factorization property, we show how a finite "hard"S matrix, SH, can be defined by replacing the free Hamiltonian with a soft-collinear asymptotic Hamiltonian. The elements of SH are gauge invariant and infrared finite and exist even in conformal field theories. One can interpret elements of SH alternatively 1) as elements of the traditional S matrix between dressed states, 2) as Wilson coefficients, or 3) as remainder functions. These multiple interpretations provide different insights into the rich structure of SH.