Constituent transverse-momentum fluctuations and the hard-scattering expansion

We show that the cross section for large-transverse-momentum reactions A+B→C+X can be expanded in terms of a sum of incoherent hard-scattering reactions where groups of interacting constituents have small transverse momenta relative to A, B, or C. The effects of large-transverse momentum of the constituents cannot be represented in terms of simple convolution integrals, but are correctly incorporated in terms of a sum of subprocesses which, in physical processes, usually correspond to nonleading terms. This hard-scattering expansion yields a series in inverse powers of →PT^_² in the case of φ³ field theory or the constituent-interchange model, and a series in inverse powers of log(logpT^_²) in the case of asymptotically free field theories.