title: Correspondence between Soft and Rapidity Anomalous Dimensions.
abstract: We establish a correspondence between ultraviolet singularities of soft factors for multiparticle production and rapidity singularities of soft factors for multiparton scattering. This correspondence is a consequence of the conformal mapping between scattering geometries. The correspondence is valid to all orders of perturbation theory and in this way, provides one with a proof of rapidity renormalization procedure for multiparton scattering [including the transverse momentum dependent (TMD) factorization as a special case]. As a by-product, we obtain an exact relation between the rapidity anomalous dimension and the well-known soft anomalous dimension. The three-loop expressions for TMD and a general multiparton scattering rapidity anomalous dimension are derived.
authors.affiliation: Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany.
authors.forename: Alexey A
authors.initials: AA
authors.lastname: Vladimirov