Alexey Vladimirov: Structure of rapidity divergences at all perturbative orders
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Europe/Berlin
SR2 (DESY Hamburg)
SR2
DESY Hamburg
Description
We discuss the origin and structure of rapidity divergences, which arise in transverse momentum dependent (TMD) factorization formulas (i.e. SCET II regime). The separation of rapidity divergence related to different field modes is necessary to complete the factorization procedure and to define corresponding parton distributions (such as TMD distributions and double-parton distributions). We establish the correspondence between ultraviolet singularities of soft factors for multi-particle production and rapidity singularities of soft factors for multi-parton scattering. This correspondence is a consequence of a conformal mapping between scattering geometries. As a by-product, we obtain an exact relation between the rapidity anomalous dimension and the well-known soft anomalous dimension. With the help of this relation, we derive the three-loop rapidity anomalous dimensions for TMD and a general multi-parton scattering. Finally, we formulate and proof the (weak form of) rapidity divergence renormalization theorem, which completes TMD factorization formulas.
