2015/11/30 by Miguel G. Echevarria, Miguel G. Echevarría, Ignazio Scimemi +1 · 142 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Deep inelastic scattering #Gluon #Hadron #High-Energy Particle Collisions Research #Inelastic scattering #Logarithm #Mathematical analysis #Multiplicity (mathematics) #Particle physics #Particle physics theoretical and experimental studies #Parton #Physics #Quantum chromodynamics #Quantum mechanics #Quark #Rapidity #Resummation #Scattering #hep-ph #hep-th
paper · pdf · doi:10.1103/physrevd.93.054004
published in Physical review. D/Physical review. D. 93(5) (American Physical Society) · 12 pages, 2 figures. v2: minor rewording, accepted for publication in PRD
openalex publication_date 2016/03/02 · arxiv created 2016/03/07 · arxiv updated 2016/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
All (un)polarized transverse momentum dependent functions (TMDs), both distribution and fragmentation functions, are defined with the same universal soft function, which cancels spurious rapidity divergences within an individual TMD and renders them well-defined hadronic quantities. Moreover, it is independent of the kinematics, whether it is Drell-Yan, deep inelastic scattering, or e+e^\ensuremath-\ensuremath→2 hadrons. In this paper, we provide this soft function at next-to-next-to-leading order (NNLO), necessary for the calculation of all TMDs at the same order, and to perform the resummation of large logarithms at next-to-next-to-next-to-leading-logarithmic accuracy. From the results we obtain the D function at NNLO, which governs the evolution of all TMDs. This work represents the first independent and direct calculation of this quantity. Given the all-order relation through a Casimir scaling between the soft function relevant for gluon TMDs and the one for quark TMDs, we also obtain the first at NNLO. The used regularization method to deal with the rapidity divergences is discussed as well.