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Universal transverse momentum dependent soft function at NNLO

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Echevarria, Miguel G. and Scimemi, Ignazio and Vladimirov, Aleksey (2016) Universal transverse momentum dependent soft function at NNLO. Physical Review D, 93 (5). ISSN 1550-7998

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Official URL: http://dx.doi.org/10.1103/PhysRevD.93.054004


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Abstract

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^−→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.


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Additional Information:

© 2016 American Physical Society.
A. V. thanks Victor Svensson for helpful discussions. M. G. E. is supported by the “Stichting voor Fundamenteel Onderzoek der Materie” (FOM), which is financially supported by the “Nederlandse Organisatie voor Wetenschappelijk Onderzoek” (NWO). I. S. is supported by the Spanish MECD Grants No. FPA2011-27853-CO2- 02 and No. FPA2014-53375-C2-2-P.

Uncontrolled Keywords:Drell-yan production; Parton distributions; Cross-sections; Renormalization; Exponentiation; Evolution; Loop.
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:37095
Deposited On:13 Apr 2016 18:43
Last Modified:10 Dec 2018 15:09

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