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Rapidity renormalized TMD soft and beam functions at two loops

  • Thomas Lübbert
  • Joel OredssonEmail author
  • Maximilian Stahlhofen
Open Access
Regular Article - Theoretical Physics

Abstract

We compute the transverse momentum dependent (TMD) soft function for the production of a color-neutral final state at the LHC within the rapidity renormalization group (RRG) framework to next-to-next-to-leading order (NNLO). We use this result to extract the universal renormalized TMD beam functions (aka TMDPDFs) in the same scheme and at the same order from known results in another scheme. We derive recurrence relations for the logarithmic structure of the soft and beam functions, which we use to cross check our calculation. We also explicitly confirm the non-Abelian exponentiation of the TMD soft function in the RRG framework at two loops. Our results provide the ingredients for resummed predictions of p -differential cross sections at NNLL′ in the RRG formalism. The RRG provides a systematic framework to resum large (rapidity) logarithms through (R)RG evolution and assess the associated perturbative uncertainties.

Keywords

QCD Phenomenology 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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© The Author(s) 2016

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • Thomas Lübbert
    • 1
  • Joel Oredsson
    • 2
    • 3
    Email author
  • Maximilian Stahlhofen
    • 2
    • 4
  1. 1.II. Institute for Theoretical PhysicsUniversity of HamburgHamburgGermany
  2. 2.Theory Group, Deutsches Elektronen-Synchrotron (DESY)HamburgGermany
  3. 3.Department of Astronomy and Theoretical PhysicsLund UniversityLundSweden
  4. 4.PRISMA Cluster of Excellence, Institute of PhysicsJohannes Gutenberg UniversityMainzGermany

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