Journal of High Energy Physics

, 2016:4 | Cite as

Unpolarized transverse momentum dependent parton distribution and fragmentation functions at next-to-next-to-leading order

  • Miguel G. Echevarria
  • Ignazio ScimemiEmail author
  • Alexey Vladimirov
Open Access
Regular Article - Theoretical Physics


The transverse momentum dependent parton distribution/fragmentation functions (TMDs) are essential in the factorization of a number of processes like Drell-Yan scattering, vector boson production, semi-inclusive deep inelastic scattering, etc. We provide a comprehensive study of unpolarized TMDs at next-to-next-to-leading order, which includes an explicit calculation of these TMDs and an extraction of their matching coefficients onto their integrated analogues, for all flavor combinations. The obtained matching coefficients are important for any kind of phenomenology involving TMDs. In the present study each individual TMD is calculated without any reference to a specific process. We recover the known results for parton distribution functions and provide new results for the fragmentation functions. The results for the gluon transverse momentum dependent fragmentation functions are presented for the first time at one and two loops. We also discuss the structure of singularities of TMD operators and TMD matrix elements, crossing relations between TMD parton distribution functions and TMD fragmentation functions, and renormalization group equations. In addition, we consider the behavior of the matching coefficients at threshold and make a conjecture on their structure to all orders in perturbation theory.


Perturbative QCD Renormalization Group Resummation Effective field theories 


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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Copyright information

© The Author(s) 2016

Authors and Affiliations

  • Miguel G. Echevarria
    • 1
  • Ignazio Scimemi
    • 2
    Email author
  • Alexey Vladimirov
    • 3
  1. 1.Departament de Física Quàntica i Astrofísica and Institut de Ciències del Cosmos, Universitat de BarcelonaBarcelonaSpain
  2. 2.Departamento de Física Teórica IIUniversidad Complutense de MadridMadridSpain
  3. 3.Institut für Theoretische PhysikUniversität RegensburgRegensburgGermany

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