Echevarria, Miguel G.Scimemi, IgnazioVladimirov, Aleksey2023-06-182023-06-182016-01-210556-282110.1103/PhysRevD.93.011502https://hdl.handle.net/20.500.14352/24395© 2016 American Physical Society. We thank Ahmad Idilbi and Takahiro Ueda for useful 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 Grant No. FPA2011-27853-CO2-02 andFPA2014-53375-C2-2-P. A. V. is supported in part by the European Community-Research Infrastructure Integrating Activity “Study of Strongly Interacting Matter” (HadronPhysics3, Grant Agreement No. 283286) and theSwedish Research Council, Grants No. 621-2011-5080 and No. 621-2013-4287.We calculate the unpolarized transverse momentum dependent fragmentation function at next-to-next-to-leading order, evaluating separately the transverse momentum dependent (TMD) soft factor and the TMD collinear correlator. For the first time, the cancellation of spurious rapidity divergences in a properly defined individual TMD beyond the first nontrivial order is shown. This represents a strong check of the given TMD definition. We extract the matching coefficient necessary to perform the transverse momentum resummation at next-to-next-to-next-to-leading-logarithmic accuracy. The universal character of the soft function, which enters the definition of all (un)polarized TMD distribution/fragmentation functions, facilitates the future calculation of all the other TMDs and their coefficients at next-to-next-to-leading order, pushing forward the accuracy of theoretical predictions for the current and next generation of high energy colliders.engjournal articlehttp://dx.doi.org/10.1103/PhysRevD.93.011502http://journals.aps.orgopen access53-71Parton distribution-functions3-loop splitting functionsExponentiationDistributionsNNLOQCD.Física (Física)22 Física