TMD fragmentation functions at N3LO
Markus Ebert (Max-Planck-Institut für Physik, Föhringer Ring 6, München, 80805, Germany, Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts, 02139, USA); Bernhard Mistlberger (SLAC National Accelerator Laboratory, Stanford University, Stanford, CA, 94039, USA); Gherardo Vita (SLAC National Accelerator Laboratory, Stanford University, Stanford, CA, 94039, USA, Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts, 02139, USA)
We compute the unpolarized quark and gluon transverse-momentum dependent fragmentation functions (TMDFFs) at next-to-next-to-next-to-leading order (N3LO) in perturbative QCD. The calculation is based on a relation between the TMDFF and the limit of the semi-inclusive deep inelastic scattering cross section where all final-state radiation becomes collinear to the detected hadron. The required cross section is obtained by analytically continuing our recent computation of the Drell-Yan and Higgs boson production cross section at N3LO expanded around the limit of all final-state radiation becoming collinear to one of the initial states. Our results agree with a recent independent calculation by Luo et al.