TMD Fragmentation Functions at N$^3$LO

Ebert, Markus A.; Mistlberger, Bernhard; Vita, Gherardo

doi:10.1007/JHEP07(2021)121

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TMD Fragmentation Functions at N$^3$LO

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Ebert, Markus A.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Mistlberger, Bernhard
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Vita, Gherardo
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

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Citation

Ebert, M. A., Mistlberger, B., & Vita, G. (2021). TMD Fragmentation Functions at N$^3$LO. Journal of High Energy Physics, 07, 121. doi:10.1007/JHEP07(2021)121.

Cite as: https://hdl.handle.net/21.11116/0000-000A-1A44-D

Abstract

We compute the unpolarized quark and gluon transverse-momentum dependent fragmentation functions (TMDFFs) at next-to-next-to-next-to-leading order (N$^3$LO) 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 N$^3$LO 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.