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arXiv · 2012.07853

TMD Fragmentation Functions at N$^3$LO

Markus A. Ebert·Bernhard Mistlberger·Gherardo Vita
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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.

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Markus A. Ebert, Bernhard Mistlberger, Gherardo Vita. 2020-12-14. TMD Fragmentation Functions at N$^3$LO. https://doi.org/10.1007/jhep07(2021)121

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