Abstract
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.
Highlights
The fragmenting parton [1,2,3,4]
The calculation is based on a relation between the transverse-momentum dependent fragmentation functions (TMDFFs) 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
Summary
We study cross sections for the production of a hadron H in DIS alongside additional radiation, which we indicate as a multiparticle state X. We focus on the hadronic part of the DIS cross section that is initiated by the scattering of a proton with momentum P1 and an electro-weak boson h with the space-like momentum q,. We take all momenta to be incoming This process is schematically depicted in figure 1 for the example of a virtual photon as the electro-weak gauge boson. The overall normalization σ0 is the Born cross section and the sum runs over parton flavors i, j. In eq (2.6), the sum runs over the number m of additional partons in the final state besides the parton of flavor j that fragments into the hadron H, and Φ1+m is the associated m + 1parton phase space. The δ functions implement the measurements of ξ and O, and the squared matrix element |Mi+h→j+m|2 corresponds to the partonic process of producing the m + 1 partons in the collision of a parton of flavor i with the hard probe h
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