Abstract
We compute the quark and gluon transverse momentum dependent parton distribution functions at next-to-next-to-next-to-leading order (N3LO) in perturbative QCD. Our calculation is based on an expansion of the differential Drell-Yan and gluon fusion Higgs production cross sections about their collinear limit. This method allows us to employ cutting edge multiloop techniques for the computation of cross sections to extract these universal building blocks of the collinear limit of QCD. The corresponding perturbative matching kernels for all channels are expressed in terms of simple harmonic polylogarithms up to weight five. As a byproduct, we confirm a previous computation of the soft function for transverse momentum factorization at N3LO. Our results are the last missing ingredient to extend the qT subtraction methods to N3LO and to obtain resummed qT spectra at N3LL′ accuracy both for gluon as well as for quark initiated processes.
Highlights
Where Bi is the so-called TMD beam function for a parton of flavor i, the sum runs over all parton flavors j, Iij is the perturbative matching kernel, and fj is the collinear PDF
We expand the diagrams for the Drell-Yan and gluon fusion Higgs boson production cross section at N3LO in the collinear limit
In ref. [57], we showed that the matching coefficient in eq (2.6) is obtained by taking the limit of eq (3.3) where all real and loop momenta are treated as being collinear to n-direction, which is referred as the strict n-collinear limit, and we refer to ref. [57] for details on its calculation: Iinjaive(z, qT ) =
Summary
We study the production of a color-singlet state h and an additional hadronic state X in a proton-proton scattering process,. Power corrections of O(qT2 /Q2) have been firstly calculated at fixed order in perturbation theory in ref. The corresponding partonic Born cross section is denoted by σ0, and the hard function Hab = 1 + O(αs) encodes virtual corrections to the Born process. It is natural to separately consider the calculation of the beam and soft functions appearing in eq (2.3), which can be combined into the TMDPDF if desired. Explicit definitions of the beam and soft functions in terms of gauge-invariant matrix elements formulated in SCET can be found in ref. We focus on TMD factorization in the perturbative regime b−T 1 ∼ qT ΛQCD, in which the TMD beam function and TMDPDF can be matched onto PDFs as [72]. The matching kernels Iij and IiTjMD are the objects of interest of this paper
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