Abstract
We describe the perturbative calculation of the transverse parton distribution functions in all partonic channels up to next-to-next-to-leading order based on a gauge invariant operator definition. We demonstrate the cancellation of light-cone divergences and show that universal process-independent transverse parton distribution functions can be obtained through a refactorization. Our results serve as the first explicit higher-order calculation of these functions starting from first principles, and can be used to perform next-to-next-to-next-to-leading logarithmic $q_T$ resummation for a large class of processes at hadron colliders.
Highlights
For most applications, the relevant factorization theorems are “collinear factorization” developed in [1,2,3]
We describe the perturbative calculation of the transverse parton distribution functions in all partonic channels up to next-to-next-to-leading order based on a gauge invariant operator definition
We demonstrate the cancellation of light-cone divergences and show that universal process-independent transverse parton distribution functions can be obtained through a refactorization
Summary
The relevant factorization theorems are “collinear factorization” developed in [1,2,3]. While the collinear PDFs are non-perturbative functions, their scale-dependence can be calculated perturbatively in terms of the DGLAP splitting kernels. These calculations have been performed up to 3 loops [6,7,8,9,10,11,12]. We will mainly be concerned with hadron collider physics, and will discuss TMD factorization and TPDFs for (unpolarized) Drell-Yan type processes in detail. Φi/N (x, μ) are the collinear PDFs with the longitudinal momentum fraction x They are non-perturbative functions describing physics at the hadronic scale ΛQCD.
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