Abstract
The singular behaviour of QCD squared amplitudes in the collinear limit is factorized and controlled by splitting kernels with a process-independent structure. We use these kernels to define collinear functions that can be used in QCD resummation formulae of hard-scattering observables. Different collinear functions are obtained by integrating the splitting kernels over different phase-space regions that depend on the hard-scattering observables of interest. The collinear functions depend on an auxiliary vector nμ that can be either light-like (n2 = 0) or time-like (n2 > 0). In the case of transverse-momentum dependent (TMD) collinear functions, we show that the use of a time-like auxiliary vector avoids the rapidity divergences, which are instead present if n2 = 0. The perturbative computation of the collinear functions lead to infrared (IR) divergences that can be properly factorized with respect to IR finite functions that embody the logarithmically-enhanced collinear contributions to hard-scattering cross sections. We evaluate various collinear functions and their nμ dependence at \( \mathcal{O} \)(αS). We compute the azimuthal-correlation component of the TMD collinear functions at \( \mathcal{O}\left({\alpha}_{\textrm{S}}^2\right) \), and we present the results of the \( \mathcal{O}\left({\alpha}_{\textrm{S}}^2\right) \) contribution of linearly-polarized gluons to transverse-momentum resummation formulae. Beyond \( \mathcal{O}\left({\alpha}_{\textrm{S}}^2\right) \) the collinear functions of initial-state colliding partons are process dependent, as a consequence of the violation of strict collinear factorization of QCD squared amplitudes.
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Catani, S., Dhani, P.K. Collinear functions for QCD resummations. J. High Energ. Phys. 2023, 200 (2023). https://doi.org/10.1007/JHEP03(2023)200
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DOI: https://doi.org/10.1007/JHEP03(2023)200