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Abstract
Following an earlier derivation by Catani, de Florian and Grazzini (2000) on the scheme dependence in the Collins–Soper–Sterman (CSS) resummation formalism in hard scattering processes, we investigate the scheme dependence of the Transverse Momentum Distributions (TMDs) and their applications. By adopting a universal C-coefficient function associated with the integrated parton distributions, the difference between various TMD schemes can be attributed to a perturbative calculable function depending on the hard momentum scale. We further apply several TMD schemes to the Drell–Yan process of lepton pair production in hadronic collisions, and find that the constrained non-perturbative form factors in different schemes are consistent with each other and with that of the standard CSS formalism.
Highlights
The Transverse Momentum Distributions (TMDs) and the nucleon tomography in momentum space have attracted strong interest in recent years [1, 2]
They unveil the strong interaction QCD dynamics in a manifest way, such as the gauge invariance leading to the sign change [3, 4] of certain TMDs in different hard scattering processes, and the QCD factorization and evolution which are crucial for predicting the scale dependence of the spin asymmetries
In the Ji-Ma-Yuan scheme (JMY) scheme, all three factors in Eq (17) depend on ρ, the final result for HT(DMYD) does not depend on ρ. This demonstrates that all the TMD factorization schemes are equivalent in the context of the CSS resummation formalism, which will be used in the phenomenological applications
Summary
The Transverse Momentum Distributions (TMDs) and the nucleon tomography in momentum space have attracted strong interest in recent years [1, 2]. TMDs provide a unique opportunity to investigate the novel correlations between the parton momentum and the nucleon spin They unveil the strong interaction QCD dynamics in a manifest way, such as the gauge invariance leading to the sign change [3, 4] of certain TMDs in different hard scattering processes, and the QCD factorization and evolution which are crucial for predicting the scale dependence of the spin asymmetries. All the TMD scheme dependence can be accounted for and the schemes can be unified and compared to the standard CSS resummation in description of the experimental data in phenomenological studies This unification provides an attractive interpretation for the CSS resummation, from which we have a clear TMD interpretation of the hard scattering processes.
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