Abstract
We systematically study the large-qT (or small-b) matching of transverse momentum dependent (TMD) distributions to the twist-2 integrated parton distributions. Performing operator product expansion for a generic TMD operator at the next-to-leading order (NLO) we found the complete set of TMD distributions that match twist-2. These are unpolarized, helicity, transversity, pretzelosity and linearly polarized gluon distributions. The NLO matching coefficients for these distributions are presented. The pretzelosity matching coefficient is zero at the presented order, however, it is evident that it is non-zero in the following orders. This result offers a natural explanation of the small value of pretzelosity found in phenomenological fits. We also demonstrate that the cancellation of rapidity divergences by the leading order soft factor imposes the necessary requirement on the Lorentz structure of TMD operators, which is supported only by the TMD distributions of leading dynamical twist. Additionally, this requirement puts restrictions on the γ5-definition in the dimensional regularization.
Highlights
The transverse momentum dependent (TMD) factorization theorems for semi-inclusive deep inelastic scattering (SIDIS) and Drell–Yan type processes formulated in [1,2,3,4] allow a consistent treatment of rapidity divergences in the definition of spindependent TMD distributions
While we have no knowledge of a calculation of the correction to the leading order of TMD factorization, our finding demonstrates that it has a different structure of rapidity divergences
To perform the matching we have evaluated the operator product expansion (OPE) of a generic TMD operator near the light-cone
Summary
The transverse momentum dependent (TMD) factorization theorems for semi-inclusive deep inelastic scattering (SIDIS) and Drell–Yan type processes formulated in [1,2,3,4] allow a consistent treatment of rapidity divergences in the definition of spin (in)dependent TMD distributions. In the δ-regularization scheme where R = 1/ S(b), the rapidity divergences take the form of ln δ and do not mix with divergences in , which yield the exact cancellation of ln δ at finite This non-trivial demand is necessary for a consistent higher--NLO evaluation and requires the matching of regularizations for different field modes (see [10]). It results into the correspondence between TMD processes and the jet production [16]. We present a uniform and consistent NLO matching of these TMD distributions
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