Abstract
We compute the contribution of twist-2 and twist-3 parton distribution functions to the small-b expansion for transverse momentum dependent (TMD) distributions at all powers of b. The computation is done by the twist-decomposition method based on the spinor formalism for all eight quark TMD distributions. The newly computed terms are accompanied by the prefactor (M2b2)n and represent the target-mass corrections to the resummed cross-section. For the first time, a non-trivial expression for the pretzelosity distribution is derived.
Highlights
IntroductionFor many transverse momentum dependent (TMD) distributions already, the leading power matching involves twist-3 functions and requires a non-trivial computation
We compute the contribution of twist-2 and twist-3 parton distribution functions to the small-b expansion for transverse momentum dependent (TMD) distributions at all powers of b
We demonstrate that Wandzura-Wilczek-type terms produce only a small part of the kT -profile of TMD distributions, and the contribution of higher twist PDFs is essential
Summary
For many TMD distributions already, the leading power matching involves twist-3 functions and requires a non-trivial computation. [14], all polarized TMDPDFs were systematically computed in a single scheme, and the agreement with previous computations had been shown All these computations were unable to find the non-trivial matching of the pretzelosity distribution, which is derived for the first time in this work. We demonstrate that Wandzura-Wilczek-type terms produce only a small part of the kT -profile of TMD distributions, and the contribution of higher twist PDFs is essential. The leading power coefficient function for unpolarized distribution has been recently computed at N3LO [22, 23]. We derive only the tree order matching, ignoring the αs-suppressed terms in the coefficient functions. The operators with the collinear twist n can be presented as a sum of operators with different geometrical twists, n
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