Abstract
We calculate the matching of the transversity and pretzelosity transverse momentum dependent distributions (TMD) on transversity collinear distribution at the next-to-next-to-leading order (NNLO). We find that the matching coefficient for pretzelosity distribution is zero, despite the matrix element for it is nontrivial. This result suggests that the pretzelosity matches a twist-4 distribution. The matching for transversity TMD distributions is provided for both parton distribution functions and fragmentation functions cases.
Highlights
The structure of ultraviolet and rapidity divergences is independent of polarization, as it is predicted by transverse momentum dependent distributions (TMD) factorization theorem [2, 5], and confirmed by the present calculation
With the result of this work, the transversity distribution is evaluated at the same level of precision as the unpolarized distributions, and it is the first example of next-to-next-to-leading order (NNLO) evaluation of polarized distribution in the TMD factorization formalism
The transversely polarized TMD distribution is parameterized in terms of four TMD parton distribution functions (TMDPDFs), which were originally introduced in momentum space [32, 33]
Summary
Where index α is transverse and n is a light-like vector. The gauge links WnT (x) are rooted at the position x and continue to the infinity along the direction n. The transversely polarized TMD distribution is parameterized in terms of four TMD parton distribution functions (TMDPDFs), which were originally introduced in momentum space [32, 33]. In a longitudinally polarized operator there is mixture with gluons at leading twist and the γ5 cannot be dropped nor in definition nor in computations (see [31] for a discussion of the different schemes for γ5 used in a NLO calculation of the helicity distribution). The terms in eq (2.3) incorporate all tensor structures of the TMD distribution parametrization in eq (2.2). [31] it has been found that the 1-loop contribution to δ⊥C is zero in four dimensions, but it can be different from zero in dimensional regularization at order O( ). This observation suggests that potentially this contribution does not vanish at two-loop level
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