Quark Transverse Parton Distribution at the Next-to-Next-to-Next-to-Leading Order

We report a calculation of the perturbative matching coefficients for the transverse-momentum-dependent parton distribution functions for quark at the next-to-next-to-next-to-leading order in QCD, which involves calculation of non-standard Feynman integrals with rapidity divergence. We introduce a set of generalized Integration-By-Parts equations, which allows an algorithmic evaluation of such integrals using the machinery of modern Feynman integral calculation.
Comment: v1:5+19 pages, 2 figures; v2: references added; v3: fig. 3 added. journal version; v4: Coefficient for d33 in (A.13) corrected, fig. 2 updated, ancillary files updated, numerical fitting added