The N$^3$LO Twist-2 Matching of TMD Quark Transversity

Abstract

We present the first next-to-next-to-next-to-leading order (N$^3$LO) calculation of the twist-2 matching coefficients for transverse momentum dependent (TMD) quark transversity parton distribution and fragmentation functions in QCD. This matching relates the TMD quark transversity functions to their collinear counterparts in the large-transverse-momentum regime, and provides essential ingredients for precision TMD phenomenology involving transversely polarized beams. As part of our analysis, we derive the next-to-next-to-leading order (NNLO) DGLAP splitting functions for collinear transversity, confirming agreement with known space-like results for parton distribution functions and providing the new time-like splitting functions relevant for fragmentation functions. These results extend the perturbative toolkit for spin-dependent observables and establish the transversity sector on the same theoretical footing as unpolarized and helicity distributions. Our findings enable high-precision extractions of transversity PDFs and facilitate improved theoretical predictions for azimuthal asymmetries in semi-inclusive deep inelastic scattering (SIDIS), especially in light of forthcoming data from the Electron-Ion Collider (EIC).