The N${}^3$LO Twist-2 Matching of Linearly Polarized Gluon TMDs

Abstract

We compute the twist-2 matching of the transverse-momentum-dependent (TMD) linearly polarized gluon parton distribution and fragmentation functions at next-to-next-to-next-to-leading order (N${}^3$LO) in QCD, supplemented by next-to-next-to-leading logarithmic (NNLL) small-$x$ resummation for the gluon TMD fragmentation functions. These results provide high-precision fixed-order and resummed inputs to TMD phenomenology, and constitute essential theoretical ingredients for future studies of the spin structure and three-dimensional tomography of hadrons at the Electron-Ion Collider (EIC).

Comments: The normalization of linearly polarized gluon TMDs is corrected, an overall minus sign is added compared to original conventions; a typo of the value of the transverse scale b_0 is corrected