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In this paper we calculate analytically the perturbative matching coefficients for unpolarized quark and gluon Transverse-Momentum-Dependent (TMD) Parton Distribution Functions (PDFs) and Fragmentation Functions (FFs) through Next-to-Next-to-Next-to-Leading Order (N$^3$LO) in QCD. The N$^3$LO TMD PDFs are calculated by solving a system of differential equation of Feynman and phase space integrals. The TMD FFs are obtained by analytic continuation from space-like quantities to time-like quantities, taking into account the probability interpretation of TMD PDFs and FFs properly. The coefficient functions for TMD FFs exhibit double logarithmic enhancement at small momentum fraction $z$. We resum such logarithmic terms to the third order in the expansion of $alpha_s$. Our results constitute important ingredients for precision determination of TMD PDFs and FFs in current and future experiments.
We compute the unpolarized quark and gluon transverse-momentum dependent fragmentation functions (TMDFFs) at next-to-next-to-next-to-leading order (N$^3$LO) in perturbative QCD. The calculation is based on a relation between the TMDFF and the limit o
We compute the quark and gluon transverse momentum dependent parton distribution functions at next-to-next-to-next-to-leading order (N$^3$LO) in perturbative QCD. Our calculation is based on an expansion of the differential Higgs boson and Drell-Yan
In the TMD approach, the average transverse momentum of the unpolarised TMD PDFs and FFs is crucial not only to reproduce unpolarised cross sections and hadron multiplicities, but also for the understanding of azimuthal and spin asymmetries. Informat
We present the analytic formula for the Energy-Energy Correlation (EEC) in electron-positron annihilation computed in perturbative QCD to next-to-next-to-next-to-leading order (N$^3$LO) in the back-to-back limit. In particular, we consider the EEC ar
We present a comprehensive impact study of future Electron-Ion Collider (EIC) data for parity-conserving and parity-violating polarization asymmetries on quark and gluon helicity distributions in the proton. The study, which is based on the JAM Monte