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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 (N3LO) in QCD. The N3LO 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 αs. Our results constitute important ingredients for precision determination of TMD PDFs and FFs in current and future experiments. [ABSTRACT FROM AUTHOR]

Abstract The transverse momentum (p T) distribution of Higgs bosons at hadron colliders enables a detailed probe of its production dynamics and is a key ingredient to precision studies of Higgs boson properties, but receives very large QCD corrections. We obtain a precision prediction for the p T spectrum by matching second-order (NNLO) QCD corrections at large p T with resummation of third-order logarithmic (N3LL) corrections at small p T. We achieve significantly improved results for p T < 35 GeV with perturbative uncertainties ≲ ± 6 % , and thus a convergent perturbative series for all values of p T. [ABSTRACT FROM AUTHOR]