Transverse momentum dependent distribution functions in the threshold limit

Abstract

We apply the joint threshold and transverse momentum dependent (TMD) factorization theorem to introduce new threshold-TMD distribution functions, including threshold-TMD parton distribution functions (PDFs) and fragmentation functions (FFs). We apply Soft-Collinear Effective Theory and renormalization group methods to carry out QCD evolution for both threshold-TMD PDFs and FFs. We show the universality of threshold-TMD functions among three standard processes, i.e. the Drell-Yan production in $pp$ collisions, semi-inclusive deep-inelastic scattering and back-to-back two hadron production in $e^{+}{e}^{-}$ collisions. In the end, we present the numerical predictions for different threshold-TMD functions and also transverse momentum distributions at $pp$, $ep$, and $e^{+}{e}^{-}$ collisions.

28 pages, 6 figures. Major update: A three-loop perturbative analysis has been added. Matches published version in JHEP

References in corpus (13)

• Drell-Yan production at small q_T, transverse parton distributions and the collinear anomaly
• Dynamical Threshold Enhancement and Resummation in Drell-Yan Production
• Unpolarized Transverse Momentum Distributions from a global fit of Drell-Yan and Semi-Inclusive Deep-Inelastic Scattering data
• Resummation of Double-Differential Cross Sections and Fully-Unintegrated Parton Distribution Functions
• Nonperturbative Determination of Collins-Soper Kernel from Quasi Transverse-Momentum Dependent Wave Functions
• The Four Loop QCD Rapidity Anomalous Dimension
• Transverse Parton Distribution and Fragmentation Functions at NNLO: the Gluon Case
• Joint resummation for slepton pair production at hadron colliders
• Kinematics of Current Region Fragmentation in Semi-Inclusive Deeply Inelastic Scattering
• Lattice Calculation of the Intrinsic Soft Function and the Collins-Soper Kernel
• Quark beam function at next-to-next-to-next-to-leading order in perturbative QCD in the generalized large-$N_c$ approximation
• Crossed Threshold Resummation
• Energy evolution of T-odd gluon TMDs at small $x$