Self-contained definition of the Collins-Soper kernel

Abstract

The rapidity anomalous dimension (RAD), or Collins-Soper kernel, defines the scaling properties of transverse momentum dependent distributions and can be extracted from the experimental data. I derive a self-contained nonperturbative definition that represents RAD without reference to a particular process. This definition makes possible exploration of the properties of RAD by theoretical methods on one side, and the properties of QCD vacuum with collider measurements on another side. To demonstrate these possibilities, I compute the power correction to RAD, its large-b asymptotic, and compare these estimations with recent phenomenological extractions.

5 pages, 3 figures; v2. minor changes, update to the journal version

References in corpus (8)

• Drell-Yan production at small q_T, transverse parton distributions and the collinear anomaly
• Momentum Flow Correlations from Event Shapes: Factorized Soft Gluons and Soft-Collinear Effective Theory
• Soft-/rapidity- anomalous dimensions correspondence
• Understanding the large-distance behavior of transverse-momentum-dependent parton densities and the Collins-Soper evolution kernel
• Extraction of unpolarized quark transverse momentum dependent parton distributions from Drell-Yan/Z-boson production
• Transverse momentum dependent factorization for lattice observables
• Non-perturbative contributions to vector-boson transverse momentum spectra in hadronic collisions
• Collinear matching for Sivers function at next-to-leading order

Cited by in corpus (34)

• Unpolarized Transverse Momentum Distributions from a global fit of Drell-Yan and Semi-Inclusive Deep-Inelastic Scattering data
• Drell-Yan $q_T$ Resummation of Fiducial Power Corrections at N${}^3$LL
• Precision Studies of QCD in the Low Energy Domain of the EIC
• Determination of the Collins-Soper Kernel from Lattice QCD
• The Four Loop QCD Rapidity Anomalous Dimension
• Extraction of the Sivers function from SIDIS, Drell-Yan, and $W^{\pm }/Z$ boson production data with TMD evolution
• PDF bias and flavor dependence in TMD distributions
• Computing Light-Front Wave Functions Without Light-Front Quantization: A Large-Momentum Effective Theory Approach
• Transverse momentum dependent operator expansion at next-to-leading power
• The Energy-Energy Correlation in the back-to-back limit at N${}^3$LO and N${}^3$LL${}^{\prime }$
• N${}^3$LO extraction of the Sivers function from SIDIS, Drell-Yan, and $W^{\pm }/Z$ data
• Lattice Calculation of the Intrinsic Soft Function and the Collins-Soper Kernel
• The $q_T$ and $\Delta \varphi$ spectra in W and Z production at the LHC at N${}^3$LL'+N${}^2$LO
• Quantum Simulation of Light-Front Parton Correlators
• High-Energy Factorization for Drell-Yan process in $pp$ and $p\bar{p}$ collisions with new Unintegrated PDFs
• Disentangling Long and Short Distances in Momentum-Space TMDs
• Transverse Momentum Dependent Fragmentation Functions from recent BELLE data
• Definition and evolution of transverse momentum dependent distribution of twist-three
• Drell-Yan Transverse-Momentum Spectra at N${}^3$LL${}^{\prime }$ and Approximate N${}^4$LL with SCETlib
• Quasi Transverse Momentum Dependent Distributions at Next-to-Next-to-Leading order
• Combining nonperturbative transverse momentum dependence with TMD evolution
• Transverse momentum moments
• Study of worm-gear-T function $g_{1T}$ with semi-inclusive DIS data
• Determination of the strong-coupling constant from the $Z$-boson transverse-momentum distribution
• Towards three-dimensional nucleon structures at the Electron-Ion Collider in China: A study of the Sivers function
• Measurement of the angle between jet axes in pp collisions at $\sqrt{s}=5.02$ TeV
• Transformation of transverse momentum distributions from Parton Branching to Collins-Soper-Sterman framework
• Nonlocal gluon condensates in QCD sum rules
• Operator product expansion for the non-local gluon condensate
• Collins-Soper Kernel in the QCD Instanton Vacuum
• Transverse momentum dependent distribution functions in the threshold limit
• Universality of the Collins-Soper kernel in lattice calculations
• Collins-Soper kernel from lattice QCD at the physical pion mass
• Revisiting the time-ordering issue of TMD soft factors: causality, coordinate space analyticity and new equalities