Connecting Different TMD Factorization Formalisms in QCD

Abstract

In the original Collins-Soper-Sterman (CSS) presentation of the results of transverse-momentum-dependent (TMD) factorization for the Drell-Yan process, results for perturbative coefficients can be obtained from calculations for collinear factorization. Here we show how to use these results, plus known results for the quark form factor, to obtain coefficients for TMD factorization in more recent formulations, e.g., that due to Collins, and apply them to known results at order ${\alpha }_s^2$ and ${\alpha }_s^3$. We also show that the "non-perturbative" functions as obtained from fits to data are equal in the two schemes. We compile the higher-order perturbative inputs needed for the updated CSS scheme by appealing to results obtained in a variety of different formalisms. In addition, we derive the connection between both versions of the CSS formalism and several formalisms based in soft-collinear effective theory (SCET). Our work uses some important new results for factorization for the quark form factor, which we derive.

30 pages, 2 Figures; Fixed typos including missing term in Eq.(60)

References in corpus (40)

• Leading-twist Single-transverse-spin asymmetries: Drell-Yan and Deep-Inelastic Scattering
• A Formalism for the Systematic Treatment of Rapidity Logarithms in Quantum Field Theory
• Drell-Yan production at small q_T, transverse parton distributions and the collinear anomaly
• Tevatron Run-1 Z Boson Data and Collins-Soper-Sterman Resummation Formalism
• TMD Parton Distribution and Fragmentation Functions with QCD Evolution
• Factorization and Momentum-Space Resummation in Deep-Inelastic Scattering
• Calculation of the quark and gluon form factors to three loops in QCD
• Factorization Theorem For Drell-Yan At Low q_T And Transverse-Momentum Distributions On-The-Light-Cone
• The Rapidity Renormalization Group
• Proof of Factorization for Diffractive Hard Scattering
• Quark and gluon form factors to three loops
• Universality of non-leading logarithmic contributions in transverse-momentum distributions
• Bootstrapping rapidity anomalous dimension for transverse-momentum resummation
• Extraction of partonic transverse momentum distributions from semi-inclusive deep-inelastic scattering, Drell-Yan and Z-boson production
• Matches and mismatches in the descriptions of semi-inclusive processes at low and high transverse momentum
• Unpolarized Transverse Momentum Dependent Parton Distribution and Fragmentation Functions at next-to-next-to-leading order
• The Quark Form Factor at Higher Orders
• Vector boson production at hadron colliders: hard-collinear coefficients at the NNLO
• Calculation of the transverse parton distribution functions at next-to-next-to-leading order
• Jet p_T Resummation in Higgs Production at NNLL'+NNLO
• Universality of the Collins-Soper-Sterman nonperturbative function in gauge boson production
• Soft-/rapidity- anomalous dimensions correspondence
• Resummation of Threshold Logarithms in Effective Field Theory For DIS, Drell-Yan and Higgs Production
• Understanding the large-distance behavior of transverse-momentum-dependent parton densities and the Collins-Soper evolution kernel
• Investigations into the flavor dependence of partonic transverse momentum
• Transverse parton distribution functions at next-to-next-to-leading order: the quark-to-quark case
• Role of the nonperturbative input in QCD resummed Drell-Yan $Q_T$-distributions
• Collins and Sivers asymmetries in muonproduction of pions and kaons off transversely polarised proton
• The three-loop cusp anomalous dimension in QCD
• Analytic Results for Massless Three-Loop Form Factors
• The three-loop cusp anomalous dimension in QCD and its supersymmetric extensions
• Rapidity renormalized TMD soft and beam functions at two loops
• Equality of Two Definitions for Transverse Momentum Dependent Parton Distribution Functions
• An Overview of Transverse Momentum Dependent Factorization and Evolution
• Measurement of azimuthal asymmetries in inclusive charged dipion production in $e^{+}{e}^{-}$ annihilations at $\sqrt{s}$ = 3.65 GeV
• Jet axes and universal transverse-momentum-dependent fragmentation
• Analytic resummation for the quark form factor in QCD
• Twist-2 matching of transverse momentum dependent distributions
• Factorization and Resummation for Generic Hierarchies between Jets
• Collins asymmetries in inclusive charged $KK$ and $K\pi$ pairs produced in $e^{+}{e}^{-}$ annihilation

Cited by in corpus (36)

• Large-Momentum Effective Theory
• Parton distributions and lattice QCD calculations: toward 3D structure
• Transverse-momentum-dependent parton distributions up to N${}^3$LL from Drell-Yan data
• Quark Transverse Parton Distribution at the Next-to-Next-to-Next-to-Leading Order
• Unpolarized Transverse Momentum Distributions from a global fit of Drell-Yan and Semi-Inclusive Deep-Inelastic Scattering data
• Determining the Nonperturbative Collins-Soper Kernel From Lattice QCD
• Towards Quasi-Transverse Momentum Dependent PDFs Computable on the Lattice
• The x-dependence of hadronic parton distributions: A review on the progress of lattice QCD
• Lattice QCD Study of Transverse-Momentum Dependent Soft Function
• A Fixed-Target Programme at the LHC: Physics Case and Projected Performances for Heavy-Ion, Hadron, Spin and Astroparticle Studies
• Factorization connecting continuum and lattice TMDs
• Effect of flavor-dependent partonic transverse momentum on the determination of the $W$ boson mass in hadronic collisions
• Probing Transverse-Momentum Dependent Evolution With Groomed Jets
• Transverse-momentum-dependent wave functions and Soft functions at one-loop in Large Momentum Effective Theory
• Testing the universality of the Collins function in pion-jet production at RHIC
• Tomography of pions and protons via transverse momentum dependent distributions
• Sivers Asymmetry in Photoproduction of $J/\psi$ and Jet at the EIC
• Predictive power of transverse-momentum-dependent distributions
• Transverse Momentum Dependent Fragmentation Functions from recent BELLE data
• Universality-breaking effects in $e^{+}{e}^{-}$ hadronic production processes
• A new approach to semi-inclusive deep-inelastic scattering with QED and QCD factorization
• Factorization of $e^{+}{e}^{-}\to HX$ cross section, differential in $z_h$, $P_T$ and thrust, in the $2$-jet limit
• Combining nonperturbative transverse momentum dependence with TMD evolution
• Rapidity-only TMD factorization at one loop
• Matching generalised transverse-momentum-dependent distributions onto generalised parton distributions at one loop
• The resolution to the problem of consistent large transverse momentum in TMDs
• On the role of soft gluons in collinear parton densities and parton shower event generators
• Rapidity evolution of TMDs with running coupling
• Suppression of Spin Transfer to $\Lambda$ Hyperon in Deep-Inelastic Scattering
• Effect of nuclear medium on the spatial distribution of pions
• Tomography of the Rho meson in the QCD Instanton Vacuum: Transverse Momentum Dependent Parton Distribution Functions
• Factorized approach to radiative corrections for inelastic lepton-hadron collisions
• Central Instanton Production
• Non-perturbative uncertainties on the transverse momentum distribution of electroweak bosons and on the determination of the $W$ boson mass at the LHC
• Tomography of Pions and Kaons in the QCD Vacuum: Transverse Momentum Dependent Parton Distribution Functions
• Kinematic regions in the $e^{+}{e}^{-}\to hX$ factorized cross section in a $2$-jet topology with thrust