An Exclusive Soft Function for Drell-Yan at Next-to-Next-to-Leading Order

Abstract

We present next-to-next-to-leading-order (NNLO) results for an exclusive soft function that appears in a recently developed factorization theorem for transverse momentum distributions. The factorization theorem, derived using the Soft Collinear Effective Theory, involves both a soft function and unintegrated nucleon distribution functions fully differential in momentum coordinates. The soft function is given by the vacuum matrix element of soft Wilson lines and is also fully differential in all components. We give results and relevant technical details for the NNLO calculation of the soft function, including finite parts, and derive the corresponding anomalous dimension. These results are necessary for achieving low transverse momentum resummation at next-to-next-to-leading-logarithmic accuracy in this effective field theory approach with unintegrated distribution functions.

20 pages, 1 figure

References in corpus (22)

• Drell-Yan production at small q_T, transverse parton distributions and the collinear anomaly
• TMD Parton Distribution and Fragmentation Functions with QCD Evolution
• The Zero-Bin and Mode Factorization in Quantum Field Theory
• Jets from Massive Unstable Particles: Top-Mass Determination
• Top Jets in the Peak Region: Factorization Analysis with NLL Resummation
• Production of Drell--Yan lepton pairs in hadron collisions: transverse-momentum resummation at next-to-next-to-leading logarithmic accuracy
• Momentum Flow Correlations from Event Shapes: Factorized Soft Gluons and Soft-Collinear Effective Theory
• Two-Loop Soft Corrections and Resummation of the Thrust Distribution in the Dijet Region
• The two-loop hemisphere soft function
• Resummation and NLO Matching of Event Shapes with Effective Field Theory
• Designing Gapped Soft Functions for Jet Production
• What exactly is a parton density?
• Non-global Structure of the O(α_s^2) Dijet Soft Function
• Wilson lines and transverse-momentum dependent parton distribution functions: A renormalization-group analysis
• Endpoint singularities in unintegrated parton distributions
• Renormalization, Wilson lines, and transverse-momentum dependent parton distribution functions
• Resummation of Large Endpoint Corrections to Color-Octet J/psi Photoproduction
• Singular and Regular Gauges in Soft Collinear Effective Theory: The Introduction of the New Wilson Line T
• On The Equivalence of Soft and Zero-Bin Subtractions
• SCET, Light-Cone Gauge and the T-Wilson Lines
• Transverse Momentum Distributions from Effective Field Theory with Numerical Results
• Transverse Momentum Distributions in the Non-Perturbative Region

Cited by in corpus (25)

• Bootstrapping rapidity anomalous dimension for transverse-momentum resummation
• Two-Loop Soft Corrections and Resummation of the Thrust Distribution in the Dijet Region
• Analytic Regularization in Soft-Collinear Effective Theory
• The Universal Transverse Momentum Dependent Soft Function at NNLO
• Calculating the Charge of a Jet
• NNLL Resummation for Jet Broadening
• Leading-logarithmic threshold resummation of the Drell-Yan process at next-to-leading power
• Leading-color fully differential two-loop soft corrections to QCD dipole showers
• Forward Z-boson production and the unintegrated sea quark density
• Threshold factorization of the Drell-Yan process at next-to-leading power
• The Four Loop QCD Rapidity Anomalous Dimension
• A Toolbox for $q_T$ and $0$-Jettiness Subtractions at N${}^3$LO
• Two-loop anomalous dimensions of generic dijet soft functions
• SCET approach to regularization-scheme dependence of QCD amplitudes
• Generic dijet soft functions at two-loop order: correlated emissions
• Joint transverse momentum and threshold resummation beyond NLL
• The two-loop soft function for heavy quark pair production at future linear colliders
• Next-to-leading power threshold corrections for finite order and resummed colour-singlet cross sections
• Evolution of cusped light-like Wilson loops and geometry of the loop space
• Automated Calculation of Dijet Soft Functions in Soft-Collinear Effective Theory
• Spin correlations and Bell nonlocality in $\Lambda \bar{\Lambda }$ pair production from $e^{+}{e}^{-}$ collisions with a thrust cut
• Transverse-Distance Dependent Parton Densities in the Large-$x$ Regime
• Geometry of gauge links in operator definitions of transverse-momentum dependent PDFs: A comparative view
• Next-to-leading power two-loop soft functions for the Drell-Yan process at threshold
• Phenomenology of electro-weak bosons at hadron colliders with novel variables