Joint Two-Dimensional Resummation in $q_T$ and $0$-Jettiness at NNLL

Abstract

We consider Drell-Yan production $pp\to Z/{\gamma }^{\ast }\to {\ell }^{+}{\ell }^{-}$ with the simultaneous measurement of the $Z$-boson transverse momentum $q_T$ and $0$-jettiness ${\mathcal{T}}_0$. Since both observables resolve the initial-state QCD radiation, the double-differential cross section in $q_T$ and ${\mathcal{T}}_0$ contains Sudakov double logarithms of both $q_T/Q$ and ${\mathcal{T}}_0/Q$, where $Q\sim m_Z$ is the dilepton invariant mass. We simultaneously resum the logarithms in $q_T$ and ${\mathcal{T}}_0$ to next-to-next-to-leading logarithmic order (NNLL) matched to next-to-leading fixed order (NLO). Our results provide the first genuinely two-dimensional analytic Sudakov resummation for initial-state radiation. Integrating the resummed double-differential spectrum with an appropriate scale choice over either ${\mathcal{T}}_0$ or $q_T$ recovers the corresponding single-differential resummation for the remaining variable. We discuss in detail the required effective field theory setups and their combination using two-dimensional resummation profile scales. We also introduce a new method to perform the $q_T$ resummation where the underlying resummation is carried out in impact-parameter space, but is consistently turned off depending on the momentum-space target value for $q_T$. Our methods apply at any order and for any color-singlet production process, such that our results can be systematically extended when the relevant perturbative ingredients become available.

arXiv comment43 pages + 10 pages in appendices, 20 figures; v2: journal version; references added, panel with fixed-order result added to figure 15; v3: fixed a typo (incorrect sign) in eq. (B.19)

References in corpus (82)

• PYTHIA 6.4 Physics and Manual
• PYTHIA 6.2 Physics and Manual
• An Introduction to PYTHIA 8.2
• Event generation with SHERPA 1.1
• Herwig++ Physics and Manual
• An effective field theory for collinear and soft gluons: heavy to light decays
• Soft-Collinear Factorization in Effective Field Theory
• The Three-Loop Splitting Functions in QCD: The Non-Singlet Case
• Herwig 7.0 / Herwig++ 3.0 Release Note
• An update on vector boson pair production at hadron colliders
• Summing Sudakov logarithms in B -> X_s + gamma in effective field theory
• The Three-Loop Splitting Functions in QCD: The Singlet Case
• Vector boson pair production at the LHC
• Invariant Operators in Collinear Effective Theory
• Hard Scattering Factorization from Effective Field Theory
• Soft-collinear effective theory and heavy-to-light currents beyond leading power
• The three-loop QCD $\beta$-function and anomalous dimensions
• Resummation of non-global QCD observables
• 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
• N-Jettiness: An Inclusive Event Shape to Veto Jets
• Thrust at N^3LL with Power Corrections and a Precision Global Fit for alphas(mZ)
• Factorization Theorem For Drell-Yan At Low q_T And Transverse-Momentum Distributions On-The-Light-Cone
• The Rapidity Renormalization Group
• Principles of general final-state resummation and automated implementation
• Factorization at the LHC: From PDFs to Initial State Jets
• Jets from Massive Unstable Particles: Top-Mass Determination
• Treating the b quark distribution function with reliable uncertainties
• Top Jets in the Peak Region: Factorization Analysis with NLL Resummation
• Away-from-jet energy flow
• Deep inelastic scattering as x -> 1 using soft-collinear effective theory
• Jet p_T Resummation in Higgs Production at NNLL'+NNLO
• Reparameterization Invariance for Collinear Operators
• The Quark Beam Function at NNLL
• Combining Higher-Order Resummation with Multiple NLO Calculations and Parton Showers in GENEVA
• Drell-Yan Production at NNLL'+NNLO Matched to Parton Showers
• Joint resummation in electroweak boson production
• An Effective Field Theory for Forward Scattering and Factorization Violation
• Resummation and NLO Matching of Event Shapes with Effective Field Theory
• An Effective Field Theory for Jet Processes
• Momentum-space resummation for transverse observables and the Higgs $p_{\perp }$ at N${}^3$LL+NNLO
• Logarithmic accuracy of parton showers: a fixed-order study
• Determining the Nonperturbative Collins-Soper Kernel From Lattice QCD
• The Quark Beam Function at Two Loops
• Recoil and Threshold Corrections in Short-distance Cross Sections
• Comparing and Counting Logs in Direct and Effective Methods of Resummation
• Enhanced Nonperturbative Effects in Z Decays to Hadrons
• Joint Resummation for Higgs Production
• Factorization and Resummation for Dijet Invariant Mass Spectra
• A new approach to the Higgs transverse-momentum resummation at NNLL+NNLO
• The Beam Thrust Cross Section for Drell-Yan at NNLL Order
• Resummation of Transverse Momentum Distributions in Distribution Space
• The Soft Function for Exclusive N-Jet Production at Hadron Colliders
• Non-Global Logarithms, Factorization, and the Soft Substructure of Jets
• Resummation of Double-Differential Cross Sections and Fully-Unintegrated Parton Distribution Functions
• Rapidity renormalized TMD soft and beam functions at two loops
• Fragmentation in Jets at NNLO
• Glauber Gluons and Multiple Parton Interactions
• Semi-numerical resummation of event shapes
• Non-perturbative QCD effects in $q_T$ spectra of Drell-Yan and $Z$-boson production
• Fully-Unintegrated Parton Distribution and Fragmentation Functions at Perturbative k_T
• Toward Multi-Differential Cross Sections: Measuring Two Angularities on a Single Jet
• Reparameterization Invariant Collinear Operators
• Unification of the $k_T$ and threshold resummations
• Problems in the resummation of soft-gluon effects in the transverse-momentum distributions of massive vector bosons in hadronic collisions
• Combining $Q_T$ and small-$x$ resummations
• Threshold and jet radius joint resummation for single-inclusive jet production
• Drell-Yan process with jet vetoes: breaking of generalized factorization
• Factorization and Resummation for Generic Hierarchies between Jets
• Transverse Momentum Distributions from Effective Field Theory with Numerical Results
• Rapidity-Dependent Jet Vetoes
• Joint transverse momentum and threshold resummation beyond NLL
• Phenomenology of single-inclusive jet production with jet radius and threshold resummation
• Combined threshold and transverse momentum resummation for inclusive observables
• Factorization for Jet Radius Logarithms in Jet Mass Spectra at the LHC
• Joint resummation of two angularities at next-to-next-to-leading logarithmic order
• Resummation Improved Rapidity Spectrum for Gluon Fusion Higgs Production
• The Fully-Differential Quark Beam Function at NNLO
• Transverse Vetoes with Rapidity Cutoff in SCET
• Integrated and Differential Accuracy in Resummed Cross Sections
• Soft Functions for Generic Jet Algorithms and Observables at Hadron Colliders
• Vector boson production in joint resummation

Cited by in corpus (29)

• 50 Years of Quantum Chromodynamics
• Transverse-momentum-dependent parton distributions up to N${}^3$LL from Drell-Yan data
• Drell-Yan $q_T$ Resummation of Fiducial Power Corrections at N${}^3$LL
• Higgs $p_T$ Spectrum and Total Cross Section with Fiducial Cuts at Third Resummed and Fixed Order in QCD
• A Toolbox for $q_T$ and $0$-Jettiness Subtractions at N${}^3$LO
• Higgs transverse momentum with a jet veto: a double-differential resummation
• The Energy-Energy Correlation in the back-to-back limit at N${}^3$LO and N${}^3$LL${}^{\prime }$
• Difficulties in the description of Drell-Yan processes at moderate invariant mass and high transverse momentum
• Matching NNLO to parton shower using N${}^3$LL colour-singlet transverse momentum resummation in GENEVA
• Higher-Order Sudakov Resummation in Coupled Gauge Theories
• Measurements of the Higgs boson inclusive and differential fiducial cross-sections in the diphoton decay channel with $pp$ collisions at $\sqrt{s}=13$ TeV with the ATLAS detector
• Quark beam function at next-to-next-to-next-to-leading order in perturbative QCD in the generalized large-$N_c$ approximation
• Disentangling Long and Short Distances in Momentum-Space TMDs
• Collinear expansion for color singlet cross sections
• Joint thrust and TMD resummation in electron-positron and electron-proton collisions
• One-loop matching for gluon lattice TMDs
• ChiliPDF: Chebyshev Interpolation for Parton Distributions
• Rapidity distribution at soft-virtual and beyond for n-colorless particles to N${}^4$LO in QCD
• Drell-Yan Transverse-Momentum Spectra at N${}^3$LL${}^{\prime }$ and Approximate N${}^4$LL with SCETlib
• Transverse Momentum Distributions of Heavy Hadrons and Polarized Heavy Quarks
• EFT for Soft Drop Double Differential Cross Section
• Analytic results for Sudakov form factors in QCD
• Prospects for strong coupling measurement at hadron colliders using soft-drop jet mass
• Spin correlations and Bell nonlocality in $\Lambda \bar{\Lambda }$ pair production from $e^{+}{e}^{-}$ collisions with a thrust cut
• A formalism for the resummation of non-factorizable observables in SCET
• Measurements of $Z\gamma +$jets differential cross sections in $pp$ collisions at $\sqrt{s}=13$ TeV with the ATLAS detector
• How much joint resummation do we need?
• N-jettiness in electroweak high-energy processes
• Nucleon Tomography with 0-jettiness