Resummation of Transverse Momentum Distributions in Distribution Space

Abstract

Differential spectra in observables that resolve additional soft or collinear QCD emissions exhibit Sudakov double logarithms in the form of logarithmic plus distributions. Important examples are the total transverse momentum $q_T$ in color-singlet production, N-jettiness (with thrust or beam thrust as special cases), but also jet mass and more complicated jet substructure observables. The all-order logarithmic structure of such distributions is often fully encoded in differential equations, so-called (renormalization group) evolution equations. We introduce a well-defined technique of distributional scale setting, which allows one to treat logarithmic plus distributions like ordinary logarithms when solving these differential equations. In particular, this allows one (through canonical scale choices) to minimize logarithmic contributions in the boundary terms of the solution, and to obtain the full distributional logarithmic structure from the solution's evolution kernel directly in distribution space. We apply this technique to the $q_T$ distribution, where the two-dimensional nature of convolutions leads to additional difficulties (compared to one-dimensional cases like thrust), and for which the resummation in distribution (or momentum) space has been a long-standing open question. For the first time, we show how to perform the RG evolution fully in momentum space, thereby directly resumming the logarithms $[{\ln }^n(q_T^2/Q^2)/q_T^2{]}_{+}$ appearing in the physical $q_T$ distribution. The resummation accuracy is then solely determined by the perturbative expansion of the associated anomalous dimensions.

arXiv comment58 pages + 12 pages in Appendices, 2 figures; v2: minor changes, journal version

References in corpus (82)

• An effective field theory for collinear and soft gluons: heavy to light decays
• Soft-Collinear Factorization in Effective Field Theory
• Summing Sudakov logarithms in B -> X_s + gamma in effective field theory
• Invariant Operators in Collinear Effective Theory
• QCD Factorization for Semi-Inclusive Deep-Inelastic Scattering at Low Transverse Momentum
• 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
• Measurement of the $Z/{\gamma }^{\ast }$ boson transverse momentum distribution in $pp$ collisions at $\sqrt{s}$ = 7 TeV with the ATLAS detector
• Soft gluon effects on lepton pairs at hadron colliders
• Thrust at N^3LL with Power Corrections and a Precision Global Fit for alphas(mZ)
• Factorization and Momentum-Space Resummation in Deep-Inelastic Scattering
• 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
• Universality of non-leading logarithmic contributions in transverse-momentum distributions
• Nonperturbative Corrections in Resummed Cross Sections
• Treating the b quark distribution function with reliable uncertainties
• Higgs Production with a Central Jet Veto at NNLL+NNLO
• Factorization of heavy-to-light form factors in soft-collinear effective theory
• Theory Uncertainties for Higgs and Other Searches Using Jet Bins
• Unpolarized Transverse Momentum Dependent Parton Distribution and Fragmentation Functions at next-to-next-to-leading order
• Soft and Collinear Factorization and Transverse Momentum Dependent Parton Distribution Functions
• Measurement of the transverse momentum and ${\varphi }_{\eta }^{\ast }$ distributions of Drell-Yan lepton pairs in proton-proton collisions at $\sqrt{s}=8$ TeV with the ATLAS detector
• Production of Drell--Yan lepton pairs in hadron collisions: transverse-momentum resummation at next-to-next-to-leading logarithmic accuracy
• Calculation of the transverse parton distribution functions at next-to-next-to-leading order
• Vector boson production at hadron colliders: hard-collinear coefficients at the NNLO
• QCD transverse-momentum resummation in gluon fusion processes
• Measurement of the Rapidity and Transverse Momentum Distributions of Z Bosons in pp Collisions at sqrt(s)=7 TeV
• Jet p_T Resummation in Higgs Production at NNLL'+NNLO
• Universality of transverse-momentum resummation and hard factors at the NNLO
• The structure of large logarithmic corrections at small transverse momentum in hadronic collisions
• Next-to-next-to-leading logarithmic corrections at small transverse momentum in hadronic collisions
• The Quark Beam Function at NNLL
• Analytic Regularization in Soft-Collinear Effective Theory
• Model Independent Evolution of Transverse Momentum Dependent Distribution Functions (TMDs) at NNLL
• W and Z transverse momentum distributions: resummation in qT-space
• Joint resummation in electroweak boson production
• Understanding the large-distance behavior of transverse-momentum-dependent parton densities and the Collins-Soper evolution kernel
• The Universal Transverse Momentum Dependent Soft Function at NNLO
• Electroweak Gauge-Boson Production at Small q_T: Infrared Safety from the Collinear Anomaly
• Designing Gapped Soft Functions for Jet Production
• Higher-Order QCD Corrections in Prompt Photon Production
• Higgs boson production at the LHC: transverse momentum resummation effects in the H->2gamma, H->WW->lnu lnu and H->ZZ->4l decay modes
• Higgs-Boson Production at Small Transverse Momentum
• A Unified Treatment of the QCD Evolution of All (Un-)Polarized TMD Functions: Collins Function as a Study Case
• Comparing and Counting Logs in Direct and Effective Methods of Resummation
• Measurement of the Z boson differential cross section in transverse momentum and rapidity in proton-proton collisions at 8 TeV
• A new approach to the Higgs transverse-momentum resummation at NNLL+NNLO
• Measurements of the Total and Differential Higgs Boson Production Cross Sections Combining the $H\to \gamma \gamma$ and $H\to Z{Z}^{\ast }\to 4\ell$ Decay Channels at $\sqrt{s}=8$ TeV with the ATLAS Detector
• Electroweak Sudakov Corrections using Effective Field Theory
• Measurements of fiducial and differential cross sections for Higgs boson production in the diphoton decay channel at $\sqrt{s}=8$ TeV with ATLAS
• Soft-Collinear Factorization and Zero-Bin Subtractions
• Higgs boson production at the LHC: transverse-momentum resummation and rapidity dependence
• Rapidity renormalized TMD soft and beam functions at two loops
• QCD evolution of (un)polarized gluon TMDPDFs and the Higgs $q_T$-distribution
• Factorization and Resummation of Higgs Boson Differential Distributions in Soft-Collinear Effective Theory
• Vector boson production at hadron colliders: transverse-momentum resummation and leptonic decay
• Fiducial and differential cross sections of Higgs boson production measured in the four-lepton decay channel in $pp$ collisions at $\sqrt{s}$=8 TeV with the ATLAS detector
• Glauber Gluons and Multiple Parton Interactions
• Non-perturbative QCD effects in $q_T$ spectra of Drell-Yan and $Z$-boson production
• Measurement of differential cross sections for Higgs boson production in the diphoton decay channel in pp collisions at sqrt(s) = 8 TeV
• Measurement of the transverse momentum spectra of weak vector bosons produced in proton-proton collisions at sqrt(s) = 8 TeV
• Higgs Boson Production at the LHC with Soft Gluon Effects
• An Overview of Transverse Momentum Dependent Factorization and Evolution
• Two-loop Jet-Function and Jet-Mass for Top Quarks
• Problems in the resummation of soft-gluon effects in the transverse-momentum distributions of massive vector bosons in hadronic collisions
• Transverse Momentum Distribution Through Soft-Gluon Resummation in Effective Field Theory
• Enhanced non-perturbative effects through the collinear anomaly
• Measurement of differential and integrated fiducial cross sections for Higgs boson production in the four-lepton decay channel in pp collisions at sqrt(s) = 7 and 8 TeV
• Resummation prescriptions and ambiguities in SCET vs. direct QCD: Higgs production as a case study
• All-orders resummation for diphoton production at hadron colliders
• Transverse momentum resummation in soft-collinear effective theory
• Sudakov Logarithm Resummation in Transverse Momentum Space for Electroweak Boson Production at Hadron Colliders
• Quantifying Comparisons of Threshold Resummations
• Measurement of fiducial differential cross sections of gluon-fusion production of Higgs bosons decaying to $W{W}^{\ast }\to e\nu \mu \nu$ with the ATLAS detector at $\sqrt{s}=8$ TeV
• Soft Gluon Resummation in Transverse Momentum Space for Electroweak Boson Production at Hadron Colliders
• Measurement of the transverse momentum spectrum of the Higgs boson produced in pp collisions at sqrt(s) = 8 TeV using H to WW decays
• The Higgs Transverse Momentum Distribution at NNLL and its Theoretical Errors
• Improved resummation prediction on Higgs boson production at hadron colliders
• On the Resummation of Subleading Logarithms in the Transverse Momentum Distribution of Vector Bosons Produced at Hadron Colliders
• A general method for the resummation of event-shape distributions in e^+e^- annihilation

Cited by in corpus (57)

• Transverse-momentum-dependent parton distributions up to N${}^3$LL from Drell-Yan data
• Fiducial distributions in Higgs and Drell-Yan production at N${}^3$LL+NNLO
• Momentum-space resummation for transverse observables and the Higgs $p_{\perp }$ at N${}^3$LL+NNLO
• Determining the Nonperturbative Collins-Soper Kernel From Lattice QCD
• Subleading Power Rapidity Divergences and Power Corrections for $q_T$
• Drell-Yan lepton-pair production: $q_T$ resummation at N${}^3$LL accuracy and fiducial cross sections at N${}^3$LO
• Towards Quasi-Transverse Momentum Dependent PDFs Computable on the Lattice
• Simplicity from Recoil: The Three-Loop Soft Function and Factorization for the Energy-Energy Correlation
• Transverse momentum dependent PDFs at N${}^3$LO
• NNLO QCD corrections to diphoton production with an additional jet at the LHC
• Drell-Yan $q_T$ Resummation of Fiducial Power Corrections at N${}^3$LL
• The transverse momentum spectrum of weak gauge bosons at N${}^3$LL+NNLO
• Higgs $p_T$ Spectrum and Total Cross Section with Fiducial Cuts at Third Resummed and Fixed Order in QCD
• The Energy Distribution of Subjets and the Jet Shape
• The transverse momentum distribution of hadrons within jets
• Systematic analysis of double-scale evolution
• Subleading Power Resummation of Rapidity Logarithms: The Energy-Energy Correlator in $\mathcal{N}=4$ SYM
• Fiducial $q_T$ resummation of color-singlet processes at N${}^3$LL+NNLO
• DYTurbo: Fast predictions for Drell-Yan processes
• PDF bias and flavor dependence in TMD distributions
• A Toolbox for $q_T$ and $0$-Jettiness Subtractions at N${}^3$LO
• Fiducial Higgs and Drell-Yan distributions at N${}^3$LL${}^{\prime }$+NNLO with RadISH
• Celestial Blocks and Transverse Spin in the Three-Point Energy Correlator
• The Energy-Energy Correlation in the back-to-back limit at N${}^3$LO and N${}^3$LL${}^{\prime }$
• Resummation of Boson-Jet Correlation at Hadron Colliders
• Factorization and Resummation for Massive Quark Effects in Exclusive Drell-Yan
• Transverse momentum in double parton scattering: factorisation, evolution and matching
• The $q_T$ and $\Delta \varphi$ spectra in W and Z production at the LHC at N${}^3$LL'+N${}^2$LO
• Joint Two-Dimensional Resummation in $q_T$ and $0$-Jettiness at NNLL
• N-jettiness beam functions at N3LO
• Matching NNLO to parton shower using N${}^3$LL colour-singlet transverse momentum resummation in GENEVA
• Event-Based Transverse Momentum Resummation
• Higher-Order Sudakov Resummation in Coupled Gauge Theories
• Threshold resummation of the rapidity distribution for Higgs production at NNLO+NNLL
• The Zγ transverse-momentum spectrum at NNLO+N3LL
• Quark beam function at next-to-next-to-next-to-leading order in perturbative QCD in the generalized large-$N_c$ approximation
• The Jet Shape at NLL${}^{\prime }$
• Collinear expansion for color singlet cross sections
• Projected transverse momentum resummation in top-antitop pair production at LHC
• Factorization of Power Corrections in the Drell-Yan Process in EFT
• Drell-Yan Transverse-Momentum Spectra at N${}^3$LL${}^{\prime }$ and Approximate N${}^4$LL with SCETlib
• A fast and accurate method for perturbative resummation of transverse momentum-dependent observables
• Sudakov Shoulder Resummation for Thrust and Heavy Jet Mass
• Combining QED and QCD transverse-momentum resummation for W and Z boson production at hadron colliders
• Vector Bosons and Jets in Proton Collisions
• Efficient Fourier Transforms for Transverse Momentum Dependent Distributions
• Resummed inclusive cross-section in ADD model at N${}^3$LL+NNLO
• Analytic results for Sudakov form factors in QCD
• Pileup and Infrared Radiation Annihilation (PIRANHA): A Paradigm for Continuous Jet Grooming
• Two-loop bottom mass effects on the Higgs transverse momentum spectrum in top-induced gluon fusion
• Study of the normalized transverse momentum distribution of $W$ bosons produced in $p\bar{p}$ collisions at $\sqrt{s}=1.96$ TeV
• Measurements of $Z\gamma +$jets differential cross sections in $pp$ collisions at $\sqrt{s}=13$ TeV with the ATLAS detector
• Polarized fragmenting jet functions in Inclusive and Exclusive Jet Production
• Rapidity Logarithms in SCET Without Modes
• Resummed transverse momentum distribution of pseudo-scalar Higgs boson at NNLO${}_A$+NNLL
• Dihadron Angular Correlations in the $e^{+}{e}^{-}$ Collision
• QCD Beyond Leading Power