A Toolbox for $q_T$ and $0$-Jettiness Subtractions at N${}^3$LO

Abstract

We derive the leading-power singular terms at three loops for both $q_T$ and 0-jettiness, ${\mathcal{T}}_0$, for generic color-singlet processes. Our results provide the complete set of differential subtraction terms for $q_T$ and ${\mathcal{T}}_0$ subtractions at N${}^3$LO, which are an important ingredient for matching N${}^3$LO calculations with parton showers. We obtain the full three-loop structure of the relevant beam and soft functions, which are necessary ingredients for the resummation of $q_T$ and ${\mathcal{T}}_0$ at N${}^3$LL${}^{\prime }$ and N${}^4$LL order, and which constitute important building blocks in other contexts as well. The nonlogarithmic boundary coefficients of the beam functions, which contribute to the integrated subtraction terms, are not yet fully known at three loops. By exploiting consistency relations between different factorization limits, we derive results for the $q_T$ and ${\mathcal{T}}_0$ beam function coefficients at N${}^3$LO in the $z\to 1$ threshold limit, and we also estimate the size of the unknown terms beyond threshold.

arXiv comment37 pages + appendices, 8 figures; v2: minor changes, journal version

References in corpus (162)

• An effective field theory for collinear and soft gluons: heavy to light decays
• Soft-Collinear Factorization in Effective Field Theory
• Parton distributions in the LHC era: MMHT 2014 PDFs
• The Three-Loop Splitting Functions in QCD: The Non-Singlet Case
• An NNLO subtraction formalism in hadron collisions and its application to Higgs boson production at the LHC
• Summing Sudakov logarithms in B -> X_s + gamma in effective field theory
• The Three-Loop Splitting Functions in QCD: The Singlet Case
• Invariant Operators in Collinear Effective Theory
• Vector boson production at hadron colliders: a fully exclusive QCD calculation at NNLO
• Higgs boson gluon-fusion production in N3LO QCD
• Hard Scattering Factorization from Effective Field Theory
• The three-loop QCD $\beta$-function and anomalous dimensions
• Antenna Subtraction at NNLO
• Combined measurements of Higgs boson production and decay using up to $80$ fb${}^{-1}$ of proton-proton collision data at $\sqrt{s}=$ 13 TeV collected with the ATLAS experiment
• Transverse-momentum resummation and the spectrum of the Higgs boson at the LHC
• 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
• Combined measurements of Higgs boson couplings in proton-proton collisions at $\sqrt{s}=$ 13 TeV
• N-Jettiness: An Inclusive Event Shape to Veto Jets
• A novel subtraction scheme for double-real radiation at NNLO
• Higgs boson production in bottom quark fusion at next-to-next-to-leading order
• Z-boson production in association with a jet at next-to-next-to-leading order in perturbative QCD
• Thrust at N^3LL with Power Corrections and a Precision Global Fit for alphas(mZ)
• Fully differential NNLO computations with MATRIX
• Fully differential VBF Higgs production at NNLO
• 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
• $W$-boson production in association with a jet at next-to-next-to-leading order in perturbative QCD
• Quark and gluon form factors to three loops
• Measurement of the $W$-boson mass in pp collisions at $\sqrt{s}=7$ TeV with the ATLAS detector
• A precise determination of alpha_s from LEP thrust data using effective field theory
• Factorization at the LHC: From PDFs to Initial State Jets
• NNLO predictions for the Higgs boson signal in the H->WW->lnu lnu and H->ZZ->4l decay channels
• Universality of non-leading logarithmic contributions in transverse-momentum distributions
• Color singlet production at NNLO in MCFM
• Three-Loop Results for Quark and Gluon Form Factors
• Treating the b quark distribution function with reliable uncertainties
• Higgs boson gluon-fusion production at threshold in N3LO QCD
• Bootstrapping rapidity anomalous dimension for transverse-momentum resummation
• Higgs Production with a Central Jet Veto at NNLL+NNLO
• Higgs Boson Production at Hadron Colliders at N3LO in QCD
• Infrared Structure at NNLO Using Antenna Subtraction
• Unpolarized Transverse Momentum Dependent Parton Distribution and Fragmentation Functions at next-to-next-to-leading order
• Top Jets in the Peak Region: Factorization Analysis with NLL Resummation
• Top-Quark Decay at Next-to-Next-to-Leading Order in QCD
• Virtual corrections to gg -> H to two loops in the heavy top limit
• The Quark Form Factor at Higher Orders
• Two-Loop Quark and Gluon Form Factors in Dimensional Regularisation
• Higher-Order threshold effects to inclusive processes in QCD
• Vector-boson fusion Higgs production at N${}^3$LO in QCD
• 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
• Jet p_T Resummation in Higgs Production at NNLL'+NNLO
• Four-dimensional formulation of the sector-improved residue subtraction scheme
• Reparameterization Invariance for Collinear Operators
• The structure of large logarithmic corrections at small transverse momentum in hadronic collisions
• The Quark Beam Function at NNLL
• Two-Loop Soft Corrections and Resummation of the Thrust Distribution in the Dijet Region
• Nested soft-collinear subtractions in NNLO QCD computations
• Soft-/rapidity- anomalous dimensions correspondence
• The two-loop hemisphere soft function
• Combining Higher-Order Resummation with Multiple NLO Calculations and Parton Showers in GENEVA
• Drell-Yan Production at NNLL'+NNLO Matched to Parton Showers
• Fiducial distributions in Higgs and Drell-Yan production at N${}^3$LL+NNLO
• Joint resummation in electroweak boson production
• A subtraction scheme for NNLO computations
• Subleading Power Corrections for N-Jettiness Subtractions
• Resummation and NLO Matching of Event Shapes with Effective Field Theory
• The Universal Transverse Momentum Dependent Soft Function at NNLO
• Three-jet production in electron-positron collisions using the CoLoRFulNNLO method
• Transverse parton distribution functions at next-to-next-to-leading order: the quark-to-quark case
• Factorization and N^3LL_p+NNLO Predictions for the Higgs Cross Section with a Jet Veto
• Higgs boson production at the LHC using the $q_T$ subtraction formalism at N${}^3$LO QCD
• Quark Transverse Parton Distribution at the Next-to-Next-to-Next-to-Leading Order
• Drell-Yan Production at Threshold to Third Order in QCD
• Determining the Nonperturbative Collins-Soper Kernel From Lattice QCD
• Recoil and Threshold Corrections in Short-distance Cross Sections
• The Quark Beam Function at Two Loops
• Subleading Power Rapidity Divergences and Power Corrections for $q_T$
• Associated production of a Higgs boson at NNLO
• Power Corrections in the N-jettiness Subtraction Scheme
• Analytic Results for Massless Three-Loop Form Factors
• Transverse-momentum resummation for heavy-quark hadroproduction
• Matching Fully Differential NNLO Calculations and Parton Showers
• Joint Resummation for Higgs Production
• Factorization and Resummation for Dijet Invariant Mass Spectra
• The fully differential decay rate of a Higgs boson to bottom-quarks at NNLO in QCD
• Resummed Higgs cross section at N${}^3$LL
• Soft-virtual corrections to Higgs production at N${}^3$LO
• Towards Quasi-Transverse Momentum Dependent PDFs Computable on the Lattice
• Resummation of Transverse Momentum Distributions in Distribution Space
• The Soft Function for Exclusive N-Jet Production at Hadron Colliders
• A Precise Determination of ${\alpha }_s$ from the C-parameter Distribution
• Transverse-momentum resummation for top-quark pairs at hadron colliders
• Higgs boson decay into b-quarks at NNLO accuracy
• Non-global Structure of the O(α_s^2) Dijet Soft Function
• Transverse momentum dependent PDFs at N${}^3$LO
• Resummation of Double-Differential Cross Sections and Fully-Unintegrated Parton Distribution Functions
• Rapidity renormalized TMD soft and beam functions at two loops
• Precision Predictions at N${}^3$LO for the Higgs Boson Rapidity Distribution at the LHC
• Precise QCD Description of the Higgs Boson Transverse Momentum Spectrum
• Transverse Parton Distribution and Fragmentation Functions at NNLO: the Quark Case
• Glauber Gluons and Multiple Parton Interactions
• Higgs production in bottom-quark fusion to third order in the strong coupling
• Next-to-leading-logarithmic power corrections for $N$-jettiness subtraction in color-singlet production
• The Gluon Beam Function at Two Loops
• Using 1-Jettiness to Measure 2 Jets in DIS 3 Ways
• Fully-Unintegrated Parton Distribution and Fragmentation Functions at Perturbative k_T
• Local Analytic Sector Subtraction at NNLO
• N-Jettiness Subtractions for $gg\to H$ at Subleading Power
• The Three-loop Quark Jet Function
• Higgs boson production at hadron colliders: hard-collinear coefficients at the NNLO
• Rapidity Distributions in Drell-Yan and Higgs Productions at Threshold to Third Order in QCD
• Power Corrections for N-Jettiness Subtractions at $\mathcal{O}({\alpha }_s)$
• Measurement of fiducial and differential $W^{+}{W}^{-}$ production cross-sections at $\sqrt{s}=$13 TeV with the ATLAS detector
• Measurement of the transverse momentum spectra of weak vector bosons produced in proton-proton collisions at sqrt(s) = 8 TeV
• QCD threshold corrections to di-lepton and Higgs rapidity distributions beyond N${}^2$LO
• Geometric IR subtraction for real radiation
• Linearly polarized gluons at next-to-next-to leading order and the Higgs transverse momentum distribution
• Reparameterization Invariant Collinear Operators
• Unification of the $k_T$ and threshold resummations
• Transverse Parton Distribution and Fragmentation Functions at NNLO: the Gluon Case
• Fragmentation in Jets: Cone and Threshold Effects
• The $Hb\bar{b}$ form factor to three loops in QCD
• Analytic results for color-singlet production at NNLO QCD with the nested soft-collinear subtraction scheme
• NNLO predictions for Z-boson pair production at the LHC
• Drell-Yan process with jet vetoes: breaking of generalized factorization
• Resummation of Boson-Jet Correlation at Hadron Colliders
• Next-to-leading power corrections to $V+1$ jet production in $N$-jettiness subtraction
• Top-quark forward-backward asymmetry in e+e- annihilation at NNLO in QCD
• Rapidity-Dependent Jet Vetoes
• Factorization and Resummation for Massive Quark Effects in Exclusive Drell-Yan
• Factorisation and Subtraction beyond NLO
• Threshold resummation of the rapidity distribution for Drell-Yan production at NNLO+NNLL
• Joint Two-Dimensional Resummation in $q_T$ and $0$-Jettiness at NNLL
• Impact of Isolation and Fiducial Cuts on $q_T$ and N-Jettiness Subtractions
• Gluon jet function at three loops in QCD
• Electroweak prodution of top-quark pairs in e+e- annihilation at NNLO in QCD: the vector contributions
• Joint transverse momentum and threshold resummation beyond NLL
• Generic dijet soft functions at two-loop order: correlated emissions
• Resummed prediction for Higgs boson production through $b\bar{b}$ annihilation at N${}^3$LL
• An Enhanced Threshold Resummation Formalism for Lepton Pair Production and Its Effects in the Determination of Parton Distribution Functions
• N-jettiness beam functions at N3LO
• H+1 jet production revisited
• MT: a Mathematica package to compute convolutions
• Higgs Boson Production via Gluon Fusion: Soft-Gluon Resummation including Mass Effects
• Higher-order power corrections in a transverse-momentum cut for colour-singlet production at NLO
• Resummation Improved Rapidity Spectrum for Gluon Fusion Higgs Production
• Search for anomalous triple gauge couplings in WW and WZ production in lepton + jet events in proton-proton collisions at $\sqrt{s}=$ 13 TeV
• An Exclusive Soft Function for Drell-Yan at Next-to-Next-to-Leading Order
• Threshold resummation of the rapidity distribution for Higgs production at NNLO+NNLL
• The Fully-Differential Quark Beam Function at NNLO
• Jet Veto Resummation with Jet Rapidity Cuts
• Quark beam function at next-to-next-to-next-to-leading order in perturbative QCD in the generalized large-$N_c$ approximation
• Two-Loop Beam and Soft Functions for Rapidity-Dependent Jet Vetoes
• Double-real contribution to the quark beam function at N${}^3$LO QCD
• A transverse momentum dependent framework for back-to-back photon+jet production
• Triple-real contribution to the quark beam function in QCD at next-to-next-to-next-to-leading order
• Calculating Soft Radiation at One Loop
• Soft Functions for Generic Jet Algorithms and Observables at Hadron Colliders

Cited by in corpus (29)

• 50 Years of Quantum Chromodynamics
• Collider Physics at the Precision Frontier
• 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
• Event Generators for High-Energy Physics Experiments
• Di-lepton Rapidity Distribution in Drell-Yan Production to Third Order in QCD
• The Energy-Energy Correlation in the back-to-back limit at N${}^3$LO and N${}^3$LL${}^{\prime }$
• Les Houches 2021: Physics at TeV Colliders: Report on the Standard Model Precision Wishlist
• Transverse Mass Distribution and Charge Asymmetry in W Boson Production to Third Order in QCD
• TMD Fragmentation Functions at N${}^3$LO
• $t\bar{t}H$ production at NNLO: the flavour off-diagonal channels
• Locally finite two-loop amplitudes for off-shell multi-photon production in electron-positron annihilation
• Fiducial perturbative power corrections within the q${}_{\mathbf{T}}$ subtraction formalism
• Unpolarized Quark and Gluon TMD PDFs and FFs at N${}^3$LO
• Zero-jettiness resummation for top-quark pair production at the LHC
• 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
• Drell-Yan Transverse-Momentum Spectra at N${}^3$LL${}^{\prime }$ and Approximate N${}^4$LL with SCETlib
• Beam functions for $N$-jettiness at N${}^3$LO in perturbative QCD
• Locally finite two-loop QCD amplitudes from IR universality for electroweak production
• Computational challenges for multi-loop collider phenomenology
• Double Higgs production at NNLO interfaced to parton showers in GENEVA
• Non-local slicing approaches for NNLO QCD in MCFM
• Jet-veto resummation at N${}^3$LL${}_{\text{p}}$+NNLO in boson production processes
• Zero-jettiness soft function to third order in perturbative QCD
• Refining the GENEVA method for Higgs boson production via gluon fusion
• Transverse Momentum-Dependent Heavy-Quark Fragmentation at Next-to-Leading Order
• High-precision measurement of the W boson mass with the CMS experiment
• Les Houches 2023 -- Physics at TeV Colliders: Report on the Standard Model Precision Wishlist
• Monte Carlo Event Generators for Future Lepton Colliders