The Four Loop QCD Rapidity Anomalous Dimension

Abstract

The rapidity anomalous dimension controls the scaling of transverse momentum dependent observables in the Sudakov region. In a conformal theory it is equivalent to the soft anomalous dimension, but in QCD this relation is broken by anomalous terms proportional to the $\beta$-function. In this paper we first give a simple proof of this relation using two different representations of the energy-energy correlator observable. We then calculate the anomalous terms to three loops by computing the three-loop fully differential soft function to $\mathcal{O}(\epsilon )$. Combined with recent perturbative data from the study of on-shell form factors and splitting functions, this allows us to derive the four loop rapidity anomalous dimension in QCD.

arXiv commentreferences added

References in corpus (143)

• 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
• The four-loop beta-function in Quantum Chromodynamics
• Higgs boson production at hadron colliders in NNLO QCD
• Multiloop integrals in dimensional regularization made simple
• 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
• Conformal collider physics: Energy and charge correlations
• QCD Factorization for Semi-Inclusive Deep-Inelastic Scattering at Low Transverse Momentum
• Five-Loop Running of the QCD coupling constant
• A Formalism for the Systematic Treatment of Rapidity Logarithms in Quantum Field Theory
• The five-loop beta function of Yang-Mills theory with fermions
• Structure functions for large $x$ and renormalization of Wilson loops
• Thrust at N^3LL with Power Corrections and a Precision Global Fit for alphas(mZ)
• The Rapidity Renormalization Group
• A precise determination of alpha_s from LEP thrust data using effective field theory
• Power corrections to event shapes and factorization
• Comments on operators with large spin
• Dynamical Threshold Enhancement and Resummation in Drell-Yan Production
• Three-Loop Results for Quark and Gluon Form Factors
• Higgs boson gluon-fusion production at threshold in N3LO QCD
• Bootstrapping rapidity anomalous dimension for transverse-momentum resummation
• Factorization and Endpoint Singularities in Heavy-to-Light decays
• Deep inelastic scattering as x -> 1 using soft-collinear effective theory
• Universal structure of subleading infrared poles in gauge theory amplitudes
• Soft triple-real radiation for Higgs production at N3LO
• Sudakov Form Factors
• Momentum Flow Correlations from Event Shapes: Factorized Soft Gluons and Soft-Collinear Effective Theory
• Three-loop corrections to the soft anomalous dimension in multi-leg scattering
• Cusp and collinear anomalous dimensions in four-loop QCD from form factors
• Transverse-momentum-dependent parton distributions up to N${}^3$LL from Drell-Yan data
• Soft-/rapidity- anomalous dimensions correspondence
• The five-loop Beta function for a general gauge group and anomalous dimensions beyond Feynman gauge
• Gluon Regge Trajectory in the two-loop Approximation
• The Collinear Limit of the Energy-Energy Correlator
• Analytic Regularization in Soft-Collinear Effective Theory
• Anomalous dimensions of high-spin operators beyond the leading order
• From correlation functions to Wilson loops
• Four-Loop Non-Singlet Splitting Functions in the Planar Limit and Beyond
• On quartic colour factors in splitting functions and the gluon cusp anomalous dimension
• Rethinking Jets with Energy Correlators: Tracks, Resummation and Analytic Continuation
• Fiducial distributions in Higgs and Drell-Yan production at N${}^3$LL+NNLO
• The Universal Transverse Momentum Dependent Soft Function at NNLO
• From correlation functions to event shapes
• Anomalous Dimension of Non-Singlet Wilson Operators at O(1/N_f) in Deep Inelastic Scattering
• Momentum-space resummation for transverse observables and the Higgs $p_{\perp }$ at N${}^3$LL+NNLO
• Jets and Quantum Field Theory
• 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
• Threshold Resummation for Higgs Production in Effective Field Theory
• Large-nf Contributions to the Four-Loop Splitting Functions in QCD
• The two-loop soft current in dimensional regularization
• Determining the Nonperturbative Collins-Soper Kernel From Lattice QCD
• Event shapes in N=4 super-Yang-Mills theory
• Collins-Soper Kernel for TMD Evolution from Lattice QCD
• Subleading Power Rapidity Divergences and Power Corrections for $q_T$
• Five-loop renormalisation of QCD in covariant gauges
• Higher-spin correlators
• Two-loop corrections to Higgs boson production
• Energy-energy correlations in N=4 SYM
• Bootstrapping the QCD soft anomalous dimension
• Single soft gluon emission at two loops
• The three-loop cusp anomalous dimension in QCD and its supersymmetric extensions
• Integrability and Transcendentality
• Drell-Yan lepton-pair production: $q_T$ resummation at N${}^3$LL accuracy and fiducial cross sections at N${}^3$LO
• Lattice-QCD Calculations of TMD Soft Function Through Large-Momentum Effective Theory
• Soft-virtual corrections to Higgs production at N${}^3$LO
• Simplicity from Recoil: The Three-Loop Soft Function and Factorization for the Energy-Energy Correlation
• A Precise Determination of ${\alpha }_s$ from the C-parameter Distribution
• Transforming differential equations of multi-loop Feynman integrals into canonical form
• Constraining Light-Quark Yukawa Couplings from Higgs Distributions
• Soft Expansion of Double-Real-Virtual Corrections to Higgs Production at N${}^3$LO
• Transverse momentum dependent PDFs at N${}^3$LO
• Four-loop photon quark form factor and cusp anomalous dimension in the large-$N_c$ limit of QCD
• N${}^3$LO Higgs and Drell-Yan production at threshold: the one-loop two-emission contribution
• Evolution equation for gluon Regge trajectory
• Drell-Yan $q_T$ Resummation of Fiducial Power Corrections at N${}^3$LL
• Precise QCD Description of the Higgs Boson Transverse Momentum Spectrum
• Matter dependence of the four-loop cusp anomalous dimension
• The transverse momentum spectrum of weak gauge bosons at N${}^3$LL+NNLO
• Reggeization of quark-quark scattering amplitude in QCD
• Higgs $p_T$ Spectrum and Total Cross Section with Fiducial Cuts at Third Resummed and Fixed Order in QCD
• Transverse-Momentum-Dependent Parton Distribution Functions from Large-Momentum Effective Theory
• Di-lepton Rapidity Distribution in Drell-Yan Production to Third Order in QCD
• The Transverse Energy-Energy Correlator in the Back-to-Back Limit
• Third order fiducial predictions for Drell-Yan at the LHC
• Energy correlations in the end-point region
• Light quark Yukawa couplings from Higgs kinematics
• Lattice QCD Study of Transverse-Momentum Dependent Soft Function
• Five-loop contributions to low-N non-singlet anomalous dimensions in QCD
• Quark and gluon form factors to four loop order in QCD: the $N_f^3$ contributions
• The high energy limit of QCD at two loops
• Self-contained definition of the Collins-Soper kernel
• Infrared Singularities of Scattering Amplitudes and N${}^3$LL Resummation for $n$-Jet Processes
• Four-Loop Nonplanar Cusp Anomalous Dimension in N=4 Supersymmetric Yang-Mills Theory
• Fiducial $q_T$ resummation of color-singlet processes at N${}^3$LL+NNLO
• Subleading Power Resummation of Rapidity Logarithms: The Energy-Energy Correlator in $\mathcal{N}=4$ SYM
• On the Gluon Regge Trajectory in $O({\alpha }_s^2)$
• Four-loop quark form factor with quartic fundamental colour factor
• Three-loop gluon scattering in QCD and the gluon Regge trajectory
• The $n_f^2$ contributions to fermionic four-loop form factors
• On the Computation of Form Factors in Massless QCD with Finite Master Integrals
• Four-loop collinear anomalous dimensions in QCD and $\mathcal{N}=4$ super Yang-Mills
• Analytic resummation for the quark form factor in QCD
• Threshold Resummation for Drell-Yan Process in Soft-Collinear Effective Theory
• The Sudakov form factor at four loops in maximal super Yang-Mills theory
• Soft corrections to inclusive deep-inelastic scattering at four loops and beyond
• Analytic Continuation and Reciprocity Relation for Collinear Splitting in QCD
• Matter dependence of the four-loop QCD cusp anomalous dimension: from small angles to all angles
• The Sudakov radiator for jet observables and the soft physical coupling
• Quark and gluon form factors in four-loop QCD
• Approximate four-loop QCD corrections to the Higgs-boson production cross section
• The Energy-Energy Correlation in the back-to-back limit at N${}^3$LO and N${}^3$LL${}^{\prime }$
• Triple (and quadruple) soft-gluon radiation in QCD hard scattering
• On the Casimir scaling violation in the cusp anomalous dimension at small angle
• Precise determination of ${\alpha }_S(M_Z)$ from a global fit of energy-energy correlation to NNLO+NNLL predictions
• Energy-energy correlators in Deep Inelastic Scattering
• The $q_T$ and $\Delta \varphi$ spectra in W and Z production at the LHC at N${}^3$LL'+N${}^2$LO
• TMD Fragmentation Functions at N${}^3$LO
• Four-Loop Collinear Anomalous Dimension in N = 4 Yang-Mills Theory
• Disentangling the Regge cut and Regge pole in perturbative QCD
• The Four-Loop Cusp Anomalous Dimension from the $\mathcal{N}=4$ Sudakov Form Factor
• Transverse-Energy-Energy Correlations in Deep Inelastic Scattering
• Scattering amplitudes in the Regge limit and the soft anomalous dimension through four loops
• Fine structure of anomalous dimensions in N=4 super Yang-Mills theory
• The virtual scaling function of AdS/CFT
• The quark Regge trajectory at two loops
• Beyond cusp anomalous dimension from integrability
• Anomalous Dimensions from a Spinning D5-Brane
• The Principle of Maximal Transcendentality and the Four-Loop Collinear Anomalous Dimension
• An Exclusive Soft Function for Drell-Yan at Next-to-Next-to-Leading Order
• Unpolarized Quark and Gluon TMD PDFs and FFs at N${}^3$LO
• Groomed jet mass at high precision
• Quark and gluon form factors in four loop QCD: the $N_f^2$ and $N_{q\gamma }{N}_f$ contributions
• The gluon Regge trajectory at three loops from planar Yang-Mills theory
• Relating amplitude and PDF factorisation through Wilson-line geometries
• Multiple soft radiation at one-loop order and the emission of a soft quark-antiquark pair
• Conformal symmetry of QCD in $d$-dimensions
• Planar master integrals for four-loop form factors
• On the calculation of soft phase space integral
• Fermionic corrections to quark and gluon form factors in four-loop QCD

Cited by in corpus (24)

• 50 Years of Quantum Chromodynamics
• Fiducial Drell-Yan production at the LHC improved by transverse-momentum resummation at N${}^4$LL+N${}^3$LO
• Analytic Computation of Three-point Energy Correlator in QCD
• Third order QCD predictions for fiducial W-boson production
• Probing Transverse Momentum Dependent Structures with Azimuthal Dependence of Energy Correlators
• The $N_f{C}_F^3$ contribution to the non-singlet splitting function at four-loop order
• Projected transverse momentum resummation in top-antitop pair production at LHC
• One-loop matching for gluon lattice TMDs
• Drell-Yan Transverse-Momentum Spectra at N${}^3$LL${}^{\prime }$ and Approximate N${}^4$LL with SCETlib
• Gluon Transverse-Momentum-Dependent Distributions from Large-Momentum Effective Theory
• Three-point Energy Correlators in Hadronic Higgs Decays
• Transverse Energy-Energy Correlators in the Color-Glass Condensate at the Electron-Ion Collider
• A Collinear Perspective on the Regge Limit
• Two-loop bottom mass effects on the Higgs transverse momentum spectrum in top-induced gluon fusion
• Precision three-dimensional imaging of nuclei using recoil-free jets
• The DIS 1-Jettiness Event Shape at N${}^3$LL+$\mathcal{O}({\alpha }_s^2)$
• Polarized fragmenting jet functions in Inclusive and Exclusive Jet Production
• The $q_{\mathrm{T}}$ and $\Delta {\varphi }_{t\bar{t}}$ spectra in top-antitop hadroproduction at NNLL+NNLO: the interplay of soft-collinear resummation and Coulomb singularities
• Collins-Soper Kernel in the QCD Instanton Vacuum
• Transverse momentum dependent distribution functions in the threshold limit
• Transverse Energy-Energy Correlator for Vector Boson-Tagged Hadron Production in $pp$ and $pA$ collisions
• Universality of the Collins-Soper kernel in lattice calculations
• Collins-Soper kernel from lattice QCD at the physical pion mass
• Evolution of unpolarized transverse momentum dependent parton distributions of twist-3