Four-Loop Non-Singlet Splitting Functions in the Planar Limit and Beyond

Abstract

We present the next-to-next-to-next-to-leading order (N^3LO) contributions to the non-singlet splitting functions for both parton distribution and fragmentation functions in perturbative QCD. The exact expressions are derived for the terms contributing in the limit of a large number of colours. For the remaining contributions, approximations are provided that are sufficient for all collider-physics applications. From their threshold limits we derive analytical and high-accuracy numerical results, respectively, for all contributions to the four-loop cusp anomalous dimension for quarks, including the terms proportional to quartic Casimir operators. We briefly illustrate the numerical size of the four-loop corrections, and the remarkable renormalization-scale stability of the N^3LO results, for the evolution of the non-singlet parton distribution and the fragmentation functions. Our results appear to provide a first point of contact of four-loop QCD calculations and the so-called wrapping corrections to anomalous dimensions in N=4 super Yang-Mills theory.

73 pages latex, 14 figures, ancillary Form and Fortran files, final version to appear in JHEP

References in corpus (64)

• The Three-Loop Splitting Functions in QCD: The Non-Singlet Case
• Harmonic Polylogarithms
• The four-loop beta-function in Quantum Chromodynamics
• The Three-Loop Splitting Functions in QCD: The Singlet Case
• Higgs boson gluon-fusion production in N3LO QCD
• The Four-Loop QCD Beta-Function and Anomalous Dimensions
• FORM version 4.0
• On the Structure of Infrared Singularities of Gauge-Theory Amplitudes
• Harmonic sums, Mellin transforms and Integrals
• The third-order QCD corrections to deep-inelastic scattering by photon exchange
• Group theory factors for Feynman diagrams
• Harmonic Sums and Mellin Transforms up to two-loop Order
• Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes
• The five-loop beta function of Yang-Mills theory with fermions
• Higher-Order Soft Corrections to Lepton Pair and Higgs Boson Production
• The Multithreaded version of FORM
• Numerical Evaluation of Harmonic Polylogarithms
• Efficient evolution of unpolarized and polarized parton distributions with QCD-PEGASUS
• Deep Inelastic Structure Functions at two Loops
• Universal structure of subleading infrared poles in gauge theory amplitudes
• Higher-Order threshold effects to inclusive processes in QCD
• Revisiting parton evolution and the large-x limit
• Vector-boson fusion Higgs production at N${}^3$LO in QCD
• NNLO evolution of deep-inelastic structure functions: the singlet case
• A determination of the fragmentation functions of pions, kaons, and protons with faithful uncertainties
• NNLO evolution of deep-inelastic structure functions: the non-singlet case
• Mellin Moments of the {$O({\alpha }_s^3$)} Heavy Flavor Contributions to unpolarized Deep-Inelastic Scattering at $Q^2\gg m^2$ and Anomalous Dimensions
• Four loop twist two, BFKL, wrapping and strings
• Anomalous dimensions of high-spin operators beyond the leading order
• Next-to-Next-to-Leading Order Evolution of Non-Singlet Fragmentation Functions
• Higher-Order Corrections in Threshold Resummation
• A Critical Appraisal and Evaluation of Modern PDFs
• The Three-Loop Splitting Functions in QCD: The Helicity-Dependent Case
• Anomalous Dimension of Non-Singlet Wilson Operators at O(1/N_f) in Deep Inelastic Scattering
• Five-Loop Anomalous Dimension of Twist-Two Operators
• On the Behaviour of Non--Singlet Structure Functions at Small $x$
• Large-nf Contributions to the Four-Loop Splitting Functions in QCD
• Drell-Yan Production at Threshold to Third Order in QCD
• On Third-Order Timelike Splitting Functions and Top-Mediated Higgs Decay into Hadrons
• The 3-Loop Non-Singlet Heavy Flavor Contributions and Anomalous Dimensions for the Structure Function $F_2(x,Q^2)$ and Transversity
• Third-order QCD corrections to the charged-current structure function F_3
• Two-loop corrections to Higgs boson production
• QCD Corrections to Semi-Inclusive Hadron Production in Electron-Positron Annihilation at Two Loops
• The O(α_s^3) Massive Operator Matrix Elements of O(n_f) for the Structure Function F_2(x,Q^2) and Transversity
• The three-loop cusp anomalous dimension in QCD and its supersymmetric extensions
• On the Next-to-Next-to-Leading Order Evolution of Flavour-Singlet Fragmentation Functions
• Improved Approximations for the Three-Loop Splitting Functions in QCD
• On the Drell-Levy-Yan Relation to $O({\alpha }_s^2)$
• Four-loop photon quark form factor and cusp anomalous dimension in the large-$N_c$ limit of QCD
• On Higgs decays to hadrons and the R-ratio at N^4LO
• Next-to-Leading Order Evolution of Polarized and Unpolarized Fragmentation Functions
• N=4 SUSY Yang--Mills: three loops made simple(r)
• Four-loop QCD propagators and vertices with one vanishing external momentum
• Three-loop evolution equation for flavor-nonsinglet operators in off-forward kinematics
• The Three-Loop Splitting Functions $P_{qg}^{(2)}$ and $P_{gg}^{(2,N_F)}$
• The Renormalization of Composite Operators in Yang-Mills Theories Using General Covariant Gauge
• Structure of Infrared Singularities of Gauge-Theory Amplitudes at Three and Four Loops
• The R*-operation for Feynman graphs with generic numerators
• Four loop anomalous dimension of the second moment of the non-singlet twist-2 operator in QCD
• Resummation of small-x double logarithms in QCD: semi-inclusive electron-positron annihilation
• Three loop anomalous dimension of the non-singlet transversity operator in QCD
• Comparison of the Gottfried and Adler sum rules within the large-Nc expansion
• Resummed small-x and first-moment evolution of fragmentation functions in perturbative QCD
• Master integrals for splitting functions from differential equations in QCD

Cited by in corpus (98)

• Parton distributions and lattice QCD calculations: a community white paper
• The Large Hadron-Electron Collider at the HL-LHC
• The Structure of the Proton in the LHC Precision Era
• 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
• Non-perturbative structure of semi-inclusive deep-inelastic and Drell-Yan scattering at small transverse momentum
• The Collinear Limit of the Energy-Energy Correlator
• Fiducial distributions in Higgs and Drell-Yan production at N${}^3$LL+NNLO
• Collider Physics at the Precision Frontier
• Determining the Nonperturbative Collins-Soper Kernel From Lattice QCD
• Drell-Yan lepton-pair production: $q_T$ resummation at N${}^3$LL accuracy and fiducial cross sections at N${}^3$LO
• Approximate N${}^3$LO Parton Distribution Functions with Theoretical Uncertainties: MSHT20aN${}^3$LO PDFs
• Simplicity from Recoil: The Three-Loop Soft Function and Factorization for the Energy-Energy Correlation
• Drell-Yan $q_T$ Resummation of Fiducial Power Corrections at N${}^3$LL
• Matter dependence of the four-loop cusp anomalous dimension
• Nonperturbative Determination of Collins-Soper Kernel from Quasi Transverse-Momentum Dependent Wave Functions
• The Three-loop Quark Jet Function
• Third order fiducial predictions for Drell-Yan at the LHC
• The Four Loop QCD Rapidity Anomalous Dimension
• 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
• N3LO Corrections to Jet Production in Deep Inelastic Scattering using the Projection-to-Born Method
• Four-loop quark form factor with quartic fundamental colour factor
• 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
• Quark and gluon form factors in four-loop QCD
• Fiducial Higgs and Drell-Yan distributions at N${}^3$LL${}^{\prime }$+NNLO with RadISH
• Triple (and quadruple) soft-gluon radiation in QCD hard scattering
• The Energy-Energy Correlation in the back-to-back limit at N${}^3$LO and N${}^3$LL${}^{\prime }$
• Numerical Implementation of Harmonic Polylogarithms to Weight w = 8
• Les Houches 2021: Physics at TeV Colliders: Report on the Standard Model Precision Wishlist
• Transverse momentum in double parton scattering: factorisation, evolution and matching
• Factorisation and Subtraction beyond NLO
• Disentangling the Regge cut and Regge pole in perturbative QCD
• Resummed prediction for Higgs boson production through $b\bar{b}$ annihilation at N${}^3$LL
• Renormalization and Matching for the Collins-Soper Kernel from Lattice QCD
• Scattering amplitudes in the Regge limit and the soft anomalous dimension through four loops
• On next to soft corrections to Drell-Yan and Higgs Boson productions
• Four-loop cusp anomalous dimension in QED
• Mixed EW-QCD two-loop amplitudes for $q\bar{q}\to {\ell }^{+}{\ell }^{-}$ and ${\gamma }_5$ scheme independence of multi-loop corrections
• The Principle of Maximal Transcendentality and the Four-Loop Collinear Anomalous Dimension
• Soft-gluon effective coupling and cusp anomalous dimension
• Higher-Order Sudakov Resummation in Coupled Gauge Theories
• Unpolarized Quark and Gluon TMD PDFs and FFs at N${}^3$LO
• Quark and gluon form factors in four loop QCD: the $N_f^2$ and $N_{q\gamma }{N}_f$ contributions
• Resummation of small-x double logarithms in QCD: inclusive deep-inelastic scattering
• On next to soft threshold corrections to DIS and SIA processes
• Next-to SV resummed Drell-Yan cross section beyond leading-logarithm
• Multiparton webs beyond three loops
• Relating amplitude and PDF factorisation through Wilson-line geometries
• The asymptotic behavior of the heavy quark form factors at higher order
• Complete $N_f^2$ contributions to four-loop pure-singlet splitting functions
• Nonperturbative Renormalization in Lattice QCD with three Flavors of Clover Fermions: Using Periodic and Open Boundary Conditions
• Three-loop soft function for heavy-to-light quark decays
• Two- and Three-Loop Data for Groomed Jet Mass
• Cwebs beyond three loops in multiparton amplitudes
• The Bremsstrahlung function of $\mathcal{N}=2$ SCQCD
• Renormalization and non-renormalization of scalar EFTs at higher orders
• Drell-Yan Transverse-Momentum Spectra at N${}^3$LL${}^{\prime }$ and Approximate N${}^4$LL with SCETlib
• Planar master integrals for four-loop form factors
• Beam functions for $N$-jettiness at N${}^3$LO in perturbative QCD
• Resummed Higgs boson cross section at next-to SV to $\mathrm{NNLO}+\overline{\mathrm{NNLL}}$
• Soft-gluon and Coulomb corrections to hadronic top-quark pair production beyond NNLO
• Resummed inclusive cross-section in Randall-Sundrum model at NNLO+NNLL
• Four-loop splitting functions at small $x$
• Infrared singularities of multi-leg QCD amplitudes with a massive parton at three loops
• Computational challenges for multi-loop collider phenomenology
• Combining QED and Approximate N${}^3$LO QCD Corrections in a Global PDF Fit: MSHT20qed_an3lo PDFs
• An FONLL prescription with coexisting flavor number PDFs
• Non-planar cusp and transcendental anomalous dimension at four loops in N=4 supersymmetric Yang-Mills theory
• Resummed inclusive cross-section in ADD model at N${}^3$LL+NNLO
• Renormalization of twist-two operators in covariant gauge to three loops in QCD
• Building blocks of Cwebs in multiparton scattering amplitudes
• A note on quark and gluon energy-momentum tensors
• Deciphering Colour Building Blocks of Massive Multiparton Amplitudes at 4-loops and beyond
• QCD cusp anomalous dimension: current status
• Precision QCD phenomenology of exotic spin-2 search at the LHC
• Eikonal amplitudes for three-hard legs processes at finite-N${}_c$
• Four-loop large-n_f contributions to the non-singlet structure functions F_2 and F_L
• Second order splitting functions and infrared safe cross sections in $\mathcal{N}=4$ SYM theory
• Benchmark of deep-inelastic-scattering structure functions at $\mathcal{O}({\alpha }_s^3)$
• Precision $e^{+}{e}^{-}$ Hemisphere Masses in the Dijet Region with Power Corrections
• Framing energetic top-quark pair production at the LHC
• Combination of aN${}^3$LO PDFs and implications for Higgs production cross-sections at the LHC
• Constraints for twist-two alien operators in QCD
• W-boson production in TMD factorization
• Nonplanar Four-Loop Anomalous Dimensions of Twist-Two Operators in N=4 Super Yang-Mills Theory: Higher Moment, General Result, and Cusp Anomalous Dimension
• Fermionic corrections to quark and gluon form factors in four-loop QCD
• Analytic two-Loop four-point form factor of the stress-tensor supermultiplet in $\mathcal{N}=4$ SYM
• Three-loop jet function for boosted heavy quarks
• Anomalous dimensions at small spins
• An analysis of Bayesian estimates for missing higher orders in perturbative calculations
• QCD analysis of $x{F}_3$ structure functions in deep-inelastic scattering: Mellin transform by Gegenbauer polynomial up to N${}^3$LO approximation
• Four-loop anomalous dimension of flavor non-singlet quark operator of twist two and Lorentz spin N for general gauge group: transcendental part
• Soft Integrals and Soft Anomalous Dimensions at N${}^3$LO and Beyond
• Renormalization of gluonic leading-twist Operators in covariant Gauges