The Three-Loop Splitting Functions in QCD: The Non-Singlet Case

Abstract

We compute the next-to-next-to-leading order (NNLO) contributions to the three splitting functions governing the evolution of unpolarized non-singlet combinations of quark densities in perturbative QCD. Our results agree with all partial results available in the literature. We find that the correct leading logarithmic (LL) predictions for small momentum fractions x do not provide a good estimate of the respective complete results. A new, unpredicted LL contribution is found for the colour factor d^{abc}d_{abc} entering at three loops for the first time. We investigate the size of the corrections and the stability of the NNLO evolution under variation of the renormalization scale. Except for very small x the corrections are found to be rather small even for large values of the strong coupling constant, in principle facilitating a perturbative evolution into the sub-GeV regime.

29 pages, Latex, 9 figures

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• Pseudo-scalar Form Factors at Three Loops in QCD
• Soft-gluon resummation for boosted top-quark production at hadron colliders
• Measurement and QCD analysis of double-differential inclusive jet cross sections in proton-proton collisions at $\sqrt{s}$ = 13 TeV
• Generalized double-logarithmic large-x resummation in inclusive deep-inelastic scattering
• Threshold corrections to rapidity distributions of Z and W^\pm bosons beyond N^2 LO at hadron colliders
• Transverse momentum in double parton scattering: factorisation, evolution and matching
• The MSR Mass and the $\mathcal{O}({\Lambda }_{\mathrm{QCD}})$ Renormalon Sum Rule
• Higgs boson production through $b\bar{b}$ annihilation at threshold in N${}^3$LO QCD
• Jet production in charged-current deep-inelastic scattering to third order in QCD
• Pion-induced Drell-Yan processes within TMD factorization
• Soft-gluon effects in WW production at hadron colliders
• Threshold resummation of the rapidity distribution for Drell-Yan production at NNLO+NNLL
• Recoil-free azimuthal angle for precision boson-jet correlation
• Resumming Quark's Longitudinal Momentum Logarithms in LaMET Expansion of Lattice PDFs
• On threshold resummation beyond leading 1-x order
• The $q_T$ and $\Delta \varphi$ spectra in W and Z production at the LHC at N${}^3$LL'+N${}^2$LO
• Analytic Computing Methods for Precision Calculations in Quantum Field Theory
• Soft-gluon resummation effects on parton distributions
• Two-loop evolution equation for the B-meson distribution amplitude
• Six-Loop Anomalous Dimension of Twist-Three Operators in N=4 SYM
• Jet fragmentation functions in proton-proton collisions using soft-collinear effective theory
• Approximate NNLO QCD corrections to semi-inclusive DIS
• $\text{Tr}(F^3)$ supersymmetric form factors and maximal transcendentality Part I: $\mathcal{N}=4$ super Yang-Mills
• TMD Fragmentation Functions at N${}^3$LO
• Boosted top production: factorization and resummation for single-particle inclusive distributions
• Four-Loop Collinear Anomalous Dimension in N = 4 Yang-Mills Theory
• Two-Loop SL(2) Form Factors and Maximal Transcendentality
• The Quark and Gluon Structure of the Proton
• Determination of Strange Sea Distributions from Neutrino-Nucleon Deep Inelastic Scattering
• Joint Two-Dimensional Resummation in $q_T$ and $0$-Jettiness at NNLL
• Differences between charged-current coefficient functions
• Four loop anomalous dimension of the second moment of the non-singlet twist-2 operator in QCD
• Electroweak Logarithms in Inclusive Cross Sections
• Higgs amplitudes from $\mathcal{N}=4$ super Yang-Mills theory
• On the Impact of Lepton PDFs
• Twist 3 of the sl(2) sector of N=4 SYM and reciprocity respecting evolution
• Gluon jet function at three loops in QCD
• $O({\alpha }_s)$ Heavy Flavor Corrections to Charged Current Deep-Inelastic Scattering in Mellin Space
• Resummed prediction for Higgs boson production through $b\bar{b}$ annihilation at N${}^3$LL
• Joint transverse momentum and threshold resummation beyond NLL
• Absence of pi^2 terms in physical anomalous dimensions in DIS: verification and resulting predictions
• Renormalization and Matching for the Collins-Soper Kernel from Lattice QCD
• Non-singlet QCD analysis of F_2(x,Q^2) up to NNLO
• The O(α_s^3) Heavy Flavor Contributions to the Charged Current Structure Function xF_3(x,Q^2) at Large Momentum Transfer
• N-jettiness beam functions at N3LO
• Pomeron in the N=4 supersymmetric gauge model at strong couplings
• Forcer, a FORM program for the parametric reduction of four-loop massless propagator diagrams
• Jets and QCD: A Historical Review of the Discovery of the Quark and Gluon Jets and its Impact on QCD
• On the Consistent Use of Scale Variations in PDF Fits and Predictions
• On the Soft-Gluon Resummation in Top Quark Pair Production at Hadron Colliders
• On next to soft corrections to Drell-Yan and Higgs Boson productions
• Scattering amplitudes in the Regge limit and the soft anomalous dimension through four loops
• QCD analysis of nucleon structure functions in deep-inelastic neutrino-nucleon scattering: Laplace transform and Jacobi polynomials approach
• Four-loop splitting functions in QCD -- The gluon-to-quark case
• Dimensional Regularisation and Factorisation Schemes in the BFKL Equation at Subleading Leve
• Fine structure of anomalous dimensions in N=4 super Yang-Mills theory
• Leading large-x logarithms of the quark-gluon contributions to inclusive Higgs-boson and lepton-pair production
• Effective field theory approach to heavy quark fragmentation
• The virtual scaling function of AdS/CFT
• Two-loop conformal generators for leading-twist operators in QCD
• BFKL at Next-to-Next-to-Leading Order
• Higher-Loop Integrability in N=4 Gauge Theory
• N${}^3$LO+N${}^3$LL QCD improved Higgs pair cross sections
• Non-Singlet QCD Analysis of the Structure Function F_2 in 3-Loops
• Resummation of small-x double logarithms in QCD: semi-inclusive electron-positron annihilation
• MT: a Mathematica package to compute convolutions
• Joint resummation of two angularities at next-to-next-to-leading logarithmic order
• Heavy Quark Fragmenting Jet Functions
• Dilepton production near partonic threshold in transversely polarized proton-antiproton collisions
• Massive charged-current coefficient functions in deep-inelastic scattering at NNLO and impact on strange-quark distributions
• Employing Helicity Amplitudes for Resummation
• NNLO soft function for electroweak boson production at large transverse momentum
• Beyond cusp anomalous dimension from integrability
• Improved constraints on parton distributions using LHCb, ALICE and HERA heavy-flavour measurements and implications for the predictions for prompt atmospheric-neutrino fluxes
• Renormalization-group improved fully differential cross sections for top pair production
• Collinear and soft gluon corrections to Higgs production at NNNLO
• Pseudo-scalar Higgs Boson Production at Threshold N${}^3$LO and N${}^3$LL QCD
• QCD threshold corrections for gluino pair production at hadron colliders
• Resummation Effects in Vector-Boson and Higgs Associated Production
• Three loop anomalous dimensions of twist-3 gauge operators in N=4 SYM
• Quasi parton distribution functions at NNLO: flavor non-diagonal quark contributions
• Anomalous Dimensions from a Spinning D5-Brane
• Precision Studies of the NNLO DGLAP Evolution at the LHC with CANDIA
• Minimal Subtraction vs. Physical Factorisation Schemes in Small-x QCD
• From N=4 gauge theory to N=2 conformal QCD: three-loop mixing of scalar composite operators
• Analytic Two-Loop Higgs Amplitudes in Effective Field Theory and the Maximal Transcendentality Principle
• The Principle of Maximal Transcendentality and the Four-Loop Collinear Anomalous Dimension
• Three-loop helicity amplitudes for quark-gluon scattering in QCD
• The role of F_L(x,Q^2) in parton analyses
• Resummation Improved Rapidity Spectrum for Gluon Fusion Higgs Production
• Higher order QCD corrections to charged-lepton deep-inelastic scattering and global fits of parton distributions
• RI'/SMOM scheme amplitudes for quark currents at two loops
• Analytic solution of the multiloop Baxter equation
• Associated production of Higgs boson with vector boson at threshold N${}^3$LO in QCD
• Scaling violation in power corrections to energy correlators from the light-ray OPE
• Renormalization and Scale Evolution of the Soft-Quark Soft Function
• Anomalous dimensions at twist-3 in the sl(2) sector of N=4 SYM
• Three loop anomalous dimension of the non-singlet transversity operator in QCD
• Radiative B decay spectrum: DGE at NNLO
• Secondary Heavy Quark Production in Jets through Mass Modes
• Probing nuclear dynamics in jet production with a global event shape
• Approximate NNLO Predictions for the Stop-Pair Production Cross Section at the LHC
• Extraction of ${\alpha }_s$ from deep inelastic scattering at large $x$
• Soft-gluon effective coupling and cusp anomalous dimension
• Leading transcedental contribution to the four-loop universal anomalous dimension in N=4 SYM
• Threshold resummation for computing large-$x$ parton distribution through large-momentum effective theory
• A case study of quark-gluon discrimination at NNLL' in comparison to parton showers
• Multi-Regge Limit of the Two-Loop Five-Point Amplitudes in $\mathcal{N}=4$ Super Yang-Mills and $\mathcal{N}=8$ Supergravity
• Higgs Rapidity Distribution in $b\bar{b}$ Annihilation at Threshold in N${}^3$LO QCD
• The N${}^3$LO Scheme-invariant QCD Evolution of the Non-singlet Structure Functions \boldmath $F_2^{\mathrm{NS}}(x,Q^2)$ and $g_1^{\mathrm{NS}}(x,Q^2)$
• Unpolarized Quark and Gluon TMD PDFs and FFs at N${}^3$LO
• Evolution of singlet structure functions from DGLAP equation at next-to-next-to-leading order at small-x
• Generalized Parton Distributions from Hadronic Observables: Non-Zero Skewness
• Higher-Order Sudakov Resummation in Coupled Gauge Theories
• Measurement of the inclusive $\mathrm{t}\overline{\mathrm{t}}$ cross section in pp collisions at $\sqrt{s}=$ 5.02 TeV using final states with at least one charged lepton
• The non-planar contribution to the four-loop universal anomalous dimension in N=4 Supersymmetric Yang-Mills theory
• An investigation of the ${\alpha }_S$ and heavy quark mass dependence in the MSHT20 global PDF analysis
• Jet fragmentation functions for $Z$-tagged jets
• Higgs-differential cross section at NNLO in dimensional regularisation
• Boosted Top Quarks in the Peak Region with N${}^3$LL Resummation
• Higher-order threshold resummation for semi-inclusive e^+e^- annihilation
• The Fully-Differential Quark Beam Function at NNLO
• Jet Charge: A new tool to probe the anomalous $Zb\bar{b}$ couplings at the EIC
• Resummation of small-x double logarithms in QCD: inclusive deep-inelastic scattering
• On next to soft threshold corrections to DIS and SIA processes
• Spin Chain for Quantum Strings
• Threshold Resummation at NNLL for Single-particle Production in Hadronic Collisions
• Next-to-leading power threshold corrections for finite order and resummed colour-singlet cross sections
• Polarised Amplitudes and Soft-Virtual Cross Sections for $b\bar{b}\to ZH$ at NNLO in QCD
• A two-loop test for the factorised S-matrix of planar N=4
• Subleading Logarithmic QED Initial State Corrections to $e^{+}{e}^{-}\to {\gamma }^{\ast }/{Z^0}^{\ast }$ to $O({\alpha }^6{L}^5)$
• (medium-modified) Fragmentation Functions
• $\text{Tr}(F^3)$ supersymmetric form factors and maximal transcendentality Part II: $0<\mathcal{N}<4$ super Yang-Mills
• Quark beam function at next-to-next-to-next-to-leading order in perturbative QCD in the generalized large-$N_c$ approximation
• Large-x structure of physical evolution kernels in Deep Inelastic Scattering
• Charged current deep-inelastic scattering at three loops
• The anomalous $Zb\bar{b}$ couplings at the HERA and EIC
• Extension of the functionality of the symbolic program FORM by external software
• ${\gamma }^{\ast }{\gamma }^{\ast }$ Cross Section at NLO and Properties of the BFKL Evolution at Higher Orders
• High energy behaviour of form factors
• Superspace calculation of the three-loop dilatation operator of N=4 SYM theory
• Reciprocity of gauge operators in N=4 SYM
• Threshold Resummed Spectra in B -> Xu l nu Decays in NLO (I)
• Tomography of pions and protons via transverse momentum dependent distributions
• Next-to SV resummed Drell-Yan cross section beyond leading-logarithm
• The structure of IR divergences in celestial gluon amplitudes
• Analytic Continuation of Harmonic Sums
• Leading logarithmic large-x resummation of off-diagonal splitting functions and coefficient functions
• Next-to-next-to leading order corrections to deeply virtual Compton scattering: the non-singlet case
• Resummed small-x and first-moment evolution of fragmentation functions in perturbative QCD
• Shape-Function Effects and Split Matching in B-> Xs l+ l-
• Relating amplitude and PDF factorisation through Wilson-line geometries
• Finite remainders of the Konishi at two loops in $\mathcal{N}=4$ SYM
• Precision boson-jet azimuthal decorrelation at hadron colliders
• On DIS Wilson coefficients in N = 4 super Yang-Mills theory
• The $N_f{C}_F^3$ contribution to the non-singlet splitting function at four-loop order
• Konishi Form Factor at Three Loop in $\mathcal{N}=4$ SYM
• The analytic structure and the transcendental weight of the BFKL ladder at NLL accuracy
• The Infrared Structure of QCD Amplitudes and $H\to gg$ in FDH and DRED
• The asymptotic behavior of the heavy quark form factors at higher order
• Three loop anomalous dimensions of higher moments of the non-singlet twist-2 Wilson and transversity operators in the MSbar and RI' schemes
• Higher order constraints on the Higgs production rate from fixed-target DIS data
• Analytic properties of high energy production amplitudes in N=4 SUSY
• Evolution Equations for Connected and Disconnected Sea Parton Distributions
• Universal Higher Order QED Corrections to Polarized Lepton Scattering
• Multiple soft radiation at one-loop order and the emission of a soft quark-antiquark pair
• Three-loop soft function for heavy-to-light quark decays
• Complete $N_f^2$ contributions to four-loop pure-singlet splitting functions
• Production of Stoponium at the LHC
• A two-loop relation between inclusive radiative and semileptonic B-decay spectra
• The Unpolarized and Polarized Single-Mass Three-Loop Heavy Flavor Operator Matrix Elements $A_{gg,Q}$ and $\Delta A_{gg,Q}$
• Integrable spin chains and scattering amplitudes
• Nonperturbative Renormalization in Lattice QCD with three Flavors of Clover Fermions: Using Periodic and Open Boundary Conditions
• Triple collinear splitting functions at NLO for scattering processes with photons
• Linear vs non-linear QCD evolution: from HERA data to LHC phenomenology
• Projected transverse momentum resummation in top-antitop pair production at LHC
• QCD analysis of the ATLAS and CMS $W^{\pm }$ and $Z$ cross-section measurements and implications for the strange sea density
• Collinear expansion for color singlet cross sections
• NNLO nucleon parton distributions from a light-cone quark model dressed with its virtual meson cloud
• Two real parton contributions to non-singlet kernels for exclusive QCD DGLAP evolution
• Three loop MSbar renormalization of QCD in the maximal abelian gauge
• Taming the B --> X(s) gamma spectrum by Dressed Gluon Exponentiation
• The Gluon Green's Function in N=4 Supersymmetric Yang-Mills Theory
• The curvature of $F_2^p(x,Q^2)$ as a probe of the range of validity of perturbative QCD evolutions in the small-$x$ region
• Polarized triple-collinear splitting functions at NLO for processes with photons
• Threshold resummed spectra in B ->Xu l nu decays in NLO (III)
• Phenomenology of diffractive DIS in the framework of fracture functions and determination of diffractive parton distribution functions
• N-jettiness Subtractions for NNLO QCD Calculations
• Modelling non-perturbative corrections to bottom-quark fragmentation
• Pion Valence Quark Distribution at Physical Pion mass of $N_f=2+1+1$ Lattice QCD
• QCD threshold corrections to Higgs decay and to hadroproduction in $l^{+}{l}^{-}$ annihilation
• Re-evaluation of the Gottfried sum using neural networks
• Two-loop evolution equations for light-ray operators
• Real corrections to Higgs boson pair production at NNLO in the large top quark mass limit
• One-loop matching for gluon lattice TMDs
• Higgs Boson Production from Black Holes at the LHC
• Stability of NLO Global Analysis and Implications for Hadron Collider Physics
• ChiliPDF: Chebyshev Interpolation for Parton Distributions
• Three loop MSbar operator correlation functions for deep inelastic scattering in the chiral limit
• Massless Propagators, $R(s)$ and Multiloop QCD
• Some Aspects of the Theory of Heavy Ion Collisions
• Soft Fragmentation on the Celestial Sphere
• The Two-mass Contribution to the Three-Loop Polarized Operator Matrix Element $A_{gg,Q}^{(3)}$
• Wrapping in maximally supersymmetric and marginally deformed N=4 Yang-Mills
• What did HERA teach us about the structure of the proton?
• Threshold resummation at N${}^3$LL accuracy and approximate N${}^3$LO corrections to semi-inclusive DIS
• Parton Distribution Uncertainties using Smoothness Prior
• Towards semi-inclusive deep inelastic scattering at next-to-next-to-leading order
• Two-loop splitting in double parton distributions
• Hidden Analytic Relations for Two-Loop Higgs Amplitudes in QCD
• Mixed QCD-electroweak corrections to Higgs production via gluon fusion in the small mass approximation
• NNLO QCD corrections to unpolarized and polarized SIDIS
• 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
• A dispersive approach to Sudakov resummation
• A Variable Flavour Number Scheme for Heavy Quark Production at Small x
• Improved nonsinglet QCD analysis of the fixed-target DIS data
• Next-to-next-to-leading logarithmic resummation for transverse thrust
• Systematic Improvement of $x$-dependent Unpolarized Nucleon Generalized Parton Distribution in Lattice-QCD Calculation
• Impact of Lattice Strangeness Asymmetry Data in the CTEQ-TEA Global Analysis
• The first-order factorizable contributions to the three-loop massive operator matrix elements $A_{Qg}^{(3)}$ and $\Delta A_{Qg}^{(3)}$
• Transverse Momentum in Semi-inclusive Deep Inelastic Scattering
• Charm Production and QCD Analysis at HERA and LHC
• A fast and accurate method for perturbative resummation of transverse momentum-dependent observables
• The non-planar contribution to the four-loop anomalous dimension of twist-2 operators: first moments in N=4 SYM and non-singlet QCD
• Quark and gluon spin-2 form factors to two-loops in QCD
• The SAGEX Review on Scattering Amplitudes, Chapter 4: Multi-loop Feynman Integrals
• The Fully-Differential Gluon Beam Function at NNLO
• Threshold Improved QCD Corrections for Stop-Antistop production at Hadron colliders
• Structure of rapidity divergences in soft factors
• Beam functions for $N$-jettiness at N${}^3$LO in perturbative QCD
• Analytical solutions of the QCD$\otimes$QED DGLAP evolution equations based on the Mellin transform technique in NLO approximation
• Two-Loop QCD Corrections to the Higgs plus three-parton amplitudes with Top Mass Correction
• IR-Improved DGLAP Theory: Kernels, Parton Distributions, Reduced Cross Sections
• Non-planar universal anomalous dimension of twist-two operators with general Lorentz spin at four loops in N=4 SYM theory
• Resummed Higgs boson cross section at next-to SV to $\mathrm{NNLO}+\overline{\mathrm{NNLL}}$
• New Approach to Parton Shower MC's for Precision QCD Theory: HERWIRI1.0(31)
• Two loop QCD corrections for the process Pseudo-scalar Higgs $\to 3$ partons
• Two-Loop QCD Helicity Amplitudes for (2+1)-Jet Production in Deep Inelastic Scattering
• $O({\alpha }_s^2$) Polarized Heavy Flavor Corrections}to Deep-Inelastic Scattering at $Q^2\gg m^2$
• Third-order QCD results on form factors and coefficient functions
• PDF in PDFs from Hadronic Tensor and LaMET
• Six-loop anomalous dimension of twist-two operators in planar N=4 SYM theory
• Toward NNLL Threshold Resummation for Hadron Pair Production in Hadronic Collisions
• HERWIRI1.0: MC Realization of IR-Improved DGLAP-CS Parton Showers
• Resummed inclusive cross-section in Randall-Sundrum model at NNLO+NNLL
• Dissecting the collinear structure of quark splitting at NNLL
• Generalized threshold resummation in inclusive DIS and semi-inclusive electron-positron annihilation
• IR-Improved DGLAP Theory
• Digging for Top Squarks from Higgs data: from signal strengths to differential distributions
• Charm-quark fragmentation with an effective coupling constant
• Angularity in DIS at next-to-next-to-leading log accuracy
• The Spin Budget of the Proton at NNLO and Beyond
• Soft-gluon and Coulomb corrections to hadronic top-quark pair production beyond NNLO
• Nucleon Helicity Parton Distribution Function in the Continuum Limit with Self-Renormalization
• NNLO Logarithmic Expansions and Precise Determinations of the Neutral Currents near the Z Resonance at the LHC: The Drell-Yan case
• Anomalous Dimensions from Soft Regge Constants
• Triple-collinear splittings with massive particles
• A planar four-loop form factor and cusp anomalous dimension in QCD
• Soft Theorem to Three Loops in QCD and $\mathcal{N}=4$ Super Yang-Mills Theory
• Momentum-space threshold resummation in $tW$ production at the LHC
• Going beyond Soft plus Virtual
• N=4 Super-Yang-Mills Theory, QCD and Collider Physics
• Review of AdS/CFT Integrability, Chapter III.4: Twist states and the cusp anomalous dimension
• The Two-Loop Massless Off-Shell QCD Operator Matrix Elements to Finite Terms
• Three-dimensional Imaging of Pion using Lattice QCD: Generalized Parton Distributions
• The property of maximal transcendentality: calculation of master integrals
• Four-loop splitting functions at small $x$
• Master integrals for splitting functions from differential equations in QCD
• Towards massless and massive event shapes in the large-${\beta }_0$ limit
• Running-coupling effects in the triple-differential charmless semileptonic decay width
• Infrared singularities of multi-leg QCD amplitudes with a massive parton at three loops
• Mathematical Structure of Anomalous Dimensions and QCD Wilson Coefficients in Higher Order
• Quark and gluon two-loop beam functions for leading-jet $p_T$ and slicing at NNLO
• NNLO corrections to B --> X_u l nu and the determination of |V_ub|
• Shape-function independent relations of charmless inclusive B-decay spectra
• Impact of Inclusive Electron Ion Collider Data on Collinear Parton Distributions
• Double Higgs production at NNLO interfaced to parton showers in GENEVA
• Perturbative and nonperturbative contributions to the strange quark asymmetry in the nucleon
• The NNLO non-singlet QCD analysis of parton distributions based on Bernstein polynomials
• Stairway to discovery: a report on the CMS programme of cross section measurements from millibarns to femtobarns
• Phenomenology of leading nucleon production in $ep$ collisions at HERA in the framework of fracture functions
• Determination of neutron fracture functions from a global QCD analysis of leading neutron production at HERA
• The inverse Mellin transform via analytic continuation
• Impact of Jet Veto Resummation on Slepton Searches
• Anti-$k_T$ jet function at next-to-next-to-leading order
• Three loop form factors of a massive spin-2 particle with nonuniversal coupling
• Heavy Quark Fragmentation in $e^{+}{e}^{-}$ Collisions to NNLO+NNLL Accuracy in Perturbative QCD
• Massive neutral gauge boson production as a probe of nuclear modifications of parton distributions at the LHC
• Double-logs, Gribov-Lipatov reciprocity and wrapping
• Parton distribution functions and constraints on the intrinsic charm content of the proton using BHPS approach
• The SAGEX Review on Scattering Amplitudes, Chapter 15: The Multi-Regge Limit
• Comparison of NNLO DIS scheme splitting functions with results from exact gluon kinematics at small x
• Next to SV resummed prediction for pseudoscalar Higgs boson production at NNLO$+\overline{\text{NNLL}}$
• High Energy Photoproduction
• The property of maximal transcendentality: calculation of Feynman integrals
• Large spin expansion of the long-range Baxter equation in the sl(2) sector of N=4 SYM
• Form factors with two operator insertions and the principle of maximal transcendentality
• A Phenomenological Solution Small $x$ to the Longitudinal Structure Function Dynamical Behavior
• The Virtual Photon Structure to the Next-to-next-to-leading Order in QCD
• QCD$\times$QED evolution of TMDs
• Resummed inclusive cross-section in ADD model at N${}^3$LL+NNLO
• The NNLO quark beam function for jet-veto resummation
• Large spin behavior of anomalous dimensions and short-long strings duality
• Zero-jettiness soft function to third order in perturbative QCD
• Renormalization of twist-two operators in covariant gauge to three loops in QCD
• The QCD Splitting Functions at Three Loops: Methods and Results
• Sum rules for higher twist sl(2)operators in N=4 SYM
• Refining the GENEVA method for Higgs boson production via gluon fusion
• Magnons and BFKL
• Threshold enhanced cross sections for colorless productions
• Scheme-invariant NNLO evolution for unpolarized DIS structure functions
• Soft anomalous dimensions and resummation in QCD
• Photon structure function revisited
• NNLO QCD corrections to production of a spin-2 particle with non-universal couplings in the DY process
• Iterating QCD scattering amplitudes in the high-energy limit
• Vector boson production in joint resummation
• Four-loop massive cusp anomalous dimension in QCD: a calculation from asymptotics
• Yangians in Integrable Field Theories, Spin Chains and Gauge-String Dualities
• The dark side of the proton
• Resummed next-to-soft corrections to rapidity distribution of Higgs Boson to $\text{NNLO}+\overline{\text{NNLL}}$
• Constant terms in threshold resummation and the quark form factor
• First $O({\alpha }_s^3)$ heavy flavor contributions to deeply inelastic scattering
• Next-to-leading Log Resummation of Scalar and Pseudoscalar Higgs Boson Differential Cross-Sections at the LHC and Tevatron
• Renormalization of the next-to-leading-power $\gamma \gamma \to h$ and $gg\to h$ soft quark functions
• QCD analysis of $W$- and $Z$-boson production at Tevatron
• Next-to-soft-virtual resummed rapidity distribution for Drell-Yan process to $\text{NNLO}+\overline{\text{NNLL}}$
• Review of AdS/CFT Integrability, Chapter I.2: The spectrum from perturbative gauge theory
• From weak coupling to spinning strings
• Fully NLO Parton Shower in QCD
• Three loop MSbar transversity operator anomalous dimensions for fixed moment n <= 8
• Heavy Flavor DIS Wilson coefficients in the asymptotic regime
• Determination of ${\alpha }_S$ beyond NNLO using event shape averages
• Evolution of the longitudinal structure function at small x
• Large-Spin Expansions of GKP Strings
• Large x Resummation in Q^2 Evolution
• Three-loop off-forward evolution kernel for axial-vector operators in Larin's scheme
• Higgs Production at NNLL${}^{\prime }$+NNLO using Rapidity Dependent Jet Vetoes
• The non-singlet kaon fragmentation function from e^+e^- kaon production
• Spin correlations and Bell nonlocality in $\Lambda \bar{\Lambda }$ pair production from $e^{+}{e}^{-}$ collisions with a thrust cut
• Single-inclusive hadron production in electron-positron annihilation at next-to-next-to-next-to-leading order in QCD
• Global analysis of nuclear parton distribution functions at leading and next-to-leading order perturbative QCD
• Improved analysis of moments of F3 in neutrino-nucleon scattering using the Bernstein polynomial method
• On the intrinsic bottom content of the nucleon and its impact on heavy new physics at the LHC
• Three-loop helicity amplitudes for photon+jet production
• Definition and Evolution of Transverse Momentum Distributions
• Resummation for Lattice QCD Calculation of Generalized Parton Distributions at Nonzero Skewness
• Precision three-dimensional imaging of nuclei using recoil-free jets
• On next-to-eikonal exponentiation
• Strange quark-antiquark asymmetry of nucleon sea from $\Lambda /\bar{\Lambda }$ polarization
• Generalized Gribov-Lipatov Reciprocity and AdS/CFT
• Higgs boson rapidity distribution in bottom annihilation at NNLL and beyond
• Evolution and interpolation of double parton distributions using Chebyshev grids
• On higher-order flavour-singlet splitting and coefficient functions at large x
• RI'/SMOM scheme amplitudes for deep inelastic scattering operators at one loop in QCD
• QCD cusp anomalous dimension: current status
• Threshold resummation for the production of a color sextet (antitriplet) scalar at the LHC
• Thrust distribution in Higgs decays up to the fifth logarithmic order
• Renormalization of non-singlet quark operator matrix elements for off-forward hard scattering
• Precision QCD phenomenology of exotic spin-2 search at the LHC
• Analytical solution to DGLAP integro-differential equation in a simple toy-model with a fixed gauge coupling
• On Rapidity Divergences in the Soft and Collinear Limits of QCD
• Conformal constraints for anomalous dimensions of leading twist operators
• Electroweak Radiative Corrections to Higgs Production via Vector Boson Fusion using SCET: Numerical Results
• Strings for Quantumchromodynamics
• N${}^3$LL + $\mathcal{O}({\alpha }_s^2)$ predictions of lepton-jet azimuthal angular distribution in deep-inelastic scattering
• Spin-2 Form Factors at Three Loop in QCD
• Target Mass Corrections for the Virtual Photon Structure Functions to the Next-to-next-to-leading Order in QCD
• Semiclassical Strings in AdS_5 x S^5 and Automorphic Functions
• Deciphering the Maximal Transcendentality Principle via Bootstrap
• Summary of ICHEP 2004
• Mapping Parton Distributions of Hadrons with Lattice QCD
• disorder: Deep inelastic scattering at high orders
• The DIS 1-Jettiness Event Shape at N${}^3$LL+$\mathcal{O}({\alpha }_s^2)$
• Analytical solution to DGLAP integro-differential equation via complex maps in domains of contour integrals
• Polarized fragmenting jet functions in Inclusive and Exclusive Jet Production
• The photon energy spectrum in $B\to X_s\gamma$ at N${}^3$LL${}^{\prime }$
• Parton distribution functions at LO, NLO and NNLO with correlated uncertainties between orders
• Second order splitting functions and infrared safe cross sections in $\mathcal{N}=4$ SYM theory
• Three-Loop Contributions to the Gluonic Massive Operator Matrix Elements at General Values of N
• QCD-like properties for anomalous dimensions in N=4 SYM
• One-loop impact factor for the emission of two gluons
• Angularity in Higgs boson decays via $\mathbf{H}\to \mathbf{gg}$ at NNLL${}^{\prime }$ accuracy
• A New Method for Calculating Differential Distributions Directly in Mellin Space
• Higher-Order Corrections in QCD Evolution Equations and Tools for Their Calculation
• Automated calculations for multi-leg processes
• String-based axial and helicity-flip GPDs: a comparison to lattice QCD
• Three-loop soft function for energetic electroweak boson production at hadron colliders
• Two-loop evolution kernels for colour dependent double parton distributions
• Studies of Quantum Chromodynamics at the LHC
• NNLO electron structure functions (PDFs) from SCET
• NNLO QCD corrections to the resonant sneutrino/slepton production at Hadron Colliders
• On the Scale Variation of the Total Cross Section for Higgs Production at the LHC and at the Tevatron
• Framing energetic top-quark pair production at the LHC
• Hard QCD at hadron colliders
• Methods for the Reduction of Three-Loop QCD Form Factors
• Bilinear quark operator renormalization at generalized symmetric point
• The neural network approach to parton distribution functions
• New constraints on the up-quark valence distribution in the proton
• Benchmark of deep-inelastic-scattering structure functions at $\mathcal{O}({\alpha }_s^3)$
• The two-loop Higgs impact factor
• An analysis of polarized parton distribution functions with nonlinear QCD evolution equations
• On threshold resummation of singlet structure and fragmentation functions
• Entanglement entropy, Monte Carlo event generators, and soft gluons DIScovery
• Highest states in light-cone $Ad{S}_5\times S^5$ superstring
• Symbolic Summation and Higher Orders in Perturbation Theory
• Recent theoretical progress in perturbative QCD
• Structure constants of twist-two light-ray operators in the triple Regge limit
• QED corrections to parton distributions and Altarelli-Parisi splitting functions in the polarized case
• Top quark theory review for the Tevatron, LHC, and ILC
• PartonDensity.jl: a novel parton density determination code
• Universal structure of subleading infrared poles at strong coupling
• Status of MRST/MSTW PDF sets
• 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
• Global QCD fit from $Q^2=0$ to $Q^2=30000$ GeV${}^2$ with Regge-compatible initial condition
• Collins-Soper Kernel in the QCD Instanton Vacuum
• Heavy quark effects on parton distribution functions in the unpolarized virtual photon up to the next-to-leading order in QCD
• SUSY, Casimir scaling and probabilistic properties of gluon and quark jets evolution
• Single-valued representation of unpolarized and polarized semi-inclusive deep inelastic scattering at next-to-next-to-leading order
• Structural Relations between Nested Harmonic Sums
• Resummation of large logarithms in the heavy quark effects on the parton distributions inside the virtual photon
• Algorithm to find an all-order in the running coupling solution to an equation of the DGLAP type
• QCD analysis of non-singlet structure functions at NNLO accuracy, based on the Laplace transform
• Soft-Collinear Factorization and Sudakov Resummation of Heavy Meson Decay Amplitudes with Effective Field Theories
• The property of maximal transcendentality in the N=4 SYM
• N${}^3$LO soft-gluon corrections in single-particle-inclusive kinematics and $H^{+}{H}^{-}$ production
• Rapidity regulators in the semi-inclusive deep inelastic scattering and Drell-Yan processes
• The Catchment Area of Groomed Jets at NNLL
• Accuracy and Precision in Collider Event Shapes
• Basis transformation properties of anomalous dimensions for hard exclusive processes
• DGLAP and BFKL equations in $\mathcal{N}=4$ SYM: from weak to strong coupling
• $x{F}_3(x,Q^2)$ Structure Function and Gross-Llewellyn Smith Sum Rule with Nuclear Effect and Higher Twist Correction
• Collinear splitting, parton evolution and the strange-quark asymmetry of the nucleon in NNLO QCD
• Progress in Small x Resummation
• Soft gluon resummation for gluon fusion $ZH$ production
• Three-loop jet function for boosted heavy quarks
• Dynamical parton distribution functions
• Spatially dependent parton distribution functions and hard processes in nuclear collisions
• Unitarity methods for Mellin moments of Drell-Yan cross sections
• Sudakov Resummations at Higher Orders
• Anomalous dimensions at small spins
• An analysis of Bayesian estimates for missing higher orders in perturbative calculations
• Collins-Soper kernel from lattice QCD at the physical pion mass
• NNLO splitting and coefficient functions with time-like kinematics
• Analytical perturbation theory and Nucleon structure function in infrared region
• Parton distributions in the virtual photon target up to NNLO in QCD
• QCD at hadron colliders
• Experimental review of unpolarised nucleon structure functions
• Analytic Bethe Ansatz Solutions for Highest States in the su(1|1) and su(2) Sectors
• Next-to-next-to-leading order threshold soft function for $tW$ production
• Three-loop helicity amplitudes for four-quark scattering in massless QCD
• One-loop triple collinear splitting amplitudes in QCD
• Proton structure at the LHC
• Progress in computing inclusive B decay spectra
• Gauge-String Dualities and Some Applications
• Exact Results in Supersymmetric Gauge Theories
• Light-like Wilson Loops and Cusp Anomalous Dimensions in Non-conformal Gauge Theories
• A semi-analytical $x$-space solution for parton evolution -- Application to non-singlet and singlet DGLAP equation
• Pomeron in the N=4 SYM at strong couplings
• Infrared structure of $\mathcal{N}$ = 4 SYM and leading transcendentality principle in gauge theory
• QCD analysis of $x{F}_3$ structure functions in deep-inelastic scattering: Mellin transform by Gegenbauer polynomial up to N${}^3$LO approximation
• Threshold resummation for $Z$-boson pair production at NNLO+NNLL
• Effective Field Theories for the LHC
• Status of Deeply Inelastic Parton Distributions
• Pseudoscalar Higgs boson decay to three parton amplitudes at NNLO to higher orders in the dimensional regulator
• Topics in Cusped/Lightcone Wilson Loops
• The new PV prescription for IR singularities of NLO splitting functions
• Markovian MC simulation of QCD evolution at NLO level with minimum k_T
• At the Frontier of Precision QCD in the LHC Era
• MHV amplitudes, Wilson loops and the BDS ansatz in the superconformal N=2 QCD
• Four-loop anomalous dimension of flavor non-singlet quark operator of twist two and Lorentz spin N for general gauge group: transcendental part
• QCD Theory
• Approximate N${}^2$LO and N${}^3$LO QCD Predictions for $tW$ Production
• Factorization at the LHC: From PDFs to Initial State Jets (Ph.D. thesis)
• Novel Heavy-Quark Physics Phenomena
• Renormalization of gluonic leading-twist Operators in covariant Gauges
• DIS 2009 Concluding Talk: Outlook and Perspective
• Diffraction 2006: Theoretical Summary
• Pomeron in the N=4 SYM
• QCD resummation for high-p${}_T$ jet shapes at hadron colliders
• QCD evolution equations from conformal symmetry
• QCD Beyond Leading Power
• End-point resummation in squark decays
• High Energy Resummation of Jet Observables
• Higher-order corrections to the splitting functions from differential equations in QCD
• Virtual Photon Structure Functions to NNLO in QCD
• QCD analysis of valence structure functions using deep inelastic lepton-nucleon scattering
• Soft Integrals and Soft Anomalous Dimensions at N${}^3$LO and Beyond
• Fermionic contribution to the anomalous dimension of twist-2 operators in N=4 SYM theory, critical indices and integrability
• Threshold resummation for $W$-boson pair production at NNLO+NNLL
• New Applications of Resummation in Non-Abelian Gauge Theories: QED X QCD Exponentiation for LHC Physics, IR-Improved DGLAP Theory and Resummed Quantum Gravity
• On interpolating anomalous dimension of twist-two operators with general spins
• Higher-order soft and virtual corrections in $pp\to \gamma W$ production at the LHC
• The top quark jet-function at two loops
• Exploring the substructure of nucleons and nuclei with machine learning
• QCD Corrections to Dilepton Production near Partonic Threshold in proton-antiproton Scattering
• Infrared structure of $SU(N)\times U(1)$ gauge theory to three loops