The massless three-loop Wilson coefficients for the deep-inelastic structure functions $F_2,F_L,x{F}_3$ and $g_1$

Abstract

We calculate the massless unpolarized Wilson coefficients for deeply inelastic scattering for the structure functions $F_2(x,Q^2),F_L(x,Q^2),x{F}_3(x,Q^2)$ in the $\overline{\mathsf{MS}}$ scheme and the polarized Wilson coefficients of the structure function $g_1(x,Q^2)$ in the Larin scheme up to three--loop order in QCD in a fully automated way based on the method of arbitrary high Mellin moments. We work in the Larin scheme in the case of contributing axial--vector couplings or polarized nucleons. For the unpolarized structure functions we compare to results given in the literature. The polarized three--loop Wilson coefficients are calculated for the first time. As a by--product we also obtain the quarkonic three--loop anomalous dimensions from the $O(1/\epsilon )$ terms of the unrenormalized forward Compton amplitude. Expansions for small and large values of the Bjorken variable $x$ are provided.

arXiv comment159 pages Latex

References in corpus (85)

• 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 three-loop QCD $\beta$-function and anomalous dimensions
• Five-Loop Running of the QCD coupling constant
• The Four-Loop QCD Beta-Function and Anomalous Dimensions
• The renormalization of the axial anomaly in dimensional regularization
• Harmonic sums, Mellin transforms and Integrals
• High-Energy Factorization and Small-X Deep Inelastic Scattering Beyond Leading Order
• 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
• The five-loop beta function of Yang-Mills theory with fermions
• The Multiple Zeta Value Data Mine
• Calculation of the quark and gluon form factors to three loops in QCD
• The Multithreaded version of FORM
• The 3-loop QCD calculation of the moments of deep inelastic structure functions
• Harmonic Sums and Polylogarithms Generated by Cyclotomic Polynomials
• Higgs Boson Production at Hadron Colliders at N3LO in QCD
• Adler Function, Bjorken Sum Rule, and the Crewther Relation to Order alpha_s^4 in a General Gauge Theory
• MATAD: a program package for the computation of MAssive TADpoles
• Deep Inelastic Structure Functions at two Loops
• Spin Physics and Polarized Structure Functions
• Algebraic Relations Between Harmonic Sums and Associated Quantities
• 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
• Analytic and Algorithmic Aspects of Generalized Harmonic Sums and Polylogarithms
• The Drell-Yan cross section to third order in the strong coupling constant
• Some higher moments of deep inelastic structure functions at next-to-next-to leading order of perturbative QCD
• The five-loop Beta function for a general gauge group and anomalous dimensions beyond Feynman gauge
• Non--Singlet QCD Analysis of Deep Inelastic World Data at \boldmath $O({\alpha }_s^3)$
• Structural Relations of Harmonic Sums and Mellin Transforms up to Weight w = 5
• A Critical Appraisal and Evaluation of Modern PDFs
• The Three-Loop Splitting Functions in QCD: The Helicity-Dependent Case
• Target Mass Corrections for Polarized Structure Functions and New Sum Rules
• On the Behaviour of Non--Singlet Structure Functions at Small $x$
• The 3-Loop Non-Singlet Heavy Flavor Contributions and Anomalous Dimensions for the Structure Function $F_2(x,Q^2)$ and Transversity
• The 3-Loop Pure Singlet Heavy Flavor Contributions to the Structure Function $F_2(x,Q^2)$ and the Anomalous Dimension
• Third-order QCD corrections to the charged-current structure function F_3
• The Theory of Deeply Inelastic Scattering
• The Evolution of Unpolarized Singlet Structure Functions at Small x
• On the Twist 2 and Twist 3 Contributions to the Spin-dependent Electroweak Structure Functions
• The three-loop unpolarized and polarized non-singlet anomalous dimensions from off shell operator matrix elements
• On the Drell-Levy-Yan Relation to $O({\alpha }_s^2)$
• Charged Current Drell-Yan Production at N3LO
• Iterated Binomial Sums and their Associated Iterated Integrals
• The Strange Sea Density and Charm Production in Deep Inelastic Charged Current Processes
• Automated Solution of First Order Factorizable Systems of Differential Equations in One Variable
• Determining the closed forms of the $O(a_s^3)$ anomalous dimensions and Wilson coefficients from Mellin moments by means of computer algebra
• The Singlet Contribution to the Structure Function $g_1(x,Q^2)$ at Small $x$
• The Logarithmic Contributions to the O(α_s^3) Asymptotic Massive Wilson Coefficients and Operator Matrix Elements in Deeply Inelastic Scattering
• Order α_s^2 Contributions to charm production in charged-current deep-inelastic lepton-hadron scattering
• The three-loop polarized singlet anomalous dimensions from off-shell operator matrix elements
• The $O({\alpha }_s^3{n}_f{T}_F^2{C}_{A,F})$} Contributions to the Gluonic Massive Operator Matrix Elements
• The $O({\alpha }_s^2)$ Heavy Quark Corrections to Charged Current Deep-Inelastic Scattering at large Virtualities
• The O(α_s^3 T_F^2) Contributions to the Gluonic Operator Matrix Element
• Analytic Epsilon Expansions of Master Integrals Corresponding to Massless Three-Loop Form Factors and Three-Loop g-2 up to Four-Loop Transcendentality Weight
• Three Loop Massive Operator Matrix Elements and Asymptotic Wilson Coefficients with Two Different Masses
• On the twist-2 contributions to polarized structure functions and new sum rules
• The Polarized Three-Loop Anomalous Dimensions from On-Shell Massive Operator Matrix Elements
• Two-loop operator matrix elements calculated up to finite terms for polarized deep inelastic lepton-hadron scattering
• The Method of Arbitrarily Large Moments to Calculate Single Scale Processes in Quantum Field Theory
• Generalized Harmonic, Cyclotomic, and Binomial Sums, their Polylogarithms and Special Numbers
• Towards the NNLO evolution of polarised parton distributions
• Differences between charged-current coefficient functions
• The 3-Loop Non-Singlet Heavy Flavor Contributions to the Structure Function g_1(x,Q^2) at Large Momentum Transfer
• $O({\alpha }_s)$ Heavy Flavor Corrections to Charged Current Deep-Inelastic Scattering in Mellin Space
• The three-loop single mass polarized pure singlet operator matrix element
• The two-mass contribution to the three-loop pure singlet operator matrix element
• The N${}^3$LO Scheme-invariant QCD Evolution of the Non-singlet Structure Functions \boldmath $F_2^{\mathrm{NS}}(x,Q^2)$ and $g_1^{\mathrm{NS}}(x,Q^2)$
• The Polarized Transition Matrix Element $A_{gq}(N)$ of the Variable Flavor Number Scheme at $O({\alpha }_s^3)$
• Quark Model Description of Polarised Deep Inelastic Scattering and the prediction of $g_2$
• Charged current deep-inelastic scattering at three loops
• The singlet contribution to the Bjorken sum rule for polarized deep inelastic scattering
• The Polarized Two-Loop Massive Pure Singlet Wilson Coefficient for Deep-Inelastic Scattering
• The three-loop polarized pure singlet operator matrix element with two different masses
• Dimensional recurrence relations: an easy way to evaluate higher orders of expansion in $\epsilon$
• The Logarithmic Contributions to the Polarized and Operator Matrix Elements in Deeply Inelastic Scattering
• The Two-mass Contribution to the Three-Loop Polarized Operator Matrix Element $A_{gg,Q}^{(3)}$
• Perturbative Part of the Non-Singlet Structure Function F_2 in the Large-N_F Limit
• The unpolarized two-loop massive pure singlet Wilson coefficients for deep-inelastic scattering
• Twist-2 Heavy Flavor Contributions to the Structure Function $g_2(x,Q^2)$
• The Two-Loop Massless Off-Shell QCD Operator Matrix Elements to Finite Terms
• Scheme-invariant NNLO evolution for unpolarized DIS structure functions

Cited by in corpus (27)

• Analytic Solution for the Revised Helicity Evolution at Small $x$ and Large $N_c$: New Resummed Gluon-Gluon Polarized Anomalous Dimension and Intercept
• The Unpolarized and Polarized Single-Mass Three-Loop Heavy Flavor Operator Matrix Elements $A_{gg,Q}$ and $\Delta A_{gg,Q}$
• A POWHEG generator for deep inelastic scattering
• Next-to-Next-to-Leading Order QCD Corrections to Polarized Semi-Inclusive Deep-Inelastic Scattering
• Polarized semi-inclusive deep-inelastic scattering at NNLO in QCD
• Helicity Evolution at Small $x$: Revised Asymptotic Results at Large $N_c\&N_f$
• NNLO QCD corrections to unpolarized and polarized SIDIS
• The first-order factorizable contributions to the three-loop massive operator matrix elements $A_{Qg}^{(3)}$ and $\Delta A_{Qg}^{(3)}$
• Yadism: Yet Another Deep-Inelastic Scattering Module
• Global analysis of polarized DIS & SIDIS data with improved small-$x$ helicity evolution
• Neutral and Charged Current Semi-Inclusive Deep-Inelastic Scattering at NNLO QCD
• The inverse Mellin transform via analytic continuation
• Off-shell effects in bound nucleons and parton distributions from ${}^1$H, ${}^2$H, ${}^3$H and ${}^3$He data
• A Phenomenological Analysis of LHC Neutrino Scattering at NLO Accuracy Matched to Parton Showers
• Parton-shower effects in polarized deep inelastic scattering
• disorder: Deep inelastic scattering at high orders
• Four-loop large-n_f contributions to the non-singlet structure functions F_2 and F_L
• Benchmark of deep-inelastic-scattering structure functions at $\mathcal{O}({\alpha }_s^3)$
• Combination of aN${}^3$LO PDFs and implications for Higgs production cross-sections at the LHC
• General mass variable flavor number scheme for $Z$ boson production in association with a heavy quark at hadron colliders
• Entanglement entropy, Monte Carlo event generators, and soft gluons DIScovery
• The Unresolved Behaviour of Polarized Scattering Matrix Elements at NNLO in QCD
• Parton distribution functions and QCD coupling constant from LHC and non-LHC data
• Four-loop anomalous dimension of flavor non-singlet quark operator of twist two and Lorentz spin N for general gauge group: transcendental part
• QCD analysis of $x{F}_3$ structure functions in deep-inelastic scattering: Mellin transform by Gegenbauer polynomial up to N${}^3$LO approximation
• Analytic auxiliary mass flow to compute master integrals in singular kinematics
• QCD analysis of valence structure functions using deep inelastic lepton-nucleon scattering