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.

159 pages Latex

References in corpus (27)

• Higgs boson gluon-fusion production in N3LO QCD
• The five-loop beta function of Yang-Mills theory with fermions
• Adler Function, Bjorken Sum Rule, and the Crewther Relation to Order alpha_s^4 in a General Gauge Theory
• 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
• The five-loop Beta function for a general gauge group and anomalous dimensions beyond Feynman gauge
• The Three-Loop Splitting Functions in QCD: The Helicity-Dependent Case
• 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
• The three-loop unpolarized and polarized non-singlet anomalous dimensions from off shell operator matrix elements
• Iterated Binomial Sums and their Associated Iterated Integrals
• The Logarithmic Contributions to the O(α_s^3) Asymptotic Massive Wilson Coefficients and Operator Matrix Elements in Deeply Inelastic Scattering
• 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
• Towards the NNLO evolution of polarised parton distributions
• The 3-Loop Non-Singlet Heavy Flavor Contributions to the Structure Function g_1(x,Q^2) at Large Momentum Transfer
• Differences between charged-current coefficient functions
• 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 Polarized Transition Matrix Element $A_{gq}(N)$ of the Variable Flavor Number Scheme at $O({\alpha }_s^3)$
• The N${}^3$LO Scheme-invariant QCD Evolution of the Non-singlet Structure Functions \boldmath $F_2^{\mathrm{NS}}(x,Q^2)$ and $g_1^{\mathrm{NS}}(x,Q^2)$
• Charged current deep-inelastic scattering at three loops
• The three-loop polarized pure singlet operator matrix element with two different masses
• 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 $A_{gg,Q}^{(3)}$
• The unpolarized two-loop massive pure singlet Wilson coefficients for deep-inelastic scattering
• The Two-Loop Massless Off-Shell QCD Operator Matrix Elements to Finite Terms

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