The three-loop polarized singlet anomalous dimensions from off-shell operator matrix elements

Abstract

Future high luminosity polarized deep--inelastic scattering experiments will improve both the knowledge of the spin sub--structure of the nucleons and contribute further to the precision determination of the strong coupling constant, as well as, reveal currently yet unknown higher twist contributions in the polarized sector. For all these tasks to be performed, it is necessary to know the QCD leading twist scaling violations of the measured structure functions. Here an important ingredient consists in the polarized singlet anomalous dimensions and splitting functions in QCD. We recalculate these quantities to three--loop order in the M--scheme by using the traditional method of space--like off--shell massless operator matrix elements, being a gauge--dependent framework. Here one obtains the anomalous dimensions without referring to gravitational currents, needed when calculating them using the forward Compton amplitude. We also calculate the non--singlet splitting function $\Delta P_{\mathrm{qq}}^{(2),\mathrm{s},\mathrm{NS}}$ and compare the final results to the literature, also including predictions for the region of small values of Bjorken $x$.

28 pages Latex, 1 figure

References in corpus (29)

• The five-loop beta function of Yang-Mills theory with fermions
• 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
• QCD Analysis of the Polarized World Data
• The five-loop Beta function for a general gauge group and anomalous dimensions beyond Feynman gauge
• A Computer Algebra Toolbox for Harmonic Sums Related to Particle Physics
• The Three-Loop Splitting Functions in QCD: The Helicity-Dependent Case
• Five-loop quark mass and field anomalous dimensions for a general gauge group
• Five-loop renormalisation of QCD in covariant gauges
• The three-loop unpolarized and polarized non-singlet anomalous dimensions from off shell operator matrix elements
• Iterated Binomial Sums and their Associated Iterated Integrals
• Modern Summation Methods and the Computation of 2- and 3-loop Feynman Diagrams
• Analytic Epsilon Expansions of Master Integrals Corresponding to Massless Three-Loop Form Factors and Three-Loop g-2 up to Four-Loop Transcendentality Weight
• Analytic continuation of the Mellin moments of deep inelastic structure functions
• Towards the NNLO evolution of polarised parton distributions
• A Symbolic Summation Approach to Find Optimal Nested Sum Representations
• Evaluation of Multi-Sums for Large Scale Problems
• The 3-Loop Non-Singlet Heavy Flavor Contributions to the Structure Function g_1(x,Q^2) at Large Momentum Transfer
• The three-loop single mass polarized 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 $O({\alpha }_s^3)$
• Parameterized Telescoping Proves Algebraic Independence of Sums
• Two-loop application of the Breitenlohner-Maison/'t Hooft-Veltman scheme with non-anticommuting ${\gamma }_5$: Full renormalization and symmetry-restoring counterterms in an abelian chiral gauge theory
• 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
• A Difference Ring Theory for Symbolic Summation
• The Two-mass Contribution to the Three-Loop Polarized Operator Matrix Element $A_{gg,Q}^{(3)}$
• On gamma_5 in higher-order QCD calculations and the NNLO evolution of the polarized valence distribution
• The Two-Loop Massless Off-Shell QCD Operator Matrix Elements to Finite Terms
• Higher Twist contributions to the Structure Functions F_2(x,Q^2) and g_2(x,Q^2)

Cited by in corpus (29)

• Snowmass 2021 whitepaper: Proton structure at the precision frontier
• The massless three-loop Wilson coefficients for the deep-inelastic structure functions $F_2,F_L,x{F}_3$ and $g_1$
• EKO: Evolution Kernel Operators
• Quark and Gluon Helicity Evolution at Small $x$: Revised and Updated
• Analytic Solution for the Revised Helicity Evolution at Small $x$ and Large $N_c$: New Resummed Gluon-Gluon Polarized Anomalous Dimension and Intercept
• NNLO Global Analysis of Polarized Parton Distribution Functions
• Resummation of small-x double logarithms in QCD: inclusive deep-inelastic scattering
• An observation on Feynman diagrams with axial anomalous subgraphs in dimensional regularization with an anticommuting ${\gamma }_5$
• The $N_f{C}_F^3$ contribution to the non-singlet splitting function at four-loop order
• The Unpolarized and Polarized Single-Mass Three-Loop Heavy Flavor Operator Matrix Elements $A_{gg,Q}$ and $\Delta A_{gg,Q}$
• Complete $N_f^2$ contributions to four-loop pure-singlet splitting functions
• 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 $N_c\&N_f$
• The first-order factorizable contributions to the three-loop massive operator matrix elements $A_{Qg}^{(3)}$ and $\Delta A_{Qg}^{(3)}$
• NNLO QCD corrections to unpolarized and polarized SIDIS
• The SAGEX Review on Scattering Amplitudes, Chapter 4: Multi-loop Feynman Integrals
• Global analysis of polarized DIS & SIDIS data with improved small-$x$ helicity evolution
• The inverse Mellin transform via analytic continuation
• Renormalization of twist-two operators in covariant gauge to three loops in QCD
• Renormalization of the axial current operator in dimensional regularization at four-loop in QCD
• Parton-shower effects in polarized deep inelastic scattering
• Evolution and interpolation of double parton distributions using Chebyshev grids
• Two-loop evolution kernels for colour dependent double parton distributions
• Entanglement entropy, Monte Carlo event generators, and soft gluons DIScovery
• The Unresolved Behaviour of Polarized Scattering Matrix Elements at NNLO in QCD
• Toward Precision Helicity PDFs from Global DIS and SIDIS Fits with Projected EIC Measurements
• Renormalization of gluonic leading-twist Operators in covariant Gauges
• Nucleon spin structure functions, considering target mass correction and higher twist effects at the NNLO accuracy and their transverse momentum dependence