$O({\alpha }_s^2$) Polarized Heavy Flavor Corrections}to Deep-Inelastic Scattering at $Q^2\gg m^2$

Abstract

We calculate the quarkonic $O({\alpha }_s^2)$ massive operator matrix elements $\Delta A_{Qg}(N),\Delta A_{Qq}^{\mathrm{PS}}(N)$ and $\Delta A_{qq,Q}^{\mathrm{NS}}(N)$ for the twist--2 operators and the associated heavy flavor Wilson coefficients in polarized deeply inelastic scattering in the region $Q^2\gg m^2$ to $O(\epsilon )$ in the case of the inclusive heavy flavor contributions. The evaluation is performed in Mellin space, without applying the integration-by-parts method. The result is given in terms of harmonic sums. This leads to a significant compactification of the operator matrix elements and massive Wilson coefficients in the region $Q^2\gg m^2$ derived previously in \cite{BUZA2}, which we partly confirm, and also partly correct. The results allow to determine the heavy flavor Wilson coefficients for $g_1(x,Q^2)$ to $O({\alpha }_s^2)$ for all but the power suppressed terms $\propto (m^2/Q^2{)}^k,k\ge 1$. The results in momentum fraction $z$-space are also presented. We also discuss the small $x$ effects in the polarized case. Numerical results are presented. We also compute the gluonic matching coefficients in the two--mass variable flavor number scheme to $O(\epsilon )$.

arXiv comment58 pages Latex, 12 Figures

References in corpus (105)

• The Three-Loop Splitting Functions in QCD: The Non-Singlet Case
• Harmonic Polylogarithms
• The renormalization of the axial anomaly in dimensional regularization
• Harmonic sums, Mellin transforms and Integrals
• Extraction of Spin-Dependent Parton Densities and Their Uncertainties
• The third-order QCD corrections to deep-inelastic scattering by photon exchange
• A first unbiased global determination of polarized PDFs and their uncertainties
• Harmonic Sums and Mellin Transforms up to two-loop Order
• Precision Determination of the Neutron Spin Structure Function g1n
• Measurement of the Neutron Spin Structure Function $g_1^n$ with a Polarized ^3He Target
• Deep Inelastic Scattering of Polarized Electrons by Polarized ${}^3$He and the Study of the Neutron Spin Structure
• Charm electroproduction viewed in the variable-flavour number scheme versus fixed-order perturbation theory
• Measurements of the $Q^2$-Dependence of the Proton and Neutron Spin Structure Functions g1p and g1n
• QCD Analysis of Polarized Deep Inelastic Data and Parton Distributions
• Measurement of the Proton Spin Structure Function g1p with a Pure Hydrogen Target
• The Calculation of the Two-Loop Spin Splitting Functions $P_{ij}^{(1)}(x)$
• Deep Inelastic Structure Functions at two Loops
• Heavy quark coefficient functions at asymptotic values $Q^2\gg m^2$
• Spin Physics and Polarized Structure Functions
• Measurement of the Deuteron Spin Structure Function g_1^d(x) for 1 (GeV/c)^2 < Q^2 < 40 (GeV/c)^2
• Rates for Inclusive Deep-Inelastic Electroproduction of Charm Quarks at HERA
• Determination of Polarized PDFs from a QCD Analysis of Inclusive and Semi-inclusive Deep Inelastic Scattering Data
• 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
• A Rederivation of the Spin-dependent Next-to-leading Order Splitting Functions
• QCD Analysis of the Polarized World Data
• Facts of life with gamma(5)
• QCD Analysis of Polarized Deep Inelastic Scattering Data
• The spin-dependent two-loop splitting functions
• Structural Relations of Harmonic Sums and Mellin Transforms up to Weight w = 5
• The Three-Loop Splitting Functions in QCD: The Helicity-Dependent Case
• Flavor Singlet Contribution to the Structure Function $g_1$ at Small-x
• Measurement of the Spin Structure of the Deuteron in the DIS Region
• Target Mass Corrections for Polarized Structure Functions and New Sum Rules
• Simultaneous Monte Carlo analysis of parton densities and fragmentation functions
• 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 Spin Structure of the Nucleon
• Two-Loop Massive Operator Matrix Elements and Unpolarized Heavy Flavor Production at Asymptotic Values Q^2 >> m^2
• The Theory of Deeply Inelastic Scattering
• The Gluonic Operator Matrix Elements at O(α_s^2) for DIS Heavy Flavor Production
• 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
• HECTOR 1.00 - A program for the calculation of QED, QCD and electroweak corrections to ep and lN deep inelastic neutral and charged current scattering
• Two--Loop Massive Operator Matrix Elements for Unpolarized Heavy Flavor Production to $O(ε)
• On the Drell-Levy-Yan Relation to $O({\alpha }_s^2)$
• The Transition Matrix Element A_{gq}(N) of the Variable Flavor Number Scheme at O(α_s^3)
• The massless two-loop two-point function
• Precise charm-quark mass from deep-inelastic scattering
• The Longitudinal Heavy Quark Structure Function F_{L}^{Q\bar{Q}} in the Region Q^2 \gg m^2 at O(α_s^3)
• Parton momentum and helicity distributions in the nucleon
• Mellin Moments of the Next-to-next-to Leading Order Coefficient Functions for the Drell-Yan Process and Hadronic Higgs-Boson Production
• Leading and Next-to-Leading Order Gluon Polarisation in the Nucleon and Longitudinal Double Spin Asymmetries from Open Charm Muoproduction
• $O({\alpha }_s^2)$ corrections to polarized heavy flavour production at $Q^2\gg m^2$
• Mellin Representation for the Heavy Flavor Contributions to Deep Inelastic Structure Functions
• The Singlet Contribution to the Structure Function $g_1(x,Q^2)$ at Small $x$
• $O({\alpha }_s^2)$ Timelike Wilson Coefficients for Parton-Fragmentation Functions in Mellin Space
• Determination of polarized parton distribution functions with recent data on polarization asymmetries
• The Complete $O({\alpha }_s^2)$ Non-Singlet Heavy Flavor Corrections to the Structure Functions $g_{1,2}^{ep}(x,Q^2)$, $F_{1,2,L}^{ep}(x,Q^2)$, $F_{1,2,3}^{\nu (\bar{\nu })}(x,Q^2)$ and the Associated Sum Rules
• Spin asymmetry A_1^d and the spin-dependent structure function g_1^d of the deuteron at low values of x and Q^2
• The Three-Loop Splitting Functions $P_{qg}^{(2)}$ and $P_{gg}^{(2,N_F)}$
• On the Structure of the Virtual Compton Amplitude in the Generalized Bjorken Region: Integral Relations
• 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
• Final COMPASS results on the deuteron spin-dependent structure function $g_1^{\mathrm{d}}$ and the Bjorken sum rule
• 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
• Polarized Antimatter in the Proton from Global QCD Analysis
• Two-loop QED Operator Matrix Elements with Massive External Fermion Lines
• Towards the NNLO evolution of polarised parton distributions
• Photoproduction of Heavy Quarks in Next-to-Leading Order QCD with Longitudinally Polarized Initial States
• Analytic Computing Methods for Precision Calculations in Quantum Field Theory
• Constraints on spin-dependent parton distributions at large x from global QCD analysis
• The 3-Loop Non-Singlet Heavy Flavor Contributions to the Structure Function g_1(x,Q^2) at Large Momentum Transfer
• $O({\alpha }_s^2)$ and $O({\alpha }_s^3)$ Heavy Flavor Contributions to Transversity at $Q^2\gg m^2$
• First analysis of world polarized DIS data with small-$x$ helicity evolution
• The three-loop single mass polarized pure singlet operator matrix element
• The Spin Structure of a Polarized Photon
• The Variable Flavor Number Scheme at Next-to-Leading Order
• Measurement of the Q^2 Dependence of the Deuteron Spin Structure Function g_1 and its Moments at Low Q^2 with CLAS
• 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 $O({\alpha }_s^3)$
• Longitudinal double-spin asymmetry $A_1^{\mathrm{p}}$ and spin-dependent structure function $g_1^{\mathrm{p}}$ of the proton at small values of $x$ and $Q^2$
• Quark Model Description of Polarised Deep Inelastic Scattering and the prediction of $g_2$
• Next-to-Leading Order QCD Corrections to Inclusive Heavy-Flavor Production in Polarized Deep-Inelastic Scattering
• Calculation of Massive 2-Loop Operator Matrix Elements with Outer Gluon Lines
• The $O({\alpha }^2)$ Initial State QED Corrections to $e^{+}{e}^{-}\to {\gamma }^{\ast }/Z_0^{\ast }$
• The three-loop polarized pure singlet operator matrix element with two different masses
• The Polarized Two-Loop Massive Pure Singlet Wilson Coefficient for Deep-Inelastic Scattering
• Target mass and finite $t$ corrections to diffractive deeply inelastic scattering
• The Logarithmic Contributions to the Polarized and Operator Matrix Elements in Deeply Inelastic Scattering
• $O(\alpha )$ QED Corrections to Neutral Current Polarized Deep-Inelastic Lepton-Nucleon Scattering
• Target mass and finite momentum transfer corrections to unpolarized and polarized diffractive scatterin
• The unpolarized two-loop massive pure singlet Wilson coefficients for deep-inelastic scattering
• Revisiting quark and gluon polarization in the proton at the EIC
• Twist-2 Heavy Flavor Contributions to the Structure Function $g_2(x,Q^2)$
• Evaluating Two-Loop massive Operator Matrix Elements with Mellin-Barnes Integrals
• Nucleon Mass Corrections to Spin Dependent Structure Functions and Relations Between their Twist-3 Contributions
• Mathematical Structure of Anomalous Dimensions and QCD Wilson Coefficients in Higher Order
• The Two-Loop Massless Off-Shell QCD Operator Matrix Elements to Finite Terms
• First $O({\alpha }_s^3)$ heavy flavor contributions to deeply inelastic scattering
• Impact of recent COMPASS data on polarized parton distributions and structure functions
• Scheme-invariant NNLO evolution for unpolarized DIS structure functions
• Transition from real to virtual polarized photon structures

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• NNLO Global Analysis of Polarized Parton Distribution Functions
• 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
• The non-first-order-factorizable contributions to the three-loop single-mass operator matrix elements $A_{Qg}^{(3)}$ and $\Delta A_{Qg}^{(3)}$
• Renormalization of twist-two operators in covariant gauge to three loops in QCD
• General mass variable flavor number scheme for $Z$ boson production in association with a heavy quark at hadron colliders
• Toward Precision Helicity PDFs from Global DIS and SIDIS Fits with Projected EIC Measurements