The Asymptotic 3-Loop Heavy Flavor Corrections to the Charged Current Structure Functions $F_L^{W^{+}-W^{-}}(x,Q^2)$ and $F_2^{W^{+}-W^{-}}(x,Q^2)$

Abstract

We calculate the massive Wilson coefficients for the heavy flavor contributions to the non-singlet charged current deep-inelastic scattering structure functions $F_L^{W^{+}}(x,Q^2)-F_L^{W^{-}}(x,Q^2)$ and $F_2^{W^{+}}(x,Q^2)-F_2^{W^{-}}(x,Q^2)$ in the asymptotic region $Q^2\gg m^2$ to 3-loop order in Quantum Chromodynamics (QCD) at general values of the Mellin variable $N$ and the momentum fraction $x$. Besides the heavy quark pair production, also the single heavy flavor excitation $s\to c$ contributes. Numerical results are presented for the charm quark contributions and consequences on the unpolarized Bjorken sum rule and Adler sum rule are discussed.

27 pages, 8 figures

References in corpus (6)

• 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 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
• Calculating Massive 3-loop Graphs for Operator Matrix Elements by the Method of Hyperlogarithms
• The 3-Loop Non-Singlet Heavy Flavor Contributions to the Structure Function g_1(x,Q^2) at Large Momentum Transfer
• Charged current deep-inelastic scattering at three loops

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• The Polarized Transition Matrix Element $A_{gq}(N)$ of the Variable Flavor Number Scheme at $O({\alpha }_s^3)$
• The Two-mass Contribution to the Three-Loop Polarized Operator Matrix Element $A_{gg,Q}^{(3)}$
• The Two-Loop Massless Off-Shell QCD Operator Matrix Elements to Finite Terms