The three-loop single mass polarized pure singlet operator matrix element

Abstract

We calculate the massive polarized three-loop pure singlet operator matrix element $A_{Qq}^{(3),\mathrm{PS}}$ in the single mass case in the Larin scheme. This operator matrix element contributes to the massive polarized three-loop Wilson coefficient $H_{Qq}^{(3),\mathrm{PS}}$ in deep-inelastic scattering and constitutes a three-loop transition matrix element in the variable flavor number scheme. We provide analytic results in Mellin $N$ and in $x$ space and study the behaviour of this operator matrix element in the region of small and large values of the Bjorken variable $x$.

25 pages Latex, 2 Figures

References in corpus (15)

• 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 Computer Algebra Toolbox for Harmonic Sums Related to Particle Physics
• 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
• Iterated Binomial Sums and their Associated Iterated Integrals
• Modern Summation Methods and the Computation of 2- and 3-loop Feynman Diagrams
• 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
• Three Loop Massive Operator Matrix Elements and Asymptotic Wilson Coefficients with Two Different Masses
• High precision fundamental constants at the TeV scale
• Evaluation of Multi-Sums for Large Scale Problems
• 3-Loop Heavy Flavor Corrections to DIS with two Massive Fermion Lines
• The three-loop polarized pure singlet operator matrix element with two different masses
• New Heavy Flavor Contributions to the DIS Structure Function $F_2(x,Q^2)$ at $O(α_s^3)

Cited by in corpus (2)

• The three-loop polarized pure singlet operator matrix element with two different masses
• The Two-mass Contribution to the Three-Loop Polarized Operator Matrix Element $A_{gg,Q}^{(3)}$