The 3-Loop Pure Singlet Heavy Flavor Contributions to the Structure Function $F_2(x,Q^2)$ and the Anomalous Dimension

J. Ablinger; A. Behring; J. Blümlein; A. De Freitas; A. von Manteuffel; C. Schneider

Paper

The 3-Loop Pure Singlet Heavy Flavor Contributions to the Structure Function $F_2(x,Q^2)$ and the Anomalous Dimension

Abstract

The pure singlet asymptotic heavy flavor corrections to 3-loop order for the deep-inelastic scattering structure function

and the corresponding transition matrix element

in the variable flavor number scheme are computed. In Mellin-

space these inclusive quantities depend on generalized harmonic sums. We also recalculate the complete 3-loop pure singlet anomalous dimension for the first time. Numerical results for the Wilson coefficients, the operator matrix element and the contribution to the structure function

are presented.