3-Loop Heavy Flavor Corrections in Deep-Inelastic Scattering with Two Heavy Quark Lines

Abstract

We consider gluonic contributions to the heavy flavor Wilson coefficients at 3-loop order in QCD with two heavy quark lines in the asymptotic region $Q^2\gg m_{1(2)}^2$. Here we report on the complete result in the case of two equal masses $m_1=m_2$ for the massive operator matrix element $A_{gg,Q}^{(3)}$, which contributes to the corresponding heavy flavor transition matrix element in the variable flavor number scheme. Nested finite binomial sums and iterated integrals over square-root valued alphabets emerge in the result for this quantity in $N$ and $x$-space, respectively. We also present results for the case of two unequal masses for the flavor non-singlet OMEs and on the scalar integrals ic case of $A_{gg,Q}^{(3)}$, which were calculated without a further approximation. The graphs can be expressed by finite nested binomial sums over generalized harmonic sums, the alphabet of which contains rational letters in the ratio $\eta =m_1^2/m_2^2$.

10 pages LATEX, 1 Figure, Proceedings of Loops and Legs in Quantum Field Theory, Weimar April 2014

References in corpus (12)

• 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
• A Refined Difference Field Theory for Symbolic Summation
• The 3-Loop Non-Singlet Heavy Flavor Contributions and Anomalous Dimensions for the Structure Function $F_2(x,Q^2)$ and Transversity
• On the Generalized Harmonic Polylogarithms of One Complex Variable
• Light quark mass effects in the on-shell renormalization constants
• The O(α_s^3 T_F^2) Contributions to the Gluonic Operator Matrix Element
• Evaluation of Multi-Sums for Large Scale Problems
• 3-Loop Heavy Flavor Corrections to DIS with two Massive Fermion Lines
• Parameterized Telescoping Proves Algebraic Independence of Sums
• Advanced Computer Algebra Algorithms for the Expansion of Feynman Integrals
• New Heavy Flavor Contributions to the DIS Structure Function $F_2(x,Q^2)$ at $O(α_s^3)

Cited by in corpus (2)

• 3-loop Massive $O(T_F^2)$ Contributions to the DIS Operator Matrix Element $A_{gg}$
• Recent progress on the calculation of three-loop heavy flavor Wilson coefficients in deep-inelastic scattering