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 $\eta = m_1^2/m_2^2$.
- Publication:
-
Proceedings of "Loops and Legs in Quantum Field Theory
- Pub Date:
- 2014
- DOI:
- 10.48550/arXiv.1407.2821
- arXiv:
- arXiv:1407.2821
- Bibcode:
- 2014dwpp.workE..15A
- Keywords:
-
- High Energy Physics - Phenomenology
- E-Print:
- 10 pages LATEX, 1 Figure, Proceedings of Loops and Legs in Quantum Field Theory, Weimar April 2014