3Loop Heavy Flavor Corrections in DeepInelastic Scattering with Two Heavy Quark Lines
Abstract
We consider gluonic contributions to the heavy flavor Wilson coefficients at 3loop 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 squareroot 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 nonsinglet 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
 arXiv:
 arXiv:1407.2821
 Bibcode:
 2014dwpp.workE..15A
 Keywords:

 High Energy Physics  Phenomenology
 EPrint:
 10 pages LATEX, 1 Figure, Proceedings of Loops and Legs in Quantum Field Theory, Weimar April 2014