Three Loop Massive Operator Matrix Elements and Asymptotic Wilson Coefficients with Two Different Masses
J. Ablinger, J. Bl\"umlein, A. De Freitas, A. Hasselhuhn, C., Schneider, and F. Wi{\ss}brock
TL;DR
This paper extends the calculation of three-loop massive operator matrix elements and Wilson coefficients to cases with two different quark masses, providing new analytic results and methods for the variable flavor number scheme.
Contribution
It introduces a generalized renormalization procedure for two-mass cases, derives analytic results for general Mellin variable N, and develops new iterated integrals implemented in computer algebra.
Findings
Calculated moments N=2,4,6 for all operator matrix elements.
Derived analytic results for general Mellin N in non-singlet, transversity, and gluonic cases.
Established a new class of iterated integrals and their relations.
Abstract
Starting at 3-loop order, the massive Wilson coefficients for deep-inelastic scattering and the massive operator matrix elements describing the variable flavor number scheme receive contributions of Feynman diagrams carrying quark lines with two different masses. In the case of the charm and bottom quarks, the usual decoupling of one heavy mass at a time no longer holds, since the ratio of the respective masses, , is not small enough. Therefore, the usual variable flavor number scheme (VFNS) has to be generalized. The renormalization procedure in the two--mass case is different from the single mass case derived in \cite{Bierenbaum:2009mv}. We present the moments and for all contributing operator matrix elements, expanding in the ratio . We calculate the analytic results for general values of the Mellin variable in the flavor…
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