Calculation of Massive 2-Loop Operator Matrix Elements with Outer Gluon Lines
I. Bierenbaum, J. Blümlein, S. Klein
TL;DR
This paper tackles calculating massive 2-loop operator matrix elements with outer gluon lines in DIS in the asymptotic regime Q^2>>m^2. It introduces a Mellin-Barnes based method with generalized hypergeometric representations to directly evaluate the integrals and avoids the integration-by-parts reduction, exploiting Mellin-space symmetries. The authors obtain analytic results for seven genuine 2-loop scalar integrals expressed through nested harmonic sums. The work lays groundwork for precise heavy-flavor contributions to asymptotic Wilson coefficients, with the complete coefficients to be reported in a subsequent paper BBK3.
Abstract
Massive on-shell operator matrix elements and self-energy diagrams with outer gluon lines are calculated analytically at $O(α_s^2)$, using Mellin-Barnes integrals and representations through generalized hypergeometric functions. This method allows for a direct evaluation without decomposing the integrals using the integration-by-parts method.