Double fermionic contributions to the heavy-quark vacuum polarization
M. Czakon, T. Schutzmeier
TL;DR
The paper addresses the challenge of obtaining a precise, momentum-dependent heavy-quark vector-current correlator at $\mathcal{O}(\alpha_s^3 n_f^2)$ in QCD. It employs a differential-equations framework to compute both low-energy expansions up to $(p^2)^{30}$ and high-energy expansions up to $(p^2)^{-15}$, along with a full numerical solution in the Euclidean and Minkowskian regions. Key contributions include the computation of double-fermionic contributions to the vector current correlator at $\mathcal{O}(\alpha_s^3)$ and an extension of high-energy information at $\mathcal{O}(\alpha_s^2)$. These results enhance precision determinations of heavy-quark parameters and the running of the strong coupling by providing reliable momentum-dependent information for the correlator.
Abstract
We compute the virtual O(α_s^3 n_f^2) corrections to the heavy quark vector current correlator in terms of expansions in the external momentum and as an exact numerical solution. As a byproduct, the available high-energy expansion at the three-loop level is extended.