Angular Distributions of Massive Quarks and Leptons Close to Threshold

Abstract

Predictions for the angular distribution of massive quarks and leptons are presented, including QCD and QED corrections. Recent results for the fermionic part of the two-loop corrections to the electromagnetic form factors are combined with the BLM scale fixing prescription. Two distinctly different scales arise as arguments of $α_s(μ^2)$ near threshold: the relative momentum of the quarks governing the soft gluon exchange responsible for the Coulomb potential, and a large momentum scale approximately equal to twice the quark mass for the corrections induced by transverse gluons. Numerical predictions for charmed, bottom, and top quarks are given. One obtains a direct determination of $α_V(Q^2)$, the coupling in the heavy quark potential, which can be compared with lattice gauge theory predictions. The corresponding QED results for $τ$ pair production allow for a measurement of the magnetic moment of the $τ$ and could be tested at a future $τ$-charm factory.

13 pages