Two-parton contribution to the heavy-quark forward–backward asymmetry in NNLO QCD

Abstract

Forward–backward asymmetries, A FB Q , are important observables for the determination of the neutral-current couplings of heavy quarks in inclusive heavy quark production, e + e − → γ ∗ , Z ∗ → Q + X . In view of the measurement perspectives on A FB Q at a future linear collider, precise predictions of A FB Q are required for massive quarks. We compute the contribution of the Q Q ¯ final state to A FB Q to order α s 2 in the QCD coupling. We provide general formulae, and we show that this contribution to A FB Q is infrared-finite. We evaluate these two-parton contributions for b and c quarks on and near the Z resonance, and for t quarks above threshold. Moreover, near the t t ¯ threshold we obtain, by expanding in the heavy-quark velocity β, an expression for A FB t t ¯ to order α s 2 and NNLL in β. This quantity is equal, to this order in β, to the complete forward–backward asymmetry A FB t .