As a first step towards the application of the antenna subtraction formalism to NNLO QCD reactions with massive quarks, we determine the real radiation antenna function and its integrated counterpart for reactions of the type S → QQqq, where S denotes an uncolored initial state and Q, q a massive and massless quark, respectively. We compute the corresponding integrated antenna function in terms of harmonic polylogarithms. As an application and check of our results we calculate the contribution proportional to α 2 s e 2 Q N f to the inclusive heavy-quark pair production cross section in e + e − annihilation.

We set up a formalism, within the antenna subtraction framework, for computing the production of a massive quark-antiquark pair in electron positron collisions at next-to-next-to-leading order in the coupling α s of quantum chromodynamics at the differential level. Our formalism applies to the calculation of any infrared-safe observable. We apply this set-up to the production of top-quark top antiquark pairs in the continuum. We compute the production cross section and several distributions. We determine, in particular, the top-quark forward-backward asymmetry at order α 2 s . Our result agrees with previous computations of this observable.

We compute the order α 2 s QCD corrections to the b-quark forward-backward asymmetry in e + e − → bb collisions at the Z boson resonance, taking the non-zero mass of the b quark into account. We determine these corrections with respect to both the b-quark axis and the thrust axis definition of the asymmetry. We compute also the distributions of these axes with respect to the electron beam. If one neglects the flavor singlet contributions to the b-quark asymmetry, as was done in previous computations for massless b quarks, then the second-order QCD corrections for m b = 0 are smaller in magnitude than the corresponding corrections for m b = 0. Including the singlet contributions slightly increases the magnitude of the corrections. The massive α 2 s corrections to the b-quark forwardbackward asymmetry slightly diminish the well-known tension between the bare b-quark asymmetry and the standard model fit from 2.9σ to 2.6σ.

We analyze, in the antenna subtraction framework, the real radiation antenna functions for processes involving the production of a pair of heavy quarks and two gluons by an uncolored initial state at NNLO QCD. We provide explicit expressions for these functions and discuss their infrared singular behaviour. Our main results are the corresponding integrated antenna functions which are computed analytically. They are expressed in terms of harmonic polylogarithms.

We derive the integrated forms of specific initial-final tree-level four-parton antenna functions involving a massless initial-state parton and a massive final-state fermion as hard radiators. These antennae are needed in the subtraction terms required to evaluate the double real corrections to tt hadronic production at the NNLO level stemming from the partonic processes qq → ttq ′q′ and gg → ttqq.