Antenna showers with one-loop matrix elements

A bstractWe consider the probability for a colour-singlet $ q\overline{q} $ pair to emit a gluon, in strongly and smoothly ordered antenna showers. We expand to second order in αs and compare to the second-order QCD matrix elements for Z → 3 jets, neglecting terms suppressed by $ {1 \left/ {{N_C^2}} \right.} $. We give a prescription that corrects the shower to the matrix-element result at this order for both soft and hard emissions, thereby explicitly reducing its dependence on evolution- and renormalization-scale choices. We confirm that the choice of p⊥ for both of these scales absorbs all logarithms through $ \mathcal{O}\left( {\alpha_s^2} \right) $, and contrast this with various alternatives. We include these corrections in the vincia shower generator and study the impact on LEP event-shape and fragmentation observables. An uncertainty estimate is provided for each event, in the form of a vector of alternative weights.