Antenna showers with one-loop matrix elements

A bstract We consider the probability for a colour-singlet qq̄ pair to emit a gluon, in strongly and smoothly ordered antenna showers. We expand to second order in α s and compare to the second-order QCD matrix elements for Z → 3 jets, neglecting terms suppressed by 1 / NC² . . 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 O( αₛ² ) , 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.