Radiative corrections to three-jet event-shapes in lepton-proton scattering

Complete text of publication follows. The analysis of event-shape observables in e+e-annihilations and in deeply-inelastic lepton-proton scattering (DIS) proved to be a powerful method to study Quantum Chromodynamics (QCD). The standard QCD analysis of event-shapes consists of matching the next-to-leading order (NLO) and resummed next-to-leading logarithmic (NLL) predictions. Recently, much progress has been achieved in computing resummed predictions at the NLL accuracy for three-jet event shapes. In Ref. we computed predictions to the same three-jet event shapes at the NLO accuracy in order to facilitate the matching. Here, we report results of such computations for the three-jet event-shape observable Kout that measures the out-of-event-plane QCD radiation; its precise definition can be found in Ref. For the numerical computations we used the NLO-JET++ program. We computed the distributions for fixed values of the DIS kinematic variables Q2 and xB and used the same selection cuts as in the resummation computation. Figure 1. shows the differential distributions for Kout. The shaded bands correspond to the range of scales Q2/2 ≤ μ2 ≤ 2Q2, where μ is the renormalization-scale (the factorization-scale is chosen to be the same). The radiative corrections are in general large and increase with increasing value of Kout because the phase space for events with large out-of-plane radiation with three partons in the final state (at LO) is much smaller than that with four partons in the final state (real corrections). The cross sections decrease rapidly with increasing Kout, leaving the small and medium Kout-region for experimental analysis. In the small Kout-region, the logarithmic contributions of the type lnKout/Q are dominant as can be seen on the plot in the right panel. The fixed-order predictions diverge with Kout → 0 with alternating signs, which makes the resummation of these large logarithmic contributions mandatory. Reliable theoretical predictions can be obtained by match- ing the cross sections valid at the NLO and NLL accuracy. (author)