Matching of Resummed NLLA with Fixed NNLO for Event Shapes

Event shape distributions in ee annihilation processes are very popular hadronic observables, mainly due to the fact that they are well suited both for experimental measurement and for theoretical description because many of them are infrared and collinear safe. The main idea behind event shapes variables is to parameterize the energy-momentum flow of an event, such that one can smoothly describe its shape passing from pencil-like two-jet configurations, which are a limiting case in event shapes, up to multijet final states. Since the deviation from two-jet configurations is proportional to the strong coupling constant αs, the comparison of experimental measurements and theoretical prediction permits to determine αs. At LEP a set of six different event shape observables were measured in great detail: thrust T (which is substituted here by τ = 1− T ), heavy jet mass ρ, wide and total jet broadening BW and BT , C-parameter and two-to-three-jet transition parameter in the Durham algorithm y3. Until very recently, the theoretical state-of-the-art description of event shape distributions was based on the matching of the NLLA [2] onto the NLO [3, 4] calculation. Using the newly available results of the NNLO corrections for the standard set of event shapes [5] introduced above, we computed the matching of the resummed NLLA onto the fixed order NNLO.