We present a novel method for resummation of event shapes to next-to-next-to-leadinglogarithmic (NNLL) accuracy. We discuss the technique and describe its implementation in a numerical program in the case of e + e − collisions where the resummed prediction is matched to NNLO. We reproduce all the existing predictions and present new results for oblateness and thrust major. Contents 1 Introduction 2 Review of NLL resummation 3 NNLL resummation 3.1 Logarithmic counting for the resolved real emissions 3.2 Structure of the NNLL resummation 3.3 NNLL contributions due to resolved emissions 3.3.1 Soft-collinear NNLL contributions 3.3.2 Recoil and hard-collinear NNLL contributions 3.3.3 Soft wide-angle NNLL contributions 3.3.4 Soft correlated emission 4 Validation and matched results

We present a novel method for resummation of event shapes to next-to-nextto-leading-logarithmic (NNLL) accuracy. We discuss the technique and describe its implementation in a numerical program in the case of e + e − collisions where the resummed prediction is matched to NNLO. We reproduce all the existing predictions and present new results for oblateness and thrust major.

We present the first next-to-next-to-leading-logarithmic resummation for the two-jet rate in e^{+}e^{-} annihilation in the Durham and Cambridge algorithms. The results are obtained by extending the ares method to observables involving any global, recursively infrared and collinear safe jet algorithm in e^{+}e^{-} collisions. As opposed to other methods, this approach does not require a factorization theorem for the observables. We present predictions matched to next-to-next-to-leading order and a comparison to LEP data.

The non-Abelian exponentiation theorem has recently been generalised to correlators of multiple Wilson line operators. The perturbative expansions of these correlators exponentiate in terms of sets of diagrams called webs, which together give rise to colour factors corresponding to connected graphs. The colour and kinematic degrees of freedom of individual diagrams in a web are entangled by mixing matrices of purely combinatorial origin. In this paper we relate the combinatorial study of these matrices to properties of partially ordered sets (posets), and hence obtain explicit solutions for certain families of web-mixing matrix, at arbitrary order in perturbation theory. We also provide a general expression for the rank of a general class of mixing matrices, which governs the number of independent colour factors arising from such webs. Finally, we use the poset language to examine a previously conjectured sum rule for the columns of web-mixing matrices which governs the cancellation of the leading subdivergences between diagrams in the web. Our results, when combined with parallel developments in the evaluation of kinematic integrals, offer new insights into the all-order structure of infrared singularities in non-Abelian gauge theories.

Event shape observables are essential tools for studying the behaviour of high energy QCD. Yet in the dijet region, standard perturbation theory is rendered unreliable and the series must be resummed to all orders in the strong coupling. We have recently developed a general method for the resummation of event shapes, in e+e-annihilation, at next-to-next-to-leading logarithmic accuracy. We have implemented the novel method semi-numerically and reproduced four alreadyknown predictions, as well as three new results. We match our findings to fixed-order results, up to NNLO.