Caesar: Computer Automated Resummations

Global properties of energy-momentum flow in final-states, such as event shapes and jet-resolution thresholds, offer a good compromise between simplicity and sensitivity to the dynamics of QCD. Thanks to the former, it has been possible to make a wide range of theoretical predictions for them, including both fixed-order and resummed perturbative calculations as well as non-perturbative model calculations. This set of theoretical tools has been essential in helping us to learn about QCD from the extensive experimental data, having led in particular to numerous of measurements of the running coupling, αs [1], tests of the colour factors of QCD [2] and highly instructive studies concerning hadronisation (for reviews, see [3,4]). Most of the investigations so far have been carried out for observables that are sensitive to the deviation from two-jet (1+1-jet) structure in ee (DIS). This fairly straightforward environment has been of considerable value, especially in developing and refining our ideas about hadronisation. However the most stringent tests of the understanding thus gained, as well as possible novel extensions, are likely to be found in the context of multi-jet events, including those at hadron-hadron colliders. A difficulty in such studies is that the next-to-leading logarithmic (NLL) resummed calculations, needed in the limit of only soft and collinear emissions, have up to now usually been carried out by hand, a tedious and error-prone procedure, which has to be repeated separately for each new observable in each process. The complexity of such calculations can increase substantially as one goes to multi-jet processes [5]. This is to be contrasted with fixed-order calculations, usually embodied in the form of a ‘fixed-order Monte Carlo’ program (FOMC, e.g. [6]), which given a subroutine for the observable, provides, numerically, the leading and next-to-leading order (LO, NLO) coefficients of the perturbative series. Though the internal complexity of FOMCs increases for processes with extra legs, the principles of their use remain identical regardless of the process. This makes it possible, even for those not expert in higher order QCD calculations, to obtain fixed-order predictions for arbitrary observables, in a wide range of processes. It is natural therefore to ask whether analogous programs could be constructed for resummed calculations. To help explain a solution to this question, proposed in [7], it is useful to define the problem a little more precisely. We will consider a general event shape (or jet-resolution threshold), defined by some function V (q1, . . . , qN ) of the momenta q1, . . . , qN of the N particles in an event. If the observable is such that it vanishes smoothly in the limit of n narrow jets, then we