Direct extraction of ∆(_MS) from e(^+)e jet observables

We demonstrate a renormalisation group improved formulation of QCD perturbation theory. At next-to-leading order (NLO) and beyond this permits a direct extraction of the QCD dimensional transmutation parameter, A(_ms) that typifies the one parameter freedom of the theory in the limit of massless quarks. We apply this to a variety of experimental data on e(^+)e" jet observables at NLO. We take into consideration data from PETRA, PEP, TRISTAN, SLC and LEP 1 and 2. In this procedure there is no need to mention, let alone to arbitrarily vary, the unphysical renormalization scale µ, and one avoids the spurious and meaningless "theoretical error" associated with standard a(_8) determinations. An attempt is made to estimate the importance of uncalculated next-to-NLO and higher order perturbative corrections, and power corrections, by studying the scatter in the values of ∆(_MS) obtained for different observables. We also consider large infrared logarithm resummations in these jet observables and present results for the particular cases of the four-jet rate to a next-to-leading logarithm approximation and the distributions for the four-jet variables, "light hemisphere mass" and "narrow jet broadening" to a next-to-next-to-leading logarithm approximation in the perturbative expansion. We apply a simple power correction to these variables and obtain remarkably good fits to the data

The Four-Jet Rate in e+e- Annihilation

We present an analytic expression for the four-jet rate in e+e- annihilation, calculated using the coherent branching formalism in the Durham scheme. Our result resums all the leading and next-to-leading kinematic logarithms to all orders in the QCD strong coupling constant.Comment: 7 pages; Final result for R4 and D7 corrected and a couple of typos fixe

Jet Shapes and Jet Algorithms in SCET

Jet shapes are weighted sums over the four-momenta of the constituents of a jet and reveal details of its internal structure, potentially allowing discrimination of its partonic origin. In this work we make predictions for quark and gluon jet shape distributions in N-jet final states in e+e- collisions, defined with a cone or recombination algorithm, where we measure some jet shape observable on a subset of these jets. Using the framework of Soft-Collinear Effective Theory, we prove a factorization theorem for jet shape distributions and demonstrate the consistent renormalization-group running of the functions in the factorization theorem for any number of measured and unmeasured jets, any number of quark and gluon jets, and any angular size R of the jets, as long as R is much smaller than the angular separation between jets. We calculate the jet and soft functions for angularity jet shapes \tau_a to one-loop order (O(alpha_s)) and resum a subset of the large logarithms of \tau_a needed for next-to-leading logarithmic (NLL) accuracy for both cone and kT-type jets. We compare our predictions for the resummed \tau_a distribution of a quark or a gluon jet produced in a 3-jet final state in e+e- annihilation to the output of a Monte Carlo event generator and find that the dependence on a and R is very similar.Comment: 62 pages plus 21 pages of Appendices, 13 figures, uses JHEP3.cls. v2: corrections to finite parts of NLO jet functions, minor changes to plots, clarified discussion of power corrections. v3: Journal version. Introductory sections significantly reorganized for clarity, classification of logarithmic accuracy clarified, results for non-Mercedes-Benz configurations adde