Mateu, V., Stewart, I. W., & Thaler, J. (2013). Power corrections to event shapes with mass-dependent operators. Phys. Rev. D, 87(1), 014025–25pp.
Abstract: We introduce an operator depending on the "transverse velocity'' r that describes the effect of hadron masses on the leading 1/Q power correction to event-shape observables. Here, Q is the scale of the hard collision. This work builds on earlier studies of mass effects by Salam and Wicke [J. High Energy Phys. 05 (2001) 061] and of operators by Lee and Sterman [Phys. Rev. D 75, 014022 (2007)]. Despite the fact that different event shapes have different hadron mass dependence, we provide a simple method to identify universality classes of event shapes whose power corrections depend on a common nonperturbative parameter. We also develop an operator basis to show that at a fixed value of Q, the power corrections for many classic observables can be determined by two independent nonperturbative matrix elements at the 10% level. We compute the anomalous dimension of the transverse velocity operator, which is multiplicative in r and causes the power correction to exhibit nontrivial dependence on Q. The existence of universality classes and the relevance of anomalous dimensions are reproduced by the hadronization models in Pythia 8 and Herwig++, though the two programs differ in the values of their low-energy matrix elements.
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Abbate, R., Fickinger, M., Hoang, A. H., Mateu, V., & Stewart, I. W. (2012). Precision thrust cumulant moments at N^3LL. Phys. Rev. D, 86(9), 094002–22pp.
Abstract: We consider cumulant moments (cumulants) of the thrust distribution using predictions of the full spectrum for thrust including O(alpha(3)(s)) fixed order results, resummation of singular (NLL)-L-3 logarithmic contributions, and a class of leading power corrections in a renormalon-free scheme. From a global fit to the first thrust moment we extract the strong coupling and the leading power correction matrix element Omega(1). We obtain alpha(s)(m(Z)) = 0.1140 +/- (0.0004)(exp) +/- (0.0013)(hadr) +/- (0.0007)(pert), where the 1-sigma uncertainties are experimental, from hadronization (related to Omega(1)) and perturbative, respectively, and Omega(1) = 0.377 +/- (0.044)(exp) +/- (0.039)(pert) GeV. The nth thrust cumulants for n >= 2 are completely insensitive to Omega(1), and therefore a good instrument for extracting information on higher order power corrections, Omega'(n)/Q(n), from moment data. We find ((Omega) over tilde '2)(1/2) = 0.74 +/- (0.11)(exp) +/- (0.09)(pert) GeV.
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