TheCparameter distribution ine⁺e⁻annihilation

Abstract

Abstract:We study perturbative and non-perturbative aspects of the distribution of the C parameter in e + e − annihilation using renormalon techniques. We perform an exact calculation of the characteristic function, corresponding to the C parameter differential cross section for a single off-shell gluon. We then concentrate on the two-jet region, derive the Borel representation of the Sudakov exponent in the large-β 0 limit and compare the result to that of the thrust T . Analysing the exponent, we distinguish two ingredients: the jet function, depending on Q 2 C, summarizing the effects of collinear radiation, and a function describing soft emission at large angles, with momenta of order QC. The former is the same as for the thrust upon scaling C by 1/6, whereas the latter is different. We verify that the rescaled C distribution coincides with that of 1− T to next-to-leading logarithmic accuracy, as predicted by Catani and Webber, and demonstrate that this relation breaks down beyond this order owing to soft radiation at large angles. The pattern of power corrections is also similar to that of the thrust: corrections appear as odd powers of Λ/(QC). Based on the size of the renormalon ambiguity, however, the shape function is different: subleading power corrections for the C distribution appear to be significantly smaller than those for the thrust.

Running coupling and power corrections in non-linear evolution at the high-energy limit

“…It starts contributing at NLO. This is in keeping with the different origin of the terms: the transverse partial derivatives in the last term reflect the Weizsäcker-Williams field structure of the LO emission kernel (55) that is entirely driven by transverse polarizations. The middle term, in contrast, arises entirely from longitudinal polarizations that are absent at leading order.…”

“…This is a generalization of the wellknown dispersive representation of the free dressed gluon propagator, a technique that has been used to compute running-coupling corrections and estimate power corrections in a variety of applications, see e.g. [46][47][48][49][50][51][52][53][54][55].…”

Event shapes in e+e annihilation and deep inelastic scattering

“…Methods for automated resummation of arbitrary observables are currently in development for a range of processes [38], and techniques have also being developed for dealing with arbitrary processes [69]. We also note that for the e + e − thrust and heavy-jet mass there have been investigations of certain classes of corrections beyond NLL accuracy [29,70,71]. The above resummations all apply to events with only light quarks.…”

“…[28,29,64,70,71,. For the 1 + 1 jet limit of DIS, results on power corrections based on the renormalon approach can be found in [144,145].…”

Top jets in the peak region: Factorization analysis with next-to-leading-log resummation

“…For massless jets there has been a lot of work done on the program of resumming logs in event-shape variables [31,[31][32][33][34][35][36][37][38][39][40][41][42][43][44]. In this paper we do not use the traditional approach to resummation, but rather an approach that sums the same large logs based on the renormalization of operators in effective field theories, including HQET and SCET [3,7].…”