Universality of 1/Q corrections revisited

Abstract

We provide an exact analytical calculation at the two-loop level in the abelian limit of the leading power correction for the C parameter in e + e − annihilation. We compare our results to the numerical value obtained employing the soft approximation, the abelian part of the Milan factor. We demonstrate that a simple proportionality holds between the leading power corrections to the C parameter and to the longitudinal cross section in the soft region, and we verify that this proportionality holds for the full two-loop abelian contribution computed here. We comment on the possibility of extending this technique to other event shape variables and distributions, as well as to the non-abelian contributions.

Phenomenology of event shapes at hadron colliders

“…refs. [8][9][10][11][12][13][14][15][16][17][18][19] and the reviews [20,21]). From a technical point of view, the development of resummations and fixed-order calculations has benefited from comparisons of predictions for event-shape distributions obtained with both kinds of methods [22][23][24][25][26][27][28][29].…”

TheCparameter distribution ine+e−annihilation

“…Note that the combination of Sudakov effects with parametrically enhanced power corrections is definitely not unique to event-shape distributions. It appears whenever differential cross sections in QCD are evaluated near a kinematic threshold; other important examples are Drell-Yan production near the energy threshold [19,32], structure functions near the elastic limit (Bjorken x close to 1) [48,49], and fragmentation functions of light [30,38] and heavy quarks [50] near z = 1. In spite of the different nature of these processes, certain characteristics of the perturbative expansion are generic [38], and similar techniques are applicable in all cases.…”

“…In the last few years the example of the C parameter, and in particular its average value, had an important place in the ongoing debate concerning universality of power corrections, see e.g. [13,23,30,31]. On the other hand, as far as the resummation of running-coupling effects is concerned, the C parameter distribution was not analysed, and the prime example has always been the thrust [34,35].…”

On the 1/Q correction to the C-parameter at two loops

“…It was however quickly pointed out [12] that the direct application of this method fails to take sufficiently into account the details of the gluon splitting, and that a more sophisticated application is required which treats this splitting correctly. Exact calculations in the abelian limit have been performed for the 1/Q corrections to the longitudinal cross section [13] and the mean value of the C-parameter [14] in e + e − annihilation, while a more general analysis of the most commonly used variables, including non-abelian terms, was performed using the soft approximation in [15]- [17]. It is found that the effect of non-inclusiveness is simply to enhance the amplitude of the 1/Q corrections by a universal 'Milan factor', thus leaving the universality pattern unchanged.…”