Abstract
We determine the jet vertex for Mueller-Navelet jets and forward jets in the small-cone approximation for two particular choices of jet algoritms: the kt algorithm and the cone algorithm. These choices are motivated by the extensive use of such algorithms in the phenomenology of jets. The differences with the original calculations of the small-cone jet vertex by Ivanov and Papa, which is found to be equivalent to a formerly algorithm proposed by Furman, are shown at both analytic and numerical level, and turn out to be sizeable. A detailed numerical study of the error introduced by the small-cone approximation is also presented, for various observables of phenomenological interest. For values of the jet "radius" R=0.5, the use of the small-cone approximation amounts to an error of about 5% at the level of cross section, while it reduces to less than 2% for ratios of distributions such as those involved in the measure of the azimuthal decorrelation of dijets.
Highlights
The gluon Green’s function (GGF) describing the high-energy dynamics of emitted and exchanged partons — mostly gluons — and the so-called jet vertices, describing the production of a forward jet from the interaction of one incoming parton and a reggeized gluon
For values of the jet “radius” R = 0.5, the use of the small-cone approximation amounts to an error of about 5% at the level of cross section, while it reduces to less than 2% for ratios of distributions such as those involved in the measure of the azimuthal decorrelation of dijets
The experimental results were extracted by clustering jets with the kt algorithm, while the small-cone approximation (SCA) jet vertices used for the theoretical calculation were those obtained with the Furman algorithm by Ivanov and Papa (FIP)
Summary
The process we are considering was suggested long ago by Mueller and Navelet [1] in order to study the high-energy behaviour of QCD. In the high-energy Regge regime we are considering, the partonic cross section for jet production can be factorized in a (transverse momentum) convolution of (process dependent) jet vertices V and a universal factor G called gluon Green’s function (GGF). The jet vertices are perturbative finite objects without energy ( s) dependence, and are known in NLO approximation: V = αsV (0) + αs2V (1). They depend on the jet variables y, E, φ and on the arbitrary scales μR, μF , s0, in such a way that the hadronic cross section be independent of those scales up to NLL terms, i.e., the scale dependence is present only in the terms of relative order αs2(αs log(s))n. These methods are often used in BFKL phenomenological analyses, and we shall illustrate them in the following subsections: the former in order to set up the theoretical framework and the main notations; the latter in order to introduce the main subject of this paper
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