On large angle multiple gluon radiation

Department of Physics, University of Milan, Milano, Lombardy, Italy
Journal of High Energy Physics (Impact Factor: 6.11). 03/2003; 2003(3). DOI: 10.1088/1126-6708/2003/03/040
Source: arXiv


Jet shape observables which involve measurements restricted to a part of phase space are sensitive to multiplication of soft gluon with large relative angles and give rise to specific single logarithmically enhanced (SL) terms (non-global logs). We consider associated distributions in two variables which combine measurement of a jet shape V in the whole phase space (global) and that of the transverse energy flow away from the jet direction, Eout (non-global). We show that associated distributions factorize into the global distribution in V and a factor that takes into account SL contributions from multi-gluon ``hedgehog'' configurations in all orders. The latter is the same that describes the single-variable Eout distribution, but evaluated at a rescaled energy VQ. Comment: 16 pages

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Available from: Yuri Dokshitzer, Sep 24, 2013
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    • "While RGE of the functions appearing in Eq. (1.2) resums a large set of logarithms, others, such as logarithms of R [27] [28] [29] and non-global logarithms (NGLs) [30] [31] [32] [33], can present more of a challenge. Importantly, resummation of the jet size R has recently been explored in the context of subjets in [34] and in jet rates in the context of e + e − collisions in [35] [36], and in addition there has been progress in understanding NGLs both at fixed-order [37] [38] [39] [40] and more recently a few novel approaches to understanding their all-orders resummation have been proposed [41] [35] [42]. "
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    ABSTRACT: We consider the class of jet shapes known as angularities in dijet production at hadron colliders. These angularities are modified from the original definitions in e+e- collisions to be boost invariant along the beam axis. These shapes apply to the constituents of jets defined with respect to either k_T-type (anti-k_T, C/A, and k_T) algorithms and cone-type algorithms. We present an SCET factorization formula and calculate the ingredients needed to achieve next-to-leading-log (NLL) accuracy in kinematic regions where non-global logarithms are not large. The factorization formula involves previously unstudied "unmeasured beam functions," which are present for finite rapidity cuts around the beams. We derive relations between the jet functions and the shape-dependent part of the soft function that appear in the factorized cross section and those previously calculated for e+e- collisions, and present the calculation of the non-trivial, color-connected part of the soft-function to O(\alpha_s). This latter part of the soft function is universal in the sense that it applies to any experimental setup with an out-of-jet p_T veto and rapidity cuts together with two tagged jets and it is independent of the choice of jet (sub-)structure measurement. In addition, we implement the recently introduced soft-collinear refactorization to resum logarithms of the jet size, valid in the region of non-enhanced non-global logarithm effects. While our results are valid for all 2 \to 2 channels, we compute explicitly for the qq' \to qq' channel the color-flow matrices and plot the NLL resummed differential dijet cross section as an explicit example, which shows that the normalization and scale uncertainty is reduced when the soft function is refactorized. For this channel, we also plot the jet size R dependence, the p_T^{\rm cut} dependence, and the dependence on the angularity parameter a.
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    • "Collinear singularities at the boundary of a small-R jet yields large logs in the radius parameter, which appear to all orders in α s [23] [28]. Note that the jet veto distribution, studied in the latter references, disentangles from the jet mass distribution to all orders [29] and has a non-global structure analogous to the E t distribution. That is, the coefficients of both 1 We speak of the logarithmic accuracy in the exponent of the distribution. "
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    ABSTRACT: Clustering logs have been the subject of much study in recent literature. They are a class of large logs which arise for non-global jet-shape observables where final-state particles are clustered by a non-cone--like jet algorithm. Their resummation to all orders is highly non--trivial due to the non-trivial role of clustering amongst soft gluons which results in the phase-space being non-factorisable. This may therefore significantly impact the accuracy of analytical estimations of many of such observables. Nonetheless, in this paper we address this very issue for jet shapes defined using the $k_t$ and C/A algorithms, taking the jet mass as our explicit example. We calculate the coefficients of the Abelian $\alpha_s^2 L^2$, $\alpha_s^3 L^3$ and $\alpha_s^4 L^4$ NLL terms in the exponent of the resummed distribution and show that the impact of these logs is small which gives confidence on the perturbative estimate without the neglected higher-order terms. Furthermore we numerically resum the non-global logs of the jet mass distribution in the $k_t$ algorithm in the large-$N_c$ limit.
    Full-text · Article · Jul 2012 · Journal of High Energy Physics
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    • "We formulate a factorization theorem for such jet shape distributions, and aim to resum logs of the jet shape which become large for collimated jets to NLL accuracy. Ref. [50] demonstrated the factorization of such a distribution into a " global " and " non-global " part, and our methods resum the logs in the global part, and at least a subset of those in the non-global part. We do not tackle the problem of ensuring full resummation of all non-global logs generated by phase space cuts, which would require an O(α 2 s ) analysis of jet and soft functions, beyond the scope of this work. "
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    ABSTRACT: 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 next-to-leading order (NLO) in alpha_s and resum large logarithms of tau_a to next-to-leading logarithmic (NLL) accuracy for both cone and kT-type jets. We compare our predictions for the NLL 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: 57 pages plus 20 pages of Appendices, 11 figures, uses JHEP3.cls. v2: corrections to finite parts of NLO jet functions, minor changes to plots, clarified discussion of power corrections
    Full-text · Article · Jan 2010 · Journal of High Energy Physics
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