NNLL Resummation for Jet Broadening

109

Section: Jhep05(2015)102mentioning

confidence: 99%

Section: Jhep05(2015)102mentioning

confidence: 99%

A general method for the resummation of event-shape distributions in e + e − annihilation

Banfi

McAslan

Monni

et al. 2015

109

“…Of the event shapes we consider, jet broadening is most different from T 2 ; it measures momentum transverse to the thrust axis and, in the dijet limit, is sensitive to the recoil of the thrust axis due to soft emissions [83], unlike T 2 . This complicates the higher-order resummation of jet broadening, which was only recently extended to NNLL B [84] and gives a logarithmic structure that is very different from T 2 . As a result, jet broadening provides a highly nontrivial test of the accuracy and theory uncertainties of the Geneva prediction.…”

Section: Predictions For Other Event Shapesmentioning

confidence: 99%

“…13 Note the subscript on the order of resummation indicates the observable for which analytic resummation was carried out. Since resummed results for jet broadening do not exist at NNLL B , we compare to the highest available resummation NNLL B +LO 3 , where we use the results of [84], which we extend to include fixed-order matching that is necessary to describe the tail and transition regions. Finally, for heavy jet mass, N 3 LL ρ resummed results exist [51]; however, we show the NNLL ρ +NLO 3 resummation since this is consistent with the highest T 2 resummation we use.…”

Section: Predictions For Other Event Shapesmentioning

confidence: 99%

Combining higher-order resummation with multiple NLO calculations and parton showers in GENEVA

Alioli

Bauer

Berggren

et al. 2013

126

163

Abstract:We extend the lowest-order matching of tree-level matrix elements with parton showers to give a complete description at the next higher perturbative accuracy in α s at both small and large jet resolutions, which has not been achieved so far. This requires the combination of the higher-order resummation of large Sudakov logarithms at small values of the jet resolution variable with the full next-to-leading-order (NLO) matrix-element corrections at large values. As a by-product, this combination naturally leads to a smooth connection of the NLO calculations for different jet multiplicities. In this paper, we focus on the general construction of our method and discuss its application to e + e − and pp collisions. We present first results of the implementation in the Geneva Monte Carlo framework. We employ N -jettiness as the jet resolution variable, combining its next-tonext-to-leading logarithmic resummation with fully exclusive NLO matrix elements, and Pythia 8 as the backend for further parton showering and hadronization. For hadronic collisions, we take Drell-Yan production as an example to apply our construction. For e + e − → jets, taking α s (m Z ) = 0.1135 from fits to LEP thrust data, together with the Pythia 8 hadronization model, we obtain good agreement with LEP data for a variety of 2-jet observables.

“…Factorized expressions in SCET are tremendously useful as they a) allow to carry out resummation of large logarithms to very high accuracy through Renormalization Group Evolution (RGE); as is the case of thrust [1,33], Heavy-Jet Mass [7,34], C-parameter [8] at N 3 LL, Jet Broadening [35] at N 2 LL [36,37], or angularities [38,39] at NLL 5 ; b) simplify the calculation of the necessary ingredients (matrix elements and anomalous dimensions); c) confine non-perturbative effects to specific functions [22,47,48]. Factorization of event-shape cross-sections was first performed in QCD in [49][50][51] and was followed by Effective Field Theory techniques in [52][53][54].…”

Section: Scet Factorization Theorem For Oriented Event-shapesmentioning

confidence: 99%

Oriented event shapes at N3LL + $ \mathcal{O}\left( {\alpha_{\mathrm{S}}^2} \right) $

Mateu

Rodrigo

2013

We analyze oriented event-shapes in the context of Soft-Collinear Effective Theory (SCET) and in fixed-order perturbation theory. Oriented event-shapes are distributions of event-shape variables which are differential on the angle θ T that the thrust axis forms with the electron-positron beam. We show that at any order in perturbation theory and for any event shape, only two angular structures can appear: F 0 = 3/8 (1+cos 2 θ T ) and F 1 = (1 − 3 cos 2 θ T ). When integrating over θ T to recover the more familiar event-shape distributions, only F 0 survives. The validity of our proof goes beyond perturbation theory, and hence only these two structures are present at the hadron level. The proof also carries over massive particles. Using SCET techniques we show that singular terms can only arise in the F 0 term. Since only the hard function is sensitive to the orientation of the thrust axis, this statement applies also for recoil-sensitive variables such as Jet Broadening. We show how to carry out resummation of the singular terms at N 3 LL for Thrust, Heavy-Jet Mass, the sum of the Hemisphere Masses and C-parameter by using existing computations in SCET. We also compute the fixed-order distributions for these event-shapes at O(α S ) analytically and at O(α 2 S ) with the program Event2.