Soft gluon evolution and non-global logarithms

Martinez, R.; Angelis, Matthew De; Forshaw, Jeffrey R.; Plätzer, Simon; Seymour, Michael H.

doi:10.48550/arxiv.1802.08531

Cited by 14 publications

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“…The leading non-global logarithms arising in this observable in the large-N c limit can be resummed either by generating the successive emissions through a dedicated parton shower [1,2] or by solving a non-linear evolution equation, the Banfi-Marchesini-Smye (BMS) equation [3]. Both approaches were generalized beyond the large-N c limit [4,5] and first numerical results at leading-logarithmic accuracy are now available at N c = 3 [6][7][8][9]. While the subleading-color contributions are in general small at e + e − colliders, the situation is different at hadron colliders since Glauber phases lead to the occurrence of double logarithms at higher orders, while only single logarithms are present in the large-N c limit.…”

Section: Introductionmentioning

confidence: 99%

Two-loop anomalous dimension for the resummation of non-global observables

Becher¹,

Rauh²,

Xu³

2021

Preprint

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The soft radiation emitted in jet cross sections can resolve the directions and colors of individual hard partons, leading to a complicated pattern of logarithmically enhanced terms in the perturbative series. Starting from a factorization theorem and solving the renormalization group equations for its ingredients, these large logarithms can be resummed. In this paper, we extract the two-loop anomalous dimension governing the resummation of subleading logarithms in jet cross sections and other non-global observables. This anomalous dimension can be obtained by considering soft limits of hard amplitudes, but the presence of collinear singularities in intermediate expressions makes its extraction delicate. As a consistency check, we use our results to predict the known subleading non-global logarithms in the two-jet cross section.

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Section: Introductionmentioning

confidence: 99%

Two-loop anomalous dimension for the resummation of non-global observables

Becher¹,

Rauh²,

Xu³

2021

Preprint

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“…Our analysis here is based upon simulated two-jet events and our goal is to improve on the accuracy of existing simulations [2][3][4][5] by including colour correlations beyond the leading-colour approximation. To do so we pursue a new paradigm of evolution at the amplitude level in place of the traditional probabilistic algorithms (see also [6][7][8][9][10][11]). In the next section we introduce the theoretical framework, with particular emphasis on our treatment of colour.…”

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confidence: 99%

“…Large logarithms can arise if gluons are emitted with a low energy compared to the large momentum transfer, and if the observable is sensitive to those emissions. We refer to these as soft-gluon logarithms and, in [8], we presented an iterative algorithm for summing them to all orders in perturbation theory for general short-distance scattering processes. In this paper, we will sum the most important of these logarithms, though the framework is general enough to go beyond this 'leading logarithmic approximation'.…”

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confidence: 99%

“…Calculating the effect of real emission matrix elements and virtual gluon corrections involves computing matrix elements [τ |T i |σ and [τ |T i • T j |σ . Explicit expressions for these are presented in [8]. For the real emissions, the calculations are simplified since the real emission operator can either: (a) add a new colour line without changing any of the existing colour connections or (b) add a new colour line and then make a single swap.…”

mentioning

confidence: 99%

“…Explicit expressions for Γ σ , ρ and Σ στ can be computed using the results presented in [8,14]. Note that the off-diagonal contribution, Σ τ σ , is only non-zero if #(σ, τ ) = 1.…”

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confidence: 99%

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Resummation and simulation of soft gluon effects beyond leading colour

De Angelis,

Forshaw,

Plätzer

2020

Preprint

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We present first results of resumming soft gluon effects in a simulation of high energy collisions beyond the leading-colour approximation. We work to all orders in QCD perturbation theory using a new parton branching algorithm. This amplitude evolution algorithm resembles a parton shower that is able to systematically include colour-suppressed terms. We find that colour suppressed terms can significantly contribute to jet veto cross sections.

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The Sudakov radiator for jet observables and the soft physical coupling

Banfi

El-Menoufi

Monni

2019

J. High Energ. Phys.

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We present a procedure to calculate the Sudakov radiator for a generic recursive infrared and collinear (rIRC) safe observable in two-scale problems. We give closed formulae for the radiator at next-to-next-to-leading-logarithmic (NNLL) accuracy, which completes the general NNLL resummation for this class of observables in the ARES method for processes with two emitters at the Born level. As a byproduct, we define a physical coupling in the soft limit, and we provide an explicit expression for its relation to the MS coupling up to O(α 3 s ). This physical coupling constitutes one of the ingredients for a NNLL accurate parton shower algorithm. As an application we obtain analytic NNLL results, of which several are new, for all angularities τ x defined with respect to both the thrust axis and the winner-take-all axis, and for the moments of energy-energy correlation F C x in e + e − annihilation. For the latter observables we find that, for some values of x, an accurate prediction of the peak of the differential distribution requires a simultaneous resummation of the logarithmic terms originating from the two-jet limit and at the Sudakov shoulder.

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Soft gluon evolution and non-global logarithms

Cited by 14 publications

References 0 publications

Two-loop anomalous dimension for the resummation of non-global observables

Two-loop anomalous dimension for the resummation of non-global observables

Resummation and simulation of soft gluon effects beyond leading colour

The Sudakov radiator for jet observables and the soft physical coupling

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