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The Asymptotic Form of Non-Global Logarithms, Black Disc Saturation, and Gluonic Deserts
High Energy Physics - Phenomenology · Submitted 6 Oct 2016
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Comparing to the asymptotics of the conformally related evolution equation encountered in small-x physics, the Balitisky-Kovchegov (BK) equation, we find that the asymptotic form of the non-global logarithms directly maps to the black-disc unitarity limit of the BK equation, despite the contrasting physical pictures.
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The abstract, sentence by sentence
We develop an asymptotic perturbation theory for the large logarithmic behavior of the non-linear integro-differential equation describing the soft correlations of QCD jet measurements, the Banfi-Marchesini-Smye (BMS) equation. This equation captures the late-time evolution of radiating color dipoles after a hard collision. This allows us to prove that at large values of the control variable (the non-global logarithm, a function of the infra-red energy scales associated with distinct hard jets in an event), the distribution has a gaussian tail. We compute the decay width analytically, giving a closed form expression, and find it to be jet geometry independent, up to the number of legs of the dipole in the active jet. Enabling the asymptotic expansion is the correct perturbative seed, where we perturb around an anzats encoding formally no real emissions, an intuition motivated by the buffer region found in jet dynamics. This must be supplemented with the correct application of the BFKL approximation to the BMS equation in collinear limits. Comparing to the asymptotics of the conformally related evolution equation encountered in small-x physics, the Balitisky-Kovchegov (BK) equation, we find that the asymptotic form of the non-global logarithms directly maps to the black-disc unitarity limit of the BK equation, despite the contrasting physical pictures. Indeed, we recover the equations of saturation physics in the final state dynamics of QCD.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We develop an asymptotic perturbation theory for the large logarithmic behavior of the non-linear integro-differential equation describing the soft correlations of QCD jet measurements, the Banfi-Marchesini-Smye (BMS) equation. | contribution 0.97 | 0.95 | 0.10 | asserted 1.00 |
| s1 | This equation captures the late-time evolution of radiating color dipoles after a hard collision. | background 0.98 | 0.11 | 0.03 | asserted 1.00 |
| s2 | This allows us to prove that at large values of the control variable (the non-global logarithm, a function of the infra-red energy scales associated with distinct hard jets in an event), the distribution has a gaussian tail. | result 1.00 | 0.93 | 0.35 | asserted 1.00 |
| s3 | We compute the decay width analytically, giving a closed form expression, and find it to be jet geometry independent, up to the number of legs of the dipole in the active jet. | result 1.00 | 0.96 | 0.14 | asserted 1.00 |
| s4 | Enabling the asymptotic expansion is the correct perturbative seed, where we perturb around an anzats encoding formally no real emissions, an intuition motivated by the buffer region found in jet dynamics. | method 0.99 | 0.86 | 0.04 | asserted 1.00 |
| s5 | This must be supplemented with the correct application of the BFKL approximation to the BMS equation in collinear limits. | method 0.99 | 0.56 | 0.04 | asserted 0.98 |
| s6 | Comparing to the asymptotics of the conformally related evolution equation encountered in small-x physics, the Balitisky-Kovchegov (BK) equation, we find that the asymptotic form of the non-global logarithms directly maps to the black-disc unitarity limit of the BK equation, despite the contrasting physical pictures. | result 0.61 | 0.93 | 0.64 | asserted 1.00 |
| s7 | Indeed, we recover the equations of saturation physics in the final state dynamics of QCD. | interpretation 0.72 | 0.84 | 0.26 | asserted 1.00 |
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Original abstract
We develop an asymptotic perturbation theory for the large logarithmic behavior of the non-linear integro-differential equation describing the soft correlations of QCD jet measurements, the Banfi-Marchesini-Smye (BMS) equation. This equation captures the late-time evolution of radiating color dipoles after a hard collision. This allows us to prove that at large values of the control variable (the non-global logarithm, a function of the infra-red energy scales associated with distinct hard jets in an event), the distribution has a gaussian tail. We compute the decay width analytically, giving a closed form expression, and find it to be jet geometry independent, up to the number of legs of the dipole in the active jet. Enabling the asymptotic expansion is the correct perturbative seed, where we perturb around an anzats encoding formally no real emissions, an intuition motivated by the buffer region found in jet dynamics. This must be supplemented with the correct application of the BFKL approximation to the BMS equation in collinear limits. Comparing to the asymptotics of the conformally related evolution equation encountered in small-x physics, the Balitisky-Kovchegov (BK) equation, we find that the asymptotic form of the non-global logarithms directly maps to the black-disc unitarity limit of the BK equation, despite the contrasting physical pictures. Indeed, we recover the equations of saturation physics in the final state dynamics of QCD.
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References
How the literature uses it
20 arXiv papers cite this in 24 sentences
Papers citing it · 12 sentences without a confident label
Cites it as background 12 papers
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The resummation of LL non-global corrections in the large-$N_c$ limit was formulated about 20 years ago in the seminal work of Refs. [ref] , and has seen substantial interest in recent years [ref] .
Next-to-leading non-global logarithms in QCD · Introduction · 1.00
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The problem of the non-global logarithms [ref] refers to the radiation by a jet at large angles w.r.t. the jet axis, where the standard collinear radiation — which controls the hadron multiplicity produced by the jet and is enhanced by collinear logs of the type $ln(1/θ^2_jet)$, with $θ_jet≪1$ the jet opening angle — is suppressed.
Resumming double non-global logarithms in the evolution of a jet · Introduction · 1.00
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Several new formulations of the resummation have been proposed in recent years [ref] , accompanying a large amount of applications to perturbative calculations of collider observables at LL, and recently also including some class of NLL corrections (see e.g. [ref] ).
Higher-order non-global logarithms from jet calculus · Introduction · 0.93
What it cites · 34 sentences without a confident label
Uses the method or tool of 1 paper
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In the collinear limit, the solutions obey $g_ab∼1$, so we write eq:BMS_LL as: [equation] We have adopted a method-of-regions point of view [ref] , that to get the asymptotic behavior at small angles, we should expand everything in the collinear limit, including the phase space limits of integration.
Asymptotic expansion of Feynman integrals near threshold · BFKL at Small Angles · 0.98
Compares with 3 papers
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We note: [equation] It is worth noting that the calculation of the jet region dependence on the ansatz is remarkably similar to that found in one-loop soft calculations for the global anomalous dimensions [ref] .
Jet Shapes and Jet Algorithms in SCET · Regulated Eikonal Integral Using The $δ$-Regulator · 1.00
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We note: [equation] It is worth noting that the calculation of the jet region dependence on the ansatz is remarkably similar to that found in one-loop soft calculations for the global anomalous dimensions [ref] .
A Soft-Collinear Mode for Jet Cross Sections in Soft Collinear Effective Theory · Regulated Eikonal Integral Using The $δ$-Regulator · 1.00
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We note: [equation] It is worth noting that the calculation of the jet region dependence on the ansatz is remarkably similar to that found in one-loop soft calculations for the global anomalous dimensions [ref] .
Factorization for Jet Radius Logarithms in Jet Mass Spectra at the LHC · Regulated Eikonal Integral Using The $δ$-Regulator · 1.00
Cites as background 29 papers
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Much effort has been expended on analyzing NGLs, from their expansion at fixed order [ref] , to numerical resummations and phenomenology [ref] , to developing the theory of their evolution equations [ref] , as well as their relationship to soft jet factorization theorems [ref] .
Relating $e^+e^-$ annihilation to high energy scattering at weak and strong coupling · Introduction · 1.00
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Much effort has been expended on analyzing NGLs, from their expansion at fixed order [ref] , to numerical resummations and phenomenology [ref] , to developing the theory of their evolution equations [ref] , as well as their relationship to soft jet factorization theorems [ref] .
Soft gluons away from jets: distribution and correlation · Introduction · 1.00
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Much effort has been expended on analyzing NGLs, from their expansion at fixed order [ref] , to numerical resummations and phenomenology [ref] , to developing the theory of their evolution equations [ref] , as well as their relationship to soft jet factorization theorems [ref] .
Non-Global Logarithms in Filtered Jet Algorithms · Introduction · 1.00
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