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Accounting for coherence in interjet E_t flow: a case study

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Mrinal Dasgupta, Gavin P. Salam

High Energy Physics - Phenomenology · Submitted 1 Mar 2002 · 15 references

Pith's verdict: The second-order non-global calculation is clean and directly usable; the all-orders numbers are indicative only, and the authors say so themselves.

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arXiv IDhep-ph/0203009 (version 1)
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CitationGavin P. Salam, Mrinal Dasgupta. "Accounting for coherence in interjet E_t flow: a case study." arXiv:hep-ph/0203009 (2002). https://pith.science/paper/2VS3FEER
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The paper

The paper claims

Interjet energy-flow calculations are incomplete unless they include gluons radiated coherently by other large-angle gluons, not just primary emission from the hard jets.

The reading

The paper argues that leading-logarithmic calculations of interjet transverse-energy flow, and of rapidity gaps defined by energy flow, are incomplete if they include only primary emissions from the hard jets. Emissions into a restricted angular region $Omega$ can be radiated coherently from an arbitrarily complicated ensemble of softer but still large-angle gluons outside $Omega$, producing a class of single logarithms the authors call non-global logarithms. They study this in the simpler two-jet case, compute the first non-trivial coefficient $S_2$ analytically for a rapidity slice, and extend the result to all orders numerically in the large-$N_C$ limit using a dipole Monte Carlo. The correction is not merely formal: at the reference value $t=0.15$, omitting it overestimates the cross section by about 30% for a square patch and 65% for a slice.

What carries the argument

The load-bearing object is the non-global suppression factor $S(t)$, defined by $Sigma_Omega(t)=S(t)Sigma_{Omega,P}(t)$, where $t=(1/2pi)int_{Q_Omega}^{Q/2} dk_t/k_t alpha_s(k_t)$ is the evolution variable. $S_2$ is extracted from the $C_F C_A$ interference term of the two-gluon emission probability, the part that distinguishes coherent emission from two independent primary gluons; the angular integral over one gluon outside and one inside $Omega$ turns this into a calculable function of the region's geometry. For all orders the authors use a large-$N_C$ (many-colour) dipole Monte Carlo, in which each dipole branches independently, and then rescale $S_{MC}$ by $2C_F/C_A$ so that the $O(alpha_s^2)$ coefficient is exact beyond large $N_C$.

Extended reading notes

Core claim

The central claim is that for any observable sensitive only to radiation in part of phase space — a non-global observable — single-logarithmic accuracy requires secondary and higher emissions, meaning soft gluons emitted coherently from the ensemble of harder large-angle gluons outside the measured region, not just primary emission from the two hard jets. In the two-jet case the authors isolate this effect as a factor $S(t)$ multiplying the primary-emission form factor $Sigma_{Omega,P}(t)=exp[-4C_F A_Omega t]$. At second order they compute $S_2$ from the $C_F C_A$ part of the energy-ordered two-gluon matrix element and find that for a rapidity slice $S_2$ grows with the slice width and saturates at $-C_F C_A 2pi^2/3$, while for a square patch it is roughly proportional to the perimeter. At all orders the large-$N_C$ numerical result shows a suppression that, after a geometry-dependent normalisation, has a universal $t$-dependence, which the authors interpret as evidence for an empty buffer region around $Omega$.

Load-bearing premise

The all-orders result relies on the assumption that the single rescaling $S(t)=[S_{MC}(t)]^{2C_F/C_A}$ captures the finite-$N_C$ corrections at every order, even though it is fixed only by matching the second-order coefficient.

Editorial extensions

If this is right

  • Energy-flow-based rapidity-gap definitions that omit non-global logs are not correct at single-logarithmic accuracy, so earlier gap calculations need revision.
  • At $t=0.15$, ignoring non-global effects overestimates the cross section by about 30% for a square patch and 65% for a rapidity slice; the discrepancy grows quickly at larger $t$.
  • Because the large-$t$ shape of $S(t)$ is geometry-independent, the same suppression should appear in $2+2$-jet production at hadron colliders, with an overall power depending on jet number and colour.
  • The non-global factor removes the Landau-pole divergence in the $Q_Omega$ distribution, forcing the distribution to zero regardless of the size of $C_F A_Omega/(pi beta_0)$.
  • Measurements of interjet energy flow in $e^+e^-$ or DIS two-jet events would provide a clean test, complementary to hadron-collider measurements and free of underlying-event contamination.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The second-order geometry dependence — perimeter for a patch versus area for primary emission — suggests an experimental handle: varying the shape of $Omega$ at fixed area could separate the non-global correction from the primary form factor.
  • If the buffer picture is correct, the same universal $S(t)$ shape could be calibrated in $e^+e^-$ and transported to hadron colliders, with the jet-number and colour power supplied by the hard process.
  • The rescaling by $2C_F/C_A$ is the most fragile link in the quantitative claims; a finite-$N_C$ dipole shower or an exact colour-flow calculation at third order would either confirm it or shift the quoted 30–65% estimates.
  • The saturation of $S_2$ for wide slices means enlarging a rapidity slice beyond a few units adds little new non-global suppression, so the effect is controlled by the boundary of the measured region rather than its bulk.
Original abstract

Recently, interest has developed in the distribution of interjet energy flows, with for example the leading-log calculation of the highly non-trivial colour structure of primary emissions in 4-jet systems. Here we point out however that at leading-log level it is insufficient to consider only multiple primary emission from the underlying hard antenna -- additionally, one must take into account the coherent structure of emission from arbitrarily complicated ensembles of large-angle soft gluons. Similar considerations apply to certain definitions of rapidity gaps based on energy flow. We examine this new class of terms in the simpler context of 2-jet events, and discover features that point at novel aspects of the QCD dynamics.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,651 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.09 · states limitation 0.17 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.60 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

Recently, interest has developed in the distribution of interjet energy flows, with for example the leading-log calculation of the highly non-trivial colour structure of primary emissions in 4-jet systems. Here we point out however that at leading-log level it is insufficient to consider only multiple primary emission from the underlying hard antenna -- additionally, one must take into account the coherent structure of emission from arbitrarily complicated ensembles of large-angle soft gluons. Similar considerations apply to certain definitions of rapidity gaps based on energy flow. We examine this new class of terms in the simpler context of 2-jet events, and discover features that point at novel aspects of the QCD dynamics.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Recently, interest has developed in the distribution of interjet energy flows, with for example the leading-log calculation of the highly non-trivial colour structure of primary emissions in 4-jet systems. background 1.00 0.03 0.03 asserted 0.98
s1 Here we point out however that at leading-log level it is insufficient to consider only multiple primary emission from the underlying hard antenna -- additionally, one must take into account the coherent structure of emission from arbitrarily complicated ensembles of large-angle soft gluons. gap 0.65 0.56 0.83 asserted 1.00
s2 Similar considerations apply to certain definitions of rapidity gaps based on energy flow. interpretation 0.63 0.10 0.06 asserted 0.90
s3 We examine this new class of terms in the simpler context of 2-jet events, and discover features that point at novel aspects of the QCD dynamics. result 0.49 0.96 0.23 asserted 0.82

What kind of paper the classifier reports this is: theoretical result 0.60 · evidence from proof or derivation 0.51.

What was examined, and what was not

sources read
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not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. (a) veto on primary emissions going into Ω; (b) veto on energy-ordered secondary emission going into Ω; (c) veto on emissions going into Ω that are radiated coherently from the ensemble made up of all (much) harder emissions not going into Ω. definitions of diffraction based on energy cuts [3, 4] (or multiplicity cuts), there is another class of single-logarithmic (SL) terms which must be accounted for. To be more specific it was shown in Ref. [6] that for any observable that is sensitive to radiation in only a part of phase space — a non-global observable — it is necessary to…
Figure 2. The kind of diagram to be con￾sidered for the calculation of S2 in the case of a rapidity slice of width ∆η. S(t) = X n=2 Snt n . (3.2) Since this kind of contribution only starts with secondary emissions, there is no S1 term. In the calculation of S2, we shall be entitled to equate t with αs 2π ln Q 2QΩ . The exact value of S2 depends on the geom￾etry of the patch Ω. Here we calculate it ana￾lytically for the case where Ω is a slice in rapidity of width ∆η. The kind of diagram to be considered is shown in figure 2, where a and b are quarks (they may be outgoing or incoming d
Figure 3. S2 as a function of δη for two dif￾ferent definitions of Ω: a slice in rapidity (using eq. (3.11)), and a square patch in rapidity and azimuth with δφ = δη (S2 determined numeri￾cally). is shown in figure 3. For small ∆η, S2 goes to zero essentially linearly in η, S2 = −4CF CA
Figure 4. A possible structure for emissions harder than some intermediate resolution scale t ′ for an event in which Ω stays empty down to some scale t > t′ . In this scenario, at scale t ′ an empty buffer region exists between Ω and the emission closest to Ω. is that resolving only those emissions harder than some intermediate scale t’, one will see an extended empty buffer region surround￾ing Ω, as in figure 4 (shown for one side of a wide slice). The typical size of this buffer region should be of the order of ηbuffer ≃ (t − t ′ )
Figure 5. A comparison between (a) the full result for S and (b) the simple exponentiation of S2. Beyond t = 0.5 the differences between the curves for the finite and infinite slices are not significant compared to the statistical and systematic errors involved in the determination of S. In figure 5a we show the function S(t) for three different geometries for Ω: a square patch in rapidity and azimuth (∆η = ∆φ = 2), a finite slice in rapidity (∆η = 1) and an infinite slice in rapidity. We extend the t scale beyond the phenomenologically relevant region in order to better illustrate the…
Figure 6. Contour plots for the distribution of the size of the buffer region, ηbuffer, as a function of the intermediate resolution scale t ′ . For the larger t range, the irregularities of the contours are an artifact due to limited statistics. The darkest contour corresponds to 1 σ dσ dηbuffer = 2. The fact that the t-dependence of S is the same regardless of the geometry of Ω seems to suggest that the ‘buffer’ mechanism postulated above might well be responsible for the all-orders behaviour of S. To examine this idea in more detail one can use the Monte Carlo simulation to establish…
Figure 7. ΣΩ(t) for two different definitions of Ω: in the left-hand figure we consider the energy flowing into a slice of width ∆η = 1, while in the right-hand figure we consider the energy flowing into a square patch in rapidity and azimuth, of size ∆η = ∆φ = 2. The upper plots show the relation between t and QΩ for different values of the centre-of-mass energy Q. To understand the phenomenological significance of the non-global logarithms, it is interesting to compare results for Σ(t(QΩ, Q)) with only primary emissions and with the full non-global treatment. This is done in figure 7 for…

Figures reproduced from arXiv:hep-ph/0203009 by the authors.

References
How later papers used it

88 later papers cite it

Evidence: substantial. 72 of the citing papers share no author with it, and 9 of those carry a confident label from Pith's citation classifier.

Pith read 14 of the 148 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

Uses its method or tool 1 of 4 papers with this label
Compares with it 2 of 6 papers with this label

  • Found an identical expression for the NGLs' coefficient in the interjet energy flow distribution as this paper, relating its jet radius to this paper's parameter c.

    Non--global logs and clustering impact on jet mass with a jet veto distribution (2011) · 0.93 · paraphrased: the licence does not allow quoting

  • As a check of our calculation, we have also computed the LL $Σ(v)$ cumulative distribution as a function of the evolution variable $t$ defined in Eq. [ref], and reproduced the results of Ref. [ref] .

    Higher-order non-global logarithms from jet calculus (2021) · Numerical results for the $E_t$ distribution in the interjet gap at NLL · 1.00

How the literature uses it

79 arXiv papers cite this in 132 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 87 sentences without a confident label

Builds on it 1 paper
  • This evolution equation will be recognized as the Banfi-Marchesini-Smye equation [ref] , used to resum non-global soft correlations between distinct angular regions of phase space [ref] , suitably extended to account for initial state partons.

    Soft evolution after a hard scattering process · Reduced Density Matrix · 0.95

Uses its method or tool 4 papers
Compares with it 6 papers
  • [ref] (figure [ref]) is essentially equivalent to the transverse energy distribution (in other words, definition [ref] without the $sinϕ$ part).

    Dijet azimuthal decorrelation in $e^+e^-$ annihilation · NLL resummation with anti-kt · 0.88

  • We already expected, based on the work of Dasgupta and Salam [ref] contributions from emission from gluons outside the gap, but in distinction to their result which is an edge effect: emission just outside the gap produces radiation just inside, the effect we find comes from emission arbitrarily far outside the gap.

    Breakdown of Coherence ? · Consequences: Super-Leading Logarithms in Gaps Between Jets Cross Sections · 0.90

  • The resultant expression for $S_2$ in configuration $(a)$ at the limit $→0$ reads, [equation] An identical expression was found for the NGLs' coefficient in the interjet energy flow distribution [ref] [Our jet–radius, $$, is given in terms the parameter $c$, used in [ref] , by the relation: $1 - c = 2$.].

    Non--global logs and clustering impact on jet mass with a jet veto distribution · $$ term and NGLs · 0.93

Cites it as support 1 paper
  • However as was shown in Refs. [ref] for non-global observables that are affected by soft radiation in a delimited phase space region such as the interior of a jet the pattern of real-virtual cancellations that ensure the exponentiation of a single-gluon is spoiled.

    Jet masses for high p_T QCD jets at all orders · NLO estimates and non-global logarithms · 0.96

Cites it as background 27 papers
  • The resummation of non-global logarithms has been originally done in the large-$N_c$ approximation [ref] where it has been observed that including the finite-$N_c$ corrections is highly nontrivial even at the leading-logarithmic level.

    Non-global logarithms in hadron collisions at $N_c=3$ · Introduction · 0.89

  • In perturbative calculations, large logarithms, called `non–global logarithms' [ref] , of the type $(α_slnQ/ℳ)^n$ appear, where $Q$ is the center–of–mass energy and $ℳ$ is a second hard scale $Q≫ℳ≫Λ_QCD$ characterizing the observable of interest.

    Soft gluons away from jets: distribution and correlation · Introduction · 0.88

  • 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

Discussion

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