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${\cal O}(\alpha_s^3)$ analysis of inclusive jet and di-jet production in heavy ion reactions at the Large Hadron Collider

High Energy Physics - Phenomenology · Submitted 12 May 2011 · 40 references

Pith's verdict: The p+p baseline is genuinely validated and the di-jet R_AA map is new, but the headline claim about background ambiguity rests on one hand-set cutoff with no scan.

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arXiv ID1105.2566 (version 2)
Pith IDX5PCLHZK, Pith's permanent record of this paper and its review
CitationBen-Wei Zhang, Ivan Vitev, Yuncun He. "${\cal O}(\alpha_s^3)$ analysis of inclusive jet and di-jet production in heavy ion reactions at the Large Hadron Collider." arXiv:1105.2566 (2011). https://pith.science/paper/X5PCLHZK
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The paper

The paper claims

The LHC's di-jet asymmetry is only partly explained by jet quenching, with the rest traceable to how jets are separated from the heavy-ion background.

The reading

The paper asks how much of the transverse-momentum imbalance between paired jets in lead-lead collisions at the LHC is genuinely caused by partons losing energy in the quark-gluon plasma, and how much is an artifact of how experimenters subtract the enormous soft background. The authors combine a next-to-leading-order perturbative QCD calculation of single- and double-inclusive jet production, $O(α_s^3)$, validated against 7 TeV proton-proton data, with a medium-induced radiative energy-loss model, and then run both through the collision geometry of central Pb+Pb at 2.76 TeV per nucleon pair. They find that radiative quenching alone reproduces only about a third to a half of the extra broadening that ATLAS and CMS reported. Adding a single knob — a 20 GeV cutoff that mimics either a fraction of the medium-induced shower being mis-subtracted as background or that energy diffusing outside the jet cone through collisions — closes much of the gap and simultaneously erases the cone-radius dependence the pure radiative calculation predicts. If this is right, the di-jet asymmetry is a joint probe of medium properties and analysis procedure, and the apparent inconsistency between RHIC's radius-dependent jet suppression and the LHC's radius-independent asymmetry has a natural resolution.

What carries the argument

The machinery is a convolution of an exact next-to-leading-order jet calculation with a probabilistic energy-loss model. The $O(α_s^3)$ Ellis-Kunszt-Soper numerical code supplies the $2→2$ plus $2→3$ jet cross sections with realistic jet-defining phase space $S_3(p_1,p_2,p_3)$, so that jets have a finite cone radius $R$ and the tree-level constraint $E_{T1} = E_{T2}$ is broken by parton splitting. Medium effects enter through a Poisson-distributed probability $P_{q,g}(ε)$ that a parent parton loses a fraction $ε$ of its energy, multiplied by a phase-space Jacobian $|J_i(ε_i)| = 1/(1 - [1 - f(R_i,p_T^{min})]ε_i)$. The function $f(R_i,p_T^{min})$, defined as the ratio of the medium-induced radiation falling inside the cone and above $p_T^{min}$ to all of it, is the single object that carries the paper's interpretive weight: it converts the abstract question of 'how much energy left the jet' into a calculable, radius-dependent number, and the choice $p_T^{min} = 0$ versus $20$ GeV is what separates the pure-radiative scenario from the collisional-or-mis-subtraction scenario.

Extended reading notes

Core claim

The central claim is quantitative and twofold. First, at $O(α_s^3)$ the proton-proton di-jet asymmetry distribution at $√s = 7$ TeV agrees with the ATLAS measurement essentially without non-perturbative corrections, and the corresponding lead-lead calculation with only radiative energy loss produces a di-jet asymmetry $A_J$ distribution that is broader than the proton-proton baseline but accounts for only roughly one third to one half of the extra broadening seen by ATLAS and CMS. Second, if a fraction of the medium-induced parton shower is either subtracted as uncorrelated soft background or lost outside the cone through collisional processes — modeled by setting $p_T^{min} = 20$ GeV in the energy-redistribution fraction $f(R_i, p_T^{min})$, corresponding to $⟨δE_T⟩ ≃ 15$ GeV inside $R=0.5$ and $≃ 5$ GeV inside $R=0.2$ for a 100 GeV gluon jet — then the calculated asymmetry grows substantially and, notably, its dependence on the jet radius $R$ disappears. The authors also report the first calculation of the di-jet nuclear modification factor $R_{AA}^{2-jet}$ in heavy-ion collisions: it shows a broad region of suppression near $E_{T1} = E_{T2}$ and strong enhancement when the two jets are very unequal, which is what flattens the predicted $A_J$ distribution and rules out a peak at finite asymmetry from jet-quenching physics alone.

Load-bearing premise

The load-bearing premise is that a single hand-chosen cutoff of 20 GeV in the energy-redistribution fraction faithfully represents both the misassignment of medium-induced shower fragments to the soft background and the collisional diffusion of shower energy outside the cone, when only the two endpoints 0 and 20 GeV are shown and no independent experimental handle on the actually mis-subtracted energy is offered.

Editorial extensions

If this is right

  • Radiative jet quenching alone cannot reproduce the full di-jet asymmetry broadening measured by ATLAS and CMS in central Pb+Pb collisions at 2.76 TeV; a non-radiative contribution of order the radiative one is required.
  • The observed insensitivity of the di-jet asymmetry to the jet cone radius $R$ over $R = 0.2$ to $0.6$ is naturally explained if part of the shower energy is lost outside the cone or subtracted as background, since that mechanism removes the radius dependence that pure radiative quenching predicts.
  • The RHIC result that inclusive jet suppression depends strongly on cone radius and the LHC result that di-jet asymmetry does not are not necessarily in conflict; they can both hold if the asymmetry measurement is partly sensitive to background handling.
  • A statistical peak in the asymmetry distribution at finite $A_J \simeq 0.4$ is not compatible with realistic jet-quenching calculations, whose $A_J$ distribution is flat once the broad, nearly constant di-jet suppression region is accounted for.
  • Ratios of jet cross sections at two cone radii can suppress cold nuclear matter effects, but at small radii $R \sim 0.2$ non-perturbative hadronization corrections may shift those ratios by as much as 50 percent, so they must be constrained in proton-proton data first.

Reading between the lines

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

  • If the mis-subtracted energy per jet is closer to 5 GeV or 40 GeV than to 20 GeV, the paper's own accounting implies the split between radiative and non-radiative broadening shifts accordingly; a scan over $p_T^{min}$ rather than the two endpoints shown would turn this into a constraint rather than an illustration.
  • The proposal suggests a discriminating measurement: recovering the energy flow at angles larger than $R$ and checking whether it matches the missing momentum in asymmetric di-jets. Energy found outside the cone favors collisional diffusion; energy absent entirely favors mis-subtraction.
  • Photon-tagged or Z-tagged jets, where the tagging object carries no colour charge and hence no medium-induced radiation, could calibrate how much soft energy is genuinely attributable to the jet versus the underlying event, providing an independent handle on the subtraction ambiguity that this paper can only parametrize.
  • Because the same cutoff simultaneously broadens the asymmetry and flattens its radius dependence, the pair (asymmetry broadening, radius slope) forms a two-dimensional signature; future measurements of both in the same kinematic bin would over-constrain the model.
Original abstract

Jets physics in heavy ion reactions is an important new area of active research at the Relativistic Heavy Ion Collider (RHIC) and at the Large Hadron Collider (LHC) that paves the way for novel tests of QCD multi-parton dynamics in dense nuclear matter. At present, perturbative QCD calculations of hard probes in elementary nucleon-nucleon reactions can be consistently combined with the effects of the nuclear medium up to $ {\cal O}(\alpha_s^3) $. While such accuracy is desirable but not necessary for leading particle tomography, it is absolutely essential for the new jet observables. With this motivation, we present first results and predictions to $ {\cal O}(\alpha_s^3) $ for the recent LHC lead-lead (Pb+Pb) run at a center-of-mass energy of 2.76 TeV per nucleon-nucleon pair. Specifically, we focus on the suppression of the single and double inclusive jet cross sections. Our analysis includes not only final-state inelastic parton interactions in the QGP, but also initial-state cold nuclear matter effects and an estimate of the non-perturbative hadronization corrections. We demonstrate how an enhanced di-jet asymmetry in central Pb+Pb reactions at the LHC, recently measured by the ATLAS and CMS experiments, can be derived from these results. We show quantitatively that a fraction of this enhancement may be related to the ambiguity in the separation between the jet and the soft background medium and/or the diffusion of the parton shower energy away from the jet axis through collisional processes. We point to a suite of measurements that can help build a consistent picture of parton shower modification in heavy ion collisions at the LHC.

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, 7,236 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.77 · states limitation 0.45 · human participants 0.01 · controlled comparison 0.18 · randomized assignment 0.01 · states quantitative result 0.17 · compares with prior results 0.34 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

Jets physics in heavy ion reactions is an important new area of active research at the Relativistic Heavy Ion Collider (RHIC) and at the Large Hadron Collider (LHC) that paves the way for novel tests of QCD multi-parton dynamics in dense nuclear matter. At present, perturbative QCD calculations of hard probes in elementary nucleon-nucleon reactions can be consistently combined with the effects of the nuclear medium up to $ {\cal O}(\alpha_s^3) $. While such accuracy is desirable but not necessary for leading particle tomography, it is absolutely essential for the new jet observables. With this motivation, we present first results and predictions to $ {\cal O}(\alpha_s^3) $ for the recent LHC lead-lead (Pb+Pb) run at a center-of-mass energy of 2.76 TeV per nucleon-nucleon pair. Specifically, we focus on the suppression of the single and double inclusive jet cross sections. Our analysis includes not only final-state inelastic parton interactions in the QGP, but also initial-state cold nuclear matter effects and an estimate of the non-perturbative hadronization corrections. We demonstrate how an enhanced di-jet asymmetry in central Pb+Pb reactions at the LHC, recently measured by the ATLAS and CMS experiments, can be derived from these results. We show quantitatively that a fraction of this enhancement may be related to the ambiguity in the separation between the jet and the soft background medium and/or the diffusion of the parton shower energy away from the jet axis through collisional processes. We point to a suite of measurements that can help build a consistent picture of parton shower modification in heavy ion collisions at the LHC.

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 Jets physics in heavy ion reactions is an important new area of active research at the Relativistic Heavy Ion Collider (RHIC) and at the Large Hadron Collider (LHC) that paves the way for novel tests of QCD multi-parton dynamics in dense nuclear matter. background 1.00 0.04 0.03 asserted 1.00
s1 At present, perturbative QCD calculations of hard probes in elementary nucleon-nucleon reactions can be consistently combined with the effects of the nuclear medium up to $ {\cal O}(\alpha_s^3) $. background 0.98 0.07 0.05 asserted 0.99
s2 While such accuracy is desirable but not necessary for leading particle tomography, it is absolutely essential for the new jet observables. background 0.72 0.08 0.04 asserted 1.00
s3 With this motivation, we present first results and predictions to $ {\cal O}(\alpha_s^3) $ for the recent LHC lead-lead (Pb+Pb) run at a center-of-mass energy of 2.76 TeV per nucleon-nucleon pair. contribution 1.00 0.89 0.09 asserted 0.99
s4 Specifically, we focus on the suppression of the single and double inclusive jet cross sections. contribution 0.99 0.74 0.06 asserted 0.92
s5 Our analysis includes not only final-state inelastic parton interactions in the QGP, but also initial-state cold nuclear matter effects and an estimate of the non-perturbative hadronization corrections. method 0.77 0.85 0.05 asserted 1.00
s6 We demonstrate how an enhanced di-jet asymmetry in central Pb+Pb reactions at the LHC, recently measured by the ATLAS and CMS experiments, can be derived from these results. result 0.87 0.86 0.31 asserted 1.00
s7 We show quantitatively that a fraction of this enhancement may be related to the ambiguity in the separation between the jet and the soft background medium and/or the diffusion of the parton shower energy away from the jet axis through collisional processes. interpretation 0.93 0.87 0.25 hedged possibility 0.93
s8 We point to a suite of measurements that can help build a consistent picture of parton shower modification in heavy ion collisions at the LHC. future work 0.98 0.63 0.09 asserted 0.66

What kind of paper the classifier reports this is: theoretical result 0.92 · evidence from simulation or computation 0.71.

What was examined, and what was not

sources read
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not examined
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  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
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  • S sections
  • T body sentences
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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. Comparison between the R = 0.4 inclusive jet cross section measured by the ATLAS Collaboration in p+p collisions at √ s = 7 TeV and the O(α 3 s ) QCD theory which includes non-perturbative corrections. Experimental error bars are statistical only. The first obvious deficiency of the LO formalism is its in￾ability to describe the jet radius dependence of the physical ob￾servables [14]. The second much more significant shortcom￾ing is the inadequate description of the differential distribu￾tion of tagged jets [18] and di-jets due to the δ-function con￾straint in Eq. (1). At O(α 3 s )
Figure 2. A three-dimensional representation of the
Figure 3. The normalized differential distribution of the di-jet asymmetry AJ , defined in Eq. (5), is evaluated at O(α 3 s ) and compared to the ATLAS experi￾mental measurement at √ s = 7 TeV. Solid (dashed) lines include (do not in￾clude) non-perturbative corrections, respectively. With the O(α 3 s ) numerical results for ˜σ at hand, we can easily compute σ −1dσ/dAJ from Eq. (6) and confront it with the ex￾perimental data. The ATLAS Collaboration has measured the di-jet asymmetry distribution in p+p reactions at √ s = 7 TeV with the following kinematics cuts: ET 1 > 100 GeV for the leading…
Figure 4. illustrates the dependence of the suppression ratio R 1−jet AA for inclusive jets in central Pb+Pb collisions on the jet size R. The top panel shows the net suppression resulting from both initial-state and final-state effects for R = 0.2, 0.6 and the bands represent the variation in coupling strength between the jet and the medium. The dashed, solid, and dot-dashed lines correspond to gmed =1.8, 2, 2.2, respectively. Note that for small radii the suppression of jets can be comparable in magni￾tude to the suppression of inclusive particles. This is illustrated by including a…
Figure 5. Ratio of the inclusive jet cross sections in centra
Figure 6. The effects of parton shower collisional energy loss or misinter￾preting some of the jet’s energy as soft background on R 1−jet AA (top panel) and σ(R1)/σ(R2) (bottom panel) are simulated with p min T = 20 GeV and repre￾sented by a cyan band. Results are contrasted to the p min T = 0 GeV case, represented by a yellow band, which is no collisional energy loss or unam￾biguous jet/background separation. Preliminary ATLAS RCP data is shown for R = 0.2, 0.4. comment on the difficulties related to the measurement of jet observables. In central Pb+Pb collisions at the LHC, for a typ￾ica
Figure 7. O(α 3 s ) calculation of the di-jet cross section suppression ratio R 2−jet AA versus ET 1 and ET 2 in √ sNN = 2.76 TeV central Pb+Pb collisions at the LHC. Our result is for R1 = R2 = 0.2 and includes cold nuclear matter effects. ion AJ enhancement that can be attributed to the physics of jet quenching. Next, the di-jet asymmetry is computed using Eq. (6) and compared to recent experimental results published by AT￾LAS [19] and CMS [20] in
Figure 8. Di-jet asymmetry distributions for different coupling strength in cen￾tral Pb+Pb collisions at √ s = 2.76 TeV compared to data. The top panel is for leading jets of ET 1 > 100 GeV, subleading jets of ET 2 > 25 GeV (ATLAS [19], R = 0.4). The bottom panel is for leading jets of ET 1 > 120 GeV, subleading jet of ET 2 > 50 GeV (CMS [20], R = 0.5). Black lines are the results for p+p collisions under pQCD theory. Green lines assume perfect jet/background separation and are denoted p min T = 0 GeV. Red lines, denoted p min T = 20 GeV, show the consequences of the ambiguity in the…

Figures reproduced from arXiv:1105.2566 by the authors.

References
How later papers used it

63 later papers cite it

Evidence: some. 41 of the citing papers share no author with it, and 2 of those carry a confident label from Pith's citation classifier.

Pith read 16 of the 87 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 data or values 1 of 2 papers with this label
  • Used results based on this paper's analysis to find parton-initiated dijet probabilities for 120 GeV dijets in 2.76 TeV heavy-ion collisions.

    Jet momentum balance independent of shear viscosity (2011) · 0.99 · paraphrased: the licence does not allow quoting

How the literature uses it

60 arXiv papers cite this in 84 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 · 58 sentences without a confident label

Uses its method or tool 3 papers
  • To generate the medium-modified B-meson+b-jet cross section per binary collision, we first calculate the medium-modified b-quark+b-jet cross section as follows [ref] 1/⟨N_bin⟩ dσ^AA/dp_T^b dp_T^j = ∑_(s,s') ∫_0^1 dϵP_(s)(ϵ) 1/1-ϵ ∫_0^1 dϵ' P_(s')(ϵ') J_(s')(ϵ') dσ_(s,s')^LO+PS(p_T^b/(1-ϵ), J_(s')(ϵ') p_T^j)/dp_T^b dp_T^j,

    Photon-tagged and B-meson-tagged b-jet production at the LHC · Modification of tagged b-jet production in dense QCD matter · 0.84

  • Dijet spectrum in heavy ion collisions is ready to be given similarly as the inclusive jet [ref] , [equation] The two jets have symmetric final transverse momentum at leading-order.

    Jet probes of QCD matter: single jets and dijets in heavy-ion collisions · Dijet productions in HIC · 0.80

  • To quantify the transverse momentum imbalance between the leading jet and the subleading jet one defines the dijet transverse momentum asymmetry $A_J$ as, [equation] The $A_J$ distribution can be expressed from the dijet transverse energy spectrum as follows [ref] : [equation] where $E_T 1 = E_T 2(1+A_J)/(1-A_J)$ is the transverse energy for leading jet.

    Cold Nuclear Matter Effects on Dijet Productions in Relativistic Heavy-ion Reactions at LHC · Dijet Production in nucleon-nucleon Collisions · 0.91

Uses its data or values 2 papers
  • Fig. [ref] illustrates the dependence of the nuclear modification factor for single jet production $R_AA^1-jet$ in central Pb+Pb collisions on the jet size $R$ with an acceptance cut without ($p_T^min=0$ GeV) and with ($p_T^min>0$ GeV) collisional energy loss [ref] .

    Probing nuclear matter with jets · Inclusive jet production in HIC · 0.83

  • Using results based on the analysis of [ref] one finds for these parameters that the probability that the primary partons initiating the dijets are two gluons is about 37$%$, the probability for two quarks is about 21$%$, and the probability for a quark and a gluon is about 42$%$.

    Jet momentum balance independent of shear viscosity · Calculating the Parton Shower Energy Deposition Rate · 0.99

Compares with it 1 paper
Cites it as background 19 papers

What it cites · 33 sentences without a confident label

Uses the method or tool of 2 papers
  • We take into account the longitudinal Bjorken expansion of the medium and, by assuming local thermal equilibrium, we can evaluate the physical quantities, such as the Debye screening scale, the in-medium jet scattering cross sections, and the mean free paths [ref] , that are employed in the calculation of the radiative energy loss [ref] .

    Jet tomography of high-energy nucleus-nucleus collisions at next-to-leading order · Inclusive jet and di-jet production in heavy ion collisions · 0.91

  • In the calculations that follow we will take advantage of the Ellis, Kunszt and Soper (EKS) numerical implementation of $O( α_s^3 )$ jets production in hadron-hadron collisions [ref] and the CTEQ6.1M parametrization set of parton distribution functions [ref] .

    New Generation of Parton Distributions with Uncertainties from Global QCD Analysis · Inclusive jet and di-jet production in p+p collisions · 1.00

Uses data or values from 2 papers
Compares with 1 paper
Cites as support 2 papers
Cites as background 2 papers
  • Jet production and modification in high-energy nucleus-nucleus collisions have been proposed as new ways to unravel the properties of the hot and dense QCD medium and to elucidate the mechanisms of in-medium parton shower formation [ref] .

    Jet tomography of high-energy nucleus-nucleus collisions at next-to-leading order · Summary and Conclusions · 0.95

  • Jet production and modification in high-energy nucleus-nucleus collisions have been proposed as new ways to unravel the properties of the hot and dense QCD medium and to elucidate the mechanisms of in-medium parton shower formation [ref] .

    The physics of $Z^0/\gamma^*$-tagged jets at the LHC · Summary and Conclusions · 0.95

Discussion

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