Power corrections to event shapes and factorization

G.P.Korchemsky; G.Sterman

REVIEW

Power corrections to event shapes and factorization

G.P.Korchemsky, G.Sterman

High Energy Physics - Phenomenology · Submitted 15 Feb 1999 · 23 references

Pith's verdict: The shape-function convolution framework is the real contribution and it holds up, but the moment relations in Eqs. 26–28 and 37 carry a sign error a referee should catch.

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arXiv IDhep-ph/9902341 (version 1)

Pith IDNSH5OY77, Pith's permanent record of this paper and its review

CitationG.P.Korchemsky, G.Sterman. "Power corrections to event shapes and factorization." arXiv:hep-ph/9902341 (1999). https://pith.science/paper/NSH5OY77

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Editor's note

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This is the paper that put the infrared shape function on the map for event shapes, and the framework is the reason to read it. The convolution form for the differential thrust and heavy-jet-mass distributions (Eqs. 19, 21), the operator definition as a Wilson-line matrix element of an energy-flow operator (Eqs. 31, 32), and the tie to energy-energy correlations (Eq. 40) are the conceptual core. That core is right and it has aged well. The definitional element the reader flags is real — f_T is defined by Eq. 27 as the inverse Laplace transform of S_NP — but the content is the Q-independence of S_NP and the fact that the same f_T convolves with the full perturbative spectrum, not just the exponentiated form. That is more than a tautology, though it is asserted rather than proved in detail here.

Referee report

Significance

If the factorization holds, the paper supplies a framework rather than a model: it organizes the entire series of 1/(eQ)^n corrections, not just the leading shift of Eq. (1), and it gives the shape functions an operator definition (Eqs. (31)–(32)) that makes the Q-independence claim falsifiable and connects event-shape power corrections to energy-flow correlators and to the EEC (Eq. (40)). The moment sum rules of Eqs. (28) and (37) and the explicit ansatz of Eqs. (44)–(45) turn the formalism into something that can be, and has been, confronted with data at several energies. I checked the normalization of Eq. (43) against Eq. (34) with the weight of Eq. (33) and it is correct, and I verified that the moments of the ansatz in Eq. (44) reproduce both relations of Eq. (45). These are genuine strengths: a parameter-free structural prediction (Q-independence of f_T), a worked phenomenological implementation, and a clean field-theoretic interpretation.

Major objections (3)

[§2, Eqs. (13)–(15) and Eq. (21)] The heavy-mass convolution of Eq. (15) retains only the factorized part of the two-hemisphere shape function, f(ε_L,ε_R) ≈ f(ε_R)f(ε_L), while the paper itself states in Eq. (13) that the exact distribution contains a nonfactorizing term Δf, attributed to the splitting of an off-shell gluon into gluons in opposite hemispheres. The justification offered is that the perturbative expectation values factorize at NLL (Eq. (14), cited to Ref. [16]). That justifies the perturbative factor, but it does not establish that Δf is subleading at the same power in 1/(ρQ) as the terms kept in Eq. (21). Since the shape function dominates the distribution precisely for ρ ≲ µ/Q, where the neglected term is largest, the leading-power accuracy of Eq. (21) rests on an unstated bound on Δf. The paper should either estimate Δf or state explicitly that Eq. (21) is accurate only up to a nonfactorizing correction of the same parametric order, which would qualify the claim that the heavy-mass distribution is described by the same universal f.
[§2, Eqs. (22)–(23), versus abstract:s2] The abstract states that the infrared shape functions are independent of the center-of-mass energy Q, but the text states of Eq. (22) that 'in contrast with f_T, the shape function f_H depends both on the center-of-mass energy and the shape variable.' The two statements are reconcilable only because the Q-dependence of f_H enters through the upper limit ρQ and through R_J^{PT}, and is power-suppressed, as the expansion of Eq. (23) shows explicitly. As written, however, the abstract's blanket Q-independence claim is contradicted by the paper's own sentence about f_H. The abstract or the sentence in §2 should be amended to say that f_H is Q-independent up to corrections of order 1/(ρQ), so that the scope of the Q-independence claim is unambiguous.
[§3, Eq. (26)] The definition of the nonperturbative parameters λ_n(µ) should be written out explicitly, including the alternating sign and the 1/n factor carried by the intermediate expression of Eq. (26). The intermediate line contains (−ν/Q)^n/(n·n!), whereas the final line is written as (ν/Q)^n/n! λ_n(µ); the '≡' therefore defines λ_n = (−1)^{n+1} n^{−1} ∫₀^{µ²} dk⊥² k⊥^{n−2} Γ, not the integral alone. This matters because Eq. (28) then gives a variance ⟨ε²⟩−⟨ε⟩² = −λ2, which requires λ2 < 0, and Eq. (45) requires the same sign through Λ²α = λ1² − λ2. A reader who takes λ_n to be the bare integral (which is positive for n = 2, since Γ > 0) will conclude that f_T has a negative variance, which is impossible for the positive ansatz of Eq. (44). I do not believe this is an internal inconsistency: the sign is carried by the intermediate line, and Eqs. (28), (37) and (45) are mutually consistent once λ2 < 0. But the equation as printed invites the wrong reading, and since Eq. (26) is the vehicle for the 'all n' claim of abstract:s3, the definition should be displayed unambiguously.

Minor objections (6)

[§2, Eq. (18)] The overall factor in the definition of R_T^{PT}(t′,µ) is written θ(t) where it should be θ(t′); the argument of the step function should match the variable of the function being defined.
[§2, Eq. (16)] The statement that R_J^{PT}(0,µ) = R_J^{PT}(µ/Q,µ) would be easier to verify if the two arguments were shown explicitly in the integral, since the equality relies on the max(ρ,µ/Q) lower limit freezing the ρ-dependence below ρ = µ/Q.
[§2, Eqs. (9)–(10)] The notation ⟨…⟩_PT is used both for an average over the full perturbative spectrum and, inside the ε_R,ε_L integrals, for an average over the double differential distribution in the two hemisphere masses. A sentence distinguishing the two usages, and stating that the perturbative factor in Eq. (15) is the double distribution before the NLL factorization of Eq. (14) is applied, would remove the ambiguity.
[§2, paragraph after Eq. (7)] The phrase 'for e^{1/2} ≫ Λ_QCD/Q ∼ e' is hard to parse; presumably the intended statement is that the hierarchy Qe^{1/2} ≫ Qe ≫ Λ_QCD defines the region in which only powers of 1/(Qe) need be retained. Rewording would help.
[Fig. 1] The figure is reproduced from Ref. [10] and its caption defers the details to that reference. For a journal article the caption should be self-contained: state what 'scaled' means, what the vertical normalization is, and what the curves correspond to, so that the comparison across Q = 14–161 GeV can be read without consulting the proceedings.
[§3, final paragraph, and §4] There are several typographical errors, among them 'extentions' in the last paragraph of §3 and 'truely' in §4; these should be corrected in the final version.

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The paper

The paper claims

The paper argues that near the two-jet limit the thrust and heavy-jet-mass distributions factor into a convolution of one energy-independent soft shape function with a resummed perturbative spectrum, so that every power correction of the形式$

The reading

Near the two-jet limit of electron-positron annihilation, the thrust and heavy-jet-mass distributions are dominated by soft radiation carrying a small fraction of the beam energy. The paper argues that this soft radiation separates from the evolution of the narrow jets and can be packaged into a shape function: a probability distribution for how much light-cone energy the soft quanta deposit in each hemisphere. If that holds, the measured distribution is a convolution of this nonperturbative function with a perturbatively resummed spectrum, and every power correction of the form $1/(eQ)^n$ is generated by the same function rather than by a separate parameter for each $n$. The payoff is predictive: the shape function is fixed once, at a single energy, and must then describe the same physics at every energy, while its moments are vacuum expectation values of energy-flow operators that also control the energy-energy correlation.

What carries the argument

The shape function itself. For thrust it is defined by the Laplace transform $��_0^�� d�� e^{-�ͧ�/Q} f_T(��;��) = ��(-S_{NP}(Q/��,��))$, which ties its moments to the ambiguous low-momentum integrals of the resummed exponent, and equivalently by the operator expression $f_T(��) = ��0|W^��(0) ��(�� - �� d�� n w_T(n) E(n)) W(0)|0��$, where $W$ is the product of eikonal Wilson lines of the two jets and $E(n)$ is an energy-flow operator measuring energy density in direction $n$, with weight $w_T(n) = 1-|��cos��|$. The weight vanishes along the jet directions, which is why the shape function has no collinear singularities. Taking moments of $f_T$ turns the weights into integrals of Green functions $G(n_1��n_N) = ��0|W^�� E(n_1)��E(n_N) W|0��$; these are the universal objects, independent of which event shape was chosen, and the single-energy-flow correlator $G(��)$ is what the leading $1/Q$ energy-energy correlation measures.

Extended reading notes

Core claim

The central claim is that the differential thrust and heavy-jet-mass distributions in the two-jet limit, $e = 1-T$ or $e = M^2/Q^2$, can be written as convolutions of a nonperturbative infrared shape function with a resummed perturbative cross section. The shape function depends on a factorization scale $��$ that separates soft from hard dynamics, and differs from one event shape to another, but is independent of the center-of-mass energy $Q$. The authors derive this twice: once from the kinematics of soft emission, writing the hemisphere masses as perturbative pieces plus soft light-cone sums $M^2_{R,L}/Q^2 + ��_{R,L}/Q$ and factorizing the soft distribution $f(��_R,��_L)$; and once from the resummed exponent, where the nonperturbative part of the Sudakov exponent $S_{NP} = ��_{n>0} (��/Q)^n ��_n(��)/n!$ is the Laplace transform of the thrust shape function $f_T(��)$, so that the moments of $f_T$ are exactly the $��_n$. The familiar shift $d��_{PT}(t)/dt �� d��_{PT}(t-��_1/Q)/dt$ reappears as the special case in which $f_T$ is a delta function, and the same limit gives half that shift for the heavy-jet mass, a parameter-free relation between the two observables. Beyond the leading shift, the shape function organizes all powers $1/(tQ)^n$ and $1/(��Q)^n$, and its variance controls the smearing that the simple shift misses.

Load-bearing premise

Soft gluon emission from the two jets is incoherent and depends only on the jet directions and colour charges, so that the soft distribution factorizes from jet evolution and carries no dependence on the beam energy; the authors note this fails at the level of the $��f$ term from a gluon splitting into opposite hemispheres.

Editorial extensions

If this is right

A shape function fitted to thrust data at one energy predicts the thrust distribution at all higher energies with no new parameters.
All corrections of the form $1/(tQ)^n$ follow from the moments of one function, with the simple shift of the perturbative spectrum as the delta-function limit.
The nonperturbative shift of the mean heavy-jet mass is exactly half that of the mean thrust, a relation that holds for any shape function.
Moments of the shape function are universal energy-flow matrix elements, so event-shape measurements constrain the same quantities that appear in energy-energy correlations.
The variance of the thrust distribution receives no $1/Q$ correction; its leading nonperturbative piece is $1/Q^2$ and is tied to connected two-point energy-flow correlations.

Reading between the lines

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

If the shape function really carries no $Q$ dependence, a global fit across energies is over-determined, and the drift of fitted $��_1$ values with energy becomes a direct handle on the size of the neglected non-factorizing term $��f$ and of higher $1/Q$ corrections.
The Green functions are singular only where two directions coincide, and stereographic projection maps them onto a plane; that suggests the energy-flow correlators might be computable in a two-dimensional effective description, which the paper only gestures toward.
Because the construction needs only an additive weight on soft momenta that vanishes along the jets, the same convolution should exist for any infrared-safe observable of that class, making the shape-function idea as broad as the class of such weights.
The same structure should carry over to hadron-collider event shapes and jet masses, where soft radiation is emitted by more than two coloured legs; whether the shape function stays universal there is an open and testable question.

Original abstract

We study power corrections to the differential thrust, heavy mass and related event shape distributions in $e^+e^-$-annihilation, whose values, $e$, are proportional to jet masses in the two-jet limit, $e\to 0$. The factorization properties of these differential distributions imply that they may be written as convolutions of nonperturbative "shape" functions, describing the emission of soft quanta by the jets, and resummed perturbative cross sections. The infrared shape functions are different for different event shapes, and depend on a factorization scale, but are independent of the center-of-mass energy $Q$. They organize all power corrections of the form $1/(eQ)^n$, for arbitrary $n$, and carry information on a class of universal matrix elements of the energy-momentum tensor in QCD, directly related to the energy-energy correlations.

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, 3,789 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.14 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.05 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We study power corrections to the differential thrust, heavy mass and related event shape distributions in $e^+e^-$-annihilation, whose values, $e$, are proportional to jet masses in the two-jet limit, $e\to 0$. The factorization properties of these differential distributions imply that they may be written as convolutions of nonperturbative "shape" functions, describing the emission of soft quanta by the jets, and resummed perturbative cross sections. The infrared shape functions are different for different event shapes, and depend on a factorization scale, but are independent of the center-of-mass energy $Q$. They organize all power corrections of the form $1/(eQ)^n$, for arbitrary $n$, and carry information on a class of universal matrix elements of the energy-momentum tensor in QCD, directly related to the energy-energy correlations.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We study power corrections to the differential thrust, heavy mass and related event shape distributions in $e^+e^-$-annihilation, whose values, $e$, are proportional to jet masses in the two-jet limit, $e\to 0$.	contribution 0.92	0.72	0.09	asserted 0.99
s1	The factorization properties of these differential distributions imply that they may be written as convolutions of nonperturbative "shape" functions, describing the emission of soft quanta by the jets, and resummed perturbative cross sections.	interpretation 0.37	0.30	0.26	hedged possibility 0.98
s2	The infrared shape functions are different for different event shapes, and depend on a factorization scale, but are independent of the center-of-mass energy $Q$.	result 0.86	0.46	0.15	asserted 1.00
s3	They organize all power corrections of the form $1/(eQ)^n$, for arbitrary $n$, and carry information on a class of universal matrix elements of the energy-momentum tensor in QCD, directly related to the energy-energy correlations.	interpretation 0.67	0.60	0.41	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 0.75.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

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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.** The comparison of the data with the QCD prediction for the

Figures reproduced from arXiv:hep-ph/9902341 by the authors.

References

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Quantum Interference in Jet Substructure from Spinning Gluons
hep-ph 2020-11 accept novelty 7.0 of 10

The squeezed three-point energy correlator exhibits a cos(2φ) interference pattern from ± helicity gluons, resummed to all orders using a light-ray OPE developed for QCD.
Rethinking Jets with Energy Correlators: Tracks, Resummation and Analytic Continuation
hep-ph 2020-04 accept novelty 7.0 of 10

Projections of N-point energy correlators form an analytic family in N, continue to non-integer values as a measurable nu-correlator, and resum to NLL accuracy for all N, with track information entering only through i...
Three Point Energy Correlators in the Collinear Limit: Symmetries, Dualities and Analytic Results
hep-ph 2019-12 accept novelty 7.0 of 10

The three-point energy correlator in the collinear limit is computed analytically for QCD quark and gluon jets and for N=4 super Yang-Mills, revealing a duality with one-loop Feynman parameter integrals.
Energy correlations in the end-point region
hep-th 2019-05 conditional novelty 7.0 of 10

The energy-energy correlation in both end-point regions is expressed as a compact function of twist-two conformal data, reproducing known NNLO results and predicting the next order.
On the Cutoff Dependence of the Quark Mass Parameter in Angular Ordered Parton Showers
hep-ph 2018-07 accept novelty 7.0 of 10

The quark mass parameter of an angular-ordered parton shower with transverse-momentum cutoff Q0 is a short-distance mass equal to the pole mass minus (2/3) alpha_s(Q0) Q0 at NLO, not the pole mass.
First Subleading Power Resummation for Event Shapes
hep-ph 2018-04 accept novelty 7.0 of 10

Subleading-power logarithms in thrust are resummed to all orders and shown to exponentiate into a Sudakov factor governed by the cusp anomalous dimension, with a new class of theta-function jet and soft operators requ...
New Angles on Energy Correlation Functions
hep-ph 2016-09 conditional novelty 7.0 of 10

Generalizing energy correlation functions to weight v of the pairwise angles yields three new jet-substructure ratios (M_i, N_i, U_i) that outperform D2 and N-subjettiness in parton-shower studies, with N_i reproducin...
Factorization for groomed jet substructure beyond the next-to-leading logarithm
hep-ph 2016-03 conditional novelty 7.0 of 10

Soft-drop groomed jet observables factorize into single-scale collinear and collinear-soft functions with no non-global logarithms, enabling NNLL resummation of the groomed jet mass matched to fixed order for e+e- and...
Analytic Boosted Boson Discrimination
hep-ph 2015-07 conditional novelty 7.0 of 10

An all-orders QCD factorization theorem for the two-prong jet discriminant D2 reproduces Monte Carlo D2 spectra for boosted Z jets and massive QCD jets, and yields analytic signal-versus-background efficiency curves.
Toward Multi-Differential Cross Sections: Measuring Two Angularities on a Single Jet
hep-ph 2014-01 conditional novelty 7.0 of 10

The double-differential cross section for two angularities on one jet factorizes at phase-space boundaries but not in the bulk, and a scale-setting interpolation connects the two boundary factorization theorems to nex...
From correlation functions to event shapes
hep-th 2013-09 accept novelty 7.0 of 10

Event-shape (charge-flow) correlations in a conformal field theory are computed from Euclidean four-point correlation functions via a Mellin-space analytic continuation, and the result is checked against known weak- a...
Unsafe but Calculable: Ratios of Angularities in Perturbative QCD
hep-ph 2013-07 conditional novelty 7.0 of 10

The ratio of two jet angularities, though not infrared safe, has a finite calculable distribution once Sudakov logarithms are resummed, and its expansion begins at the square root of the strong coupling.
Combining Higher-Order Resummation with Multiple NLO Calculations and Parton Showers in GENEVA
hep-ph 2012-11 conditional novelty 7.0 of 10

A master formula multiplicatively matches N-jettiness resummation to fully differential NLO matrix elements and Pythia 8, giving a Monte Carlo formally accurate to relative O(alpha_s) at all jet resolutions.
Precision Jet Substructure from Boosted Event Shapes
hep-ph 2012-04 accept novelty 7.0 of 10

Boosting a Z boson to large momentum turns the 2-subjettiness ratio into a copy of the thrust distribution, computable at N3LL order, with jet-boundary and contamination effects suppressed as 1/Q.
Thrust at N^3LL with Power Corrections and a Precision Global Fit for alphas(mZ)
hep-ph 2010-06 conditional novelty 7.0 of 10

Fitting all published e+e- thrust data between 35 and 207 GeV with an N3LL resummed plus O(alpha_s^3) fixed-order calculation and a fitted nonperturbative soft-function moment yields alpha_s(m_Z) = 0.1135 +/- 0.0011.
Quark Fragmentation within an Identified Jet
hep-ph 2009-11 accept novelty 7.0 of 10

The fragmenting jet function G_i^h(s,z) factorizes into perturbative coefficients J_ij convolved with standard fragmentation functions D_j^h, and satisfies a sum rule that reduces to the inclusive jet function J_i(s).
Factorization at the LHC: From PDFs to Initial State Jets
hep-ph 2009-10 accept novelty 7.0 of 10

When the hadronic final state is restricted, the initial state of a proton collision must be described by beam functions rather than PDFs, and a factorization theorem for isolated Drell-Yan follows.
Top Jets in the Peak Region: Factorization Analysis with NLL Resummation
hep-ph 2007-11 accept novelty 7.0 of 10

Effective-theory factorization with NLL resummation gives the top-jet invariant-mass spectrum in e+e- collisions and defines a short-distance jet mass whose peak position is stable against perturbative corrections.
Jets from Massive Unstable Particles: Top-Mass Determination
hep-ph 2007-03 accept novelty 7.0 of 10

A factorization theorem shows that top-jet invariant mass peaks are shifted upward and broadened by non-perturbative soft radiation, and defines a short-distance jet mass measurable to better than the QCD scale.
A universal probe of QCD spin physics from fragmentation energy correlator
hep-ph 2026-10 conditional novelty 6.0 of 10

A jet-free energy correlator built around a single hadron is shown to factorize alike in e+e-, ep, and pp collisions, with a transverse-spin piece that probes the QCD chiral symmetry breaking scale.
From Nuclear Many-Body Correlations to Energy Detector Correlators
nucl-th 2026-09 conditional novelty 6.0 of 10

Energy-energy correlators encode nuclear ground-state multipole correlations through a systematic expansion in initial fluctuations and long-wavelength response.
Soft functions for generalised angularity event shapes at NNLO
hep-ph 2026-09 accept novelty 6.0 of 10

A modular method to compute the NNLO soft function for any generalised angularity event shape is presented, with numerical results for three new families.
Hadronization effects and electroweak contributions in DIS one-jettiness
hep-ph 2026-09 accept novelty 6.0 of 10

The leading hadronization effects in DIS 1-Jettiness event shapes tau1 and tau1a are universal and described by a single shape function, with a calculable kinematic dependence in tau1 that provides an additional lever...
The EEC-Hedron: Positivity Bounds on Energy Correlators
hep-th 2026-08 conditional novelty 6.0 of 10

Energy positivity and unitarity confine energy-energy correlator partial waves to a bounded 'EEC-hedron', yielding new upper and lower bounds on OPE coefficients in the 3d Ising and O(2) CFTs.
Energy Correlators in $V + X$ as a Benchmark Observable for Precision QCD
hep-ph 2026-08 conditional novelty 6.0 of 10

First complete NLO+NNLL matched predictions, with leading non-perturbative corrections, for projected energy correlators on the radiation recoiling against a Z boson or a photon at the LHC.
Dissecting Parton Showers with Multi-Point Energy Correlators
hep-ph 2026-07 accept novelty 6.0 of 10

Projections of four-point energy correlators cleanly separate spin from kinematic azimuthal correlations inside jets; spin effects are subdominant in accessible LHC kinematics.
The one-point charge correlator in deep inelastic scattering
hep-ph 2026-06 unverdicted novelty 6.0 of 10

Defines an IRC-safe one-point charge correlator in DIS, relates it to a new nucleon charge correlator in the forward limit and to TMDs in the back-to-back limit, with SCET derivations verified in QCD to O(alpha_s^2) a...
Energy correlators in four-dimensional gravity
hep-th 2025-12 conditional novelty 6.0 of 10

Gravitational energy correlators in four dimensions are computed at one loop, shown to be infrared-finite, and resummed in the back-to-back limit by soft-graviton exponentiation.
Factorization and Resummation for the Nearside Energy-Energy Correlators
hep-ph 2025-07 conditional novelty 6.0 of 10

A new all-order resummation formula in Fourier b_T-space for the nearside energy-energy correlator, derived from di-hadron fragmentation functions, matches fixed-order calculations and predicts a small-angle turnover.
Regge trajectories, detectors, and distributions in the critical ${\rm O}(N)$ model
hep-th 2025-06 conditional novelty 6.0 of 10

In the critical O(N) model, renormalizing detector and distribution light-ray operators at leading order in 1/N yields Regge intercepts, the leading-twist splitting function, and a BFKL-type anomalous spin.
Factorization for Collider Dataspace Correlators
hep-ph 2025-04 conditional novelty 6.0 of 10

Derives a factorization theorem and NLL resummation for SEMD-based event correlators, predicting a universal ledge in quark-jet non-Gaussianity.
Simple Scaling Laws for Energy Correlators in Nuclear Matter
hep-ph 2024-11 conditional novelty 6.0 of 10

The leading nuclear modification of the two-point energy correlator in A-A and p-A collisions is a twist-4 light-ray operator contribution, giving an EEC ratio of 1 + a theta^2.
Advancing the understanding of energy-energy correlators in heavy-ion collisions
hep-ph 2023-12 conditional novelty 6.0 of 10

Using the exact in-medium photon-to-quark-antiquark matrix element, the paper shows that semi-classical and BDMPS-Z approximations overestimate the medium-induced enhancement of the energy-energy correlator at large a...
A Coherent View of the Quark-Gluon Plasma from Energy Correlators
hep-ph 2023-03 conditional novelty 6.0 of 10

The two-point energy correlator of an in-medium quark jet, computed in three jet-quenching models, shows a two-regime power-law scaling of its medium-enhancement peak that the authors identify with the onset of colour...
Nucleon Energy Correlators for the Color Glass Condensate
hep-ph 2023-01 conditional novelty 6.0 of 10

The angular distribution of energy deposited at small angles in electron-nucleus deep inelastic scattering is predicted to turn over at an angle set by the saturation momentum, a feature absent from collinear factorization.

See all 106 Pith citations

How later papers used it

162 later papers cite it

Evidence: some. 156 of the citing papers share no author with it, and 18 of those carry a confident label from Pith's citation classifier.

Pith read 3 of the 225 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

2 later papers by other authors are listed below: 2 used its method or tool.

Uses its method or tool 2 of 14 papers with this label

Used an analytic model based on a correlation or shape function depending on very few nonperturbative parameters to include hadronization effects in its thrust distribution.

Thrust distribution in electron-positron annihilation at full NNNLL+NNLO (and beyond) in QCD (2025) · 0.96 · paraphrased: the licence does not allow quoting
For simplicity, we use a phenomenological form for the leading non-perturbative power correction as suggested in [ref] , and fit the unknown parameters from a Monte Carlo program.

NNLL Resummation for Projected Three-Point Energy Correlator (2023) · Hadronization corrections · 0.93

How the literature uses it

165 arXiv papers cite this in 233 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 whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 1 paper

We argue that for $e \sim \Lambda_{QCD}/Q$ all power corrections of the form $1/\lr{Qe}^n$ have to be taken into account for an arbitrary $n$.

Power corrections to the event shape in $e^+e^-$ annihilation · 0.80

Papers citing it · 147 sentences without a confident label

Builds on it 1 paper

This approach extends earlier studies [ref] , which included only the leading power correction and showed improved agreement with data for moderately small angles.

Collinear limit of the energy-energy correlator in $e^+ e^-$ collisions: transition from perturbative to non-perturbative regimes · Introduction · 0.94

Uses its method or tool 13 papers

In SCET, this is implemented by convolving $S_PT$ with a universal shape function $F(k)$ describing soft radiation at $k∼Λ_QCD$ [ref] , [equation] with $F(k)$ normalized as $∫dk F(k) = 1$ and independent of $μ_S$.

Centauric 1-Jettiness in DIS and Universal Power Corrections · Non-perturbative Power Corrections · 0.84
Using repl in the leading-order factorization theorem for the cross-section where an inclusive measurement of thrust is performed for $τ≪1$ [ref] , we obtain:

Parton Fragmentation within an Identified Jet at NNLL · Introduction · 0.82
Our numerical results include resummation up to NNLL$'$ resummation and include nonperturbative hadronization corrections through a shape function [ref] .

A case study of quark-gluon discrimination at NNLL' in comparison to parton showers · Introduction · 0.90

Compares with it 2 papers

The above definition provides an operator definition of $S_(ℓ_1^+,ℓ_2^+)$ in SCET, and is equivalent to the definition in Ref. [ref] .

Factorization for generic jet production · Double Differential Hemisphere Mass Distribution · 0.99
For comparison, the hemisphere soft function with outgoing Wilson appearing in the double-differential hemisphere invariant-mass distribution in $e^+e^- →2$ jets [ref] is

Factorization at the LHC: From PDFs to Initial State Jets · The $qq̅$ Soft Function · 0.98

Cites it as support 1 paper

The assumption of linearity in $Λ_QCD$ is supported by predictions from hadronization [ref] , Wilson loop [ref] and renormalon [ref] models.

Scaling violation in power corrections to energy correlators from the light-ray OPE · Introduction · 0.98

Cites it as background 59 papers

In the last several years there has been a program [ref] to systematically reformulate the study of jet substructure in terms of correlation functions of energy flow operators [ref] , so-called energy correlators.

Putting Jet Substructure on Track(s) · Introduction · 0.91
Asymptotic energy flow in collider experiments is characterized by correlation functions $⟨ℰ(n⃗_1) ℰ(n⃗_2) ⋯ℰ(n⃗_k) ⟩$ of the energy flow operator [ref] :

Non-Gaussianities in Collider Energy Flux · Introduction · 0.89
This has been achieved by using factorization formulas [ref] , that separate perturbative dynamics at short distances from non-perturbative physics at long-distance scales encoded in universal functions such as parton distribution functions (PDFs) for the initial state or shape functions [ref] related to hadronization that can be extracted from reference processes and lattice data.

Factorization for jet production in heavy-ion collisions · Introduction · 0.90

Discussion

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