Analysis note: one-point charge correlator with DELPHI Open Data

Cristian Baldenegro; Hannah Bossi; Ian Moult; Jingyu Zhang; Kyle Lee; Yen-Jie Lee; Yi Chen

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Analysis note: one-point charge correlator with DELPHI Open Data

Jingyu Zhang, Yi Chen, Kyle Lee, Ian Moult, Cristian Baldenegro, Hannah Bossi, Yen-Jie Lee

High Energy Physics - Experiment · Submitted 15 Aug 2026

Pith's verdict: First measurement of the per-angle charge-flux correlator in e+e-, a genuinely new observable with a careful analysis, but the tau-to-hadronic transfer of the charge-misID residual is the load-bearing step and is only MC-validated.

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arXiv ID2608.15367 (version 2)

Pith IDL63YHBHQ, Pith's permanent record of this paper and its review

CitationCristian Baldenegro, Hannah Bossi, Ian Moult, Jingyu Zhang, Kyle Lee, Yen-Jie Lee, Yi Chen. "Analysis note: one-point charge correlator with DELPHI Open Data." arXiv:2608.15367 (2026). https://pith.science/paper/L63YHBHQ

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Editor's note

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First thing you should know: this is the first measurement of the one-point charge correlator, the per-angle conserved charge flux, in e+e- collisions. Previous LEP/SLD work used hemisphere or jet charges, not this differential observable. Second thing: the headline sin(2θ) modulation is credible, but the correction that makes it credible—transferring the data–MC charge-misreconstruction residual from a τ+τ- control sample to hadronic events—is validated only on simulation, and the total systematic is 30–50%. Keep both in mind before you decide what this note is worth.

What it does well: the observable Q(θ) is genuinely new as a measurement, and the paper connects it cleanly to the Hofman-Maldacena / Lee–Moult charge-correlator program. The analysis is unusually thorough: two-stage corrections, closure tests, alternative binnings, alternative parametrizations, and detailed appendices including satisfying self-correction cross-checks. The raw data already show the forward-backward asymmetry, so the signal is not manufactured. Agreement with PYTHIA8.3 after correction is good, within the large uncertainties.

The main soft spot is exactly what the stress-test flags. Equation (5.3) applies δ_asym, measured in the low-occupancy τ sample and reweighted by the hadronic pT spectrum, to the high-occupancy hadronic sample, amplified by N_tot. The only evidence for environment independence is MC truth (Figure 11) and a bias-injection closure test where the same residual is injected into both samples—so the closure validates the inversion algebra, not the transfer. That is a real gap, and the TPC distortion mismatch mentioned in footnote 1 makes occupancy-dependent residuals plausible. It is not a fatal flaw, though: the measured residual is statistically consistent with zero, the central correction is small, and the quoted systematic already absorbs a 30–50% uncertainty. The paper is transparent about the limitation. I would still want either a data-based cross-check of the transfer or an explicit statement that this is a feasibility demonstration whose unassigned bias is bounded at the level of the quoted systematic. The circularity of using PYTHIA8.3 for both the detector correction and the theory benchmark is also present, but the residual data–MC correction is genuinely data-driven, so I do not see it as disqualifying. A significance estimate for the sin(2θ) modulation would be a useful addition, since the paper uses "clear" without quantifying it.

The analysis note deserves a serious referee, especially for the companion paper. I would bring it to a reading group, and I would cite it if I were working on charge correlators or archival e+e- data. The right review outcome is probably "accept after the authors either provide a data-based transfer check or temper the claim to what the current support justifies."

What would settle it

Going directly to the weakest link: measure the charge-dependent track-curvature bias from the momentum balance of $Z\to\mu^+\mu^-$ events in the same DELPHI Open Data, as earlier LEP analyses did with sagitta calibrations, convert it into a data-based sign-flip asymmetry versus $\theta$, and compare it with the $\tau$-derived $\delta_{\rm asym}(\theta)$; a disagreement larger than the propagated uncertainty would mean the transfer assumption fails and part of the measured $\sin(2\theta)$ modulation could be instrumental. A cheaper check is to rerun the full correction chain at a harder threshold, $p_T>4$ GeV, where soft-fragmentation background is further suppressed: the corrected modulation amplitude must remain inside the systematic band, or the correction chain is not closing.

Referee report

Significance

If correct, this is the first measurement of the conserved charge-flux correlator, extending the energy-correlator program to charge observables and forging a new theory–experiment connection for CFT-style charge correlation functions. The note is exemplary in experimental rigor: it documents a two-stage correction chain, bias-injection closure tests, alternative selections and binnings, per-source systematic tables, an event-by-event statistical covariance, and an honest discussion of which bias components the hadronic self-corrections can and cannot constrain (Appendix A); the CP-folding self-correction of Eq. (A.1) is a parameter-free projection. Use of public Open Data and the independent treatment of the 1994 and 1995 samples add to the reproducibility of the claim. The dominant systematic (27.6–35.6%) is set by the statistical precision of the τ control region, so the analysis is statistics-limited and the measurement program is demonstrably feasible. The main residual risk, assessed below, is the transferability of the τ-derived misreconstruction correction to the inclusive hadronic environment.

Major objections (3)

[§5.3–5.4, Eqs. (5.3)–(5.5), Figure 11] The central correction assumes that the data–MC residual of the charge-misreconstruction asymmetry measured in the low-occupancy 1+1-prong τ+τ− control sample equals the residual in the inclusive hadronic sample after pT reweighting. The only supports are the MC-truth comparison of Figure 11 and the bias-injection closure test of Section 5.4, and the closure test cannot validate the transfer: it injects the same δ_asym into both samples and thus verifies only the algebraic inversion of Eq. (5.3). The risk is concrete because footnote 1 attributes a dominant residual component to a TPC distortion correction applied to data but not to simulation; the occupancy-dependent part of such a distortion would differ between the sparse τ sample and dense hadronic events, and this mismatch would enter Q(θ) directly as δ_asym N_tot with no corresponding term in Table 4. I request a differential test (for example, injecting different δ into the two environments and verifying that the extraction degrades as expected, or splitting the hadronic sample by event multiplicity and checking the stability of the corrected Q(θ)), or, failing that, an explicit conservative systematic for the transfer with its effect on the extracted sin(2θ) amplitude.
[§7, Figure 26, Tables 4–5] The central claim of the abstract, that the corrected data exhibit a clear sin(2θ) modulation consistent with PYTHIA8.3, is not quantified anywhere in the note. With per-bin statistical uncertainties of 14–24% and a total systematic of 28–36%, a statement of agreement requires at least a fit of Q(θ) = A sin(2θ), the extracted amplitude with its total uncertainty, the significance of A, and a χ2 per degree of freedom for the data versus the PYTHIA8.3 prediction. Without these numbers the reader cannot assess whether the angular structure is established at the claimed level, nor whether the agreement with the Standard Model expectation is at the percent or the factor-of-two level.
[§4 and §7; Figures 36–39; §6.2] Both the detector correction and the theory benchmark rely on the same PYTHIA8.3 generator, and the event-selection shape correction of Section 3 is also derived from it; this introduces an element of circularity into the agreement test of Figure 26. The note itself documents a visible failure of the nominal MC to reproduce the impact-parameter distributions (σd0 = 64 µm versus 78 µm in data; Figures 36–39), yet the quantitative impact of this mismodeling on the corrected Q(θ) is covered only by the 0.6–1.6% PYTHIA-versus-KK2f systematic. Please include an explicit propagation of the d0/z0 mismodeling (for example, reweighting the MC to the data d0 distribution and repeating the correction chain, or quoting the sensitivity of the fake and misidentification rates to the IP-resolution difference), or justify numerically why the random-drop track-efficiency systematic already covers it.

Minor objections (7)

[§1] The sentence beginning 'A detailed study of the DELPHI Open Data A detailed study of the DELPHI Open Data, including measurements of event-shape observables, is presented in Ref. [39]' contains a duplicated phrase; the repetition should be deleted.
[Throughout] Minus signs and electron symbols repeatedly appear as placeholder boxes ('□') in captions and plot labels, for example 'e+e□', 'f□ − f+', '⟨N□⟩', 'Data□MC residual', and 'q □ 0' (Figures 8, 14, 15, 21, 36–39, and related); this is likely a character-encoding problem and should be fixed in the production files.
[References] The bibliography is incomplete in places: Ref. [2] lacks publication details, Ref. [4] is missing its journal and volume information, and Ref. [57] repeats 'Ph.D. thesis'.
[Figure 18] The caption of Figure 18 labels the injected MC samples as 'data'; please relabel them as 'injected MC' to avoid confusion with the actual data.
[§2] Section 2 introduces Qa, Q(θ), N±(θ), and Ntot(θ) in quick succession; a short notation summary, or an explicit statement that all of these are per-event densities per unit polar angle, would help the reader follow Eqs. (2.3)–(2.6).
[Tables 4 and 5] The per-source entries in Tables 4 and 5 are stated to be non-additive because the charge-conservation constraint is applied per source; a footnote giving the naive quadrature sum of individual entries would help readers see why the total differs from that sum.
[Appendix E] The loosened-impact-parameter cross-check (Figure 61) concludes that a residual difference from the prediction remains but does not quantify it; quoting the largest bin deviation or a χ2 value would make the consistency claim checkable.

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The paper

The paper claims

This paper reports the first measurement of the one-point charge correlator, the angular flux of electric charge in hadronic final states, using DELPHI Open Data from the $Z$ pole, and finds the corrected data exhibit the $\sin(2\theta)$…

The reading

This paper reports the first measurement of the one-point charge correlator, the angular flux of electric charge in hadronic final states, defined through the charge flux operator $Q(\vec n)$ and measured in data as $Q(\theta)=N^+(\theta)-N^-(\theta)$, the difference of positive- and negative-track densities per unit polar angle. Using DELPHI Open Data collected at the $Z$ pole ($\sqrt{s}=91.2$ GeV, 1994–1995), the analysis corrects for track reconstruction efficiency with simulation and for residual data–MC charge-misreconstruction asymmetries with a tag-and-probe measurement in $Z\to\tau^+\tau^-$ decays. The fully corrected correlator, for tracks with $p_T>2$ GeV in $20^\circ\le\theta\le160^\circ$, exhibits a clear $\sin(2\theta)$ modulation consistent with the parity-violating hadronic charge flow that the chiral structure of the $Z$ couplings imprints on the final state, and it agrees with the PYTHIA8.3 generator-level prediction over the full angular range. If this holds, it is the first measurement of the charge flux operator in hadronic final states and a demonstration that such charge-flux observables are experimentally feasible with archival $e^+e^-$ data rather than a precision test of the Standard Model.

What carries the argument

The central object is the charge flux operator $Q(\vec n)=\lim_{r\to\infty} r^2\int_0^\infty dt\, n^i J_i^Q(t,r\vec n)$ of conformal field theory, together with its binned, experimentally accessible form $Q(\theta)=N^+(\theta)-N^-(\theta)$. The argument leans on a symmetry of the Born-level cross section: because the charge flux is built from a conserved current, the parity-even $(1+\cos^2\theta)$ term cancels in $Q(\theta)$, leaving only the parity-odd $\cos\theta$ structure, which the $\sin\theta$ Jacobian of the angular measure converts into the characteristic $\sin(2\theta)$ modulation. The measurement is carried by a two-stage correction: a simulation-based efficiency and fake-rate correction, followed by a data-driven correction for the residual data–MC charge-misreconstruction asymmetry, $Q_{\rm corr}=[Q_{\rm eff}-\delta_{\rm asym}(\theta)N_{\rm tot}(\theta)]/[1-\delta_{\rm sum}(\theta)]$, where $\delta_{\rm asym}$ is measured by tag-and-probe in $Z\to\tau^+\tau^-$ decays and is amplified by the large total track yield $N_{\rm tot}$. Finally, a global charge-conservation constraint, which fixes the angular integral of the true correlator to zero, is imposed to bound the correlated systematic shifts.

Extended reading notes

Core claim

On the paper's own terms, the discovery is that the angular flux of electric charge in hadronic $Z$ decay has been measured for the first time and behaves as the parity-violating Standard Model predicts. The corrected one-point charge correlator $Q(\theta)$ is negative in the forward hemisphere and positive in the backward hemisphere, crosses zero at $\theta=90^\circ$, and has the $\sin(2\theta)$ shape that the parity-odd $\cos\theta$ term of the Born-level $Z$ cross section acquires when converted into a polar-angle density. Its sign and size match the flavor-weighted combination $\sum_q R_q Q_q A_{FB}^q$, in which down-type quark contributions dominate. The result is presented as establishing experimental viability rather than as a precision electroweak measurement: the data agree with PYTHIA8.3 within the evaluated uncertainties, the total systematic uncertainty exceeds the statistical one, and a precision extraction of the forward–backward asymmetry is explicitly deferred.

Load-bearing premise

The load-bearing premise is that the residual data–MC difference in the charge-misreconstruction asymmetry measured in the pion-dominated $Z\to\tau^+\tau^-$ control sample equals, after reweighting by the hadronic $p_T$ spectrum, the corresponding residual in the inclusive hadronic sample; this transfer is supported only by simulation truth studies and a bias-injection closure test that leaves a residual non-closure of about 5%, with no data-based cross-check provided.

Editorial extensions

If this is right

The one-point charge correlator becomes an experimentally measured observable: the corrected data resolve the hadronic parity-violating charge flow as a function of polar angle for the first time.
The sign of the $\sin(2\theta)$ modulation confirms that down-type quark contributions dominate the flavor-weighted sum $\sum_q R_q Q_q A_{FB}^q$ at the $Z$ pole.
A precision extraction of the electroweak forward–backward asymmetry is not yet possible with this dataset, because the systematic uncertainty (about 28–36% in representative bins) exceeds the statistical one and is set by the statistics of the $\tau$ control sample.
The two data-taking years, 1994 and 1995, are corrected independently and agree within uncertainties, demonstrating that the data-driven correction reproduces across detector configurations.
The feasibility demonstration opens a program of charge-flux measurements in archival $e^+e^-$ data, including energy-weighted charge correlators, identified-hadron correlators, and the two-point charge correlator.

Reading between the lines

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

My inference: if the transfer assumption holds, the same approach could be applied to the other archived LEP datasets, where independent detector calibrations would supply the data-based cross-check the present analysis lacks and would test whether the residual charge asymmetry is detector-universal.
My inference: a confirmed charge-flux measurement would supply a jet-free and event-axis-free channel to the weak mixing angle, complementary to the classic LEP and SLC jet-charge results, and would be a natural $Z$-pole observable for a future high-luminosity $e^+e^-$ collider.
My inference: the paper shows no hadronic self-correction can constrain the parity-odd component of the detector bias because it has the same angular structure as the signal; the only route to a precision measurement is dedicated detector-level calibration (sagitta, material budget, TPC distortions) applied to the Open Data reconstruction chain.
My inference: the reconstructed-MC charge imbalance the paper attributes to a possible TPC distortion calibration applied to data but not to simulation is itself testable; rerunning both samples with matched TPC calibrations should remove or confirm that imbalance, and doing so could shrink the dominant systematic.

Original abstract

We present the first measurement of the one-point charge correlator, the angular flux of electric charge in hadronic final states, using DELPHI Open Data collected at LEP-1 at $\sqrt{s} = 91.2$~GeV during 1994 and 1995. The data, corrected for detector effects, exhibit a clear $\sin(2\theta)$ modulation, consistent with the parity-violating hadronic charge flow that the chiral structure of the $Z$ couplings imprints on the final state. The measurement demonstrates the experimental feasibility of the observable and establishes strategies for controlling associated detector effects, thereby motivating a new program to measure charge-flux observables. This note documents the experimental details supporting the companion experimental paper and the joint theory--experiment Letter.

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-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,741 input tokens.

What the abstract itself states, as probabilities: claims first 0.97 · states limitation 0.30 · human participants 0.02 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.12 · compares with prior results 0.09 · mentions code or data availability 0.22.

The abstract, sentence by sentence

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

We present the first measurement of the one-point charge correlator, the angular flux of electric charge in hadronic final states, using DELPHI Open Data collected at LEP-1 at $\sqrt{s} = 91.2$~GeV during 1994 and 1995. The data, corrected for detector effects, exhibit a clear $\sin(2\theta)$ modulation, consistent with the parity-violating hadronic charge flow that the chiral structure of the $Z$ couplings imprints on the final state. The measurement demonstrates the experimental feasibility of the observable and establishes strategies for controlling associated detector effects, thereby motivating a new program to measure charge-flux observables. This note documents the experimental details supporting the companion experimental paper and the joint theory--experiment Letter.

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 present the first measurement of the one-point charge correlator, the angular flux of electric charge in hadronic final states, using DELPHI Open Data collected at LEP-1 at $\sqrt{s} = 91.2$~GeV during 1994 and 1995.	contribution 0.99	0.96	0.20	asserted 1.00
s1	The data, corrected for detector effects, exhibit a clear $\sin(2\theta)$ modulation, consistent with the parity-violating hadronic charge flow that the chiral structure of the $Z$ couplings imprints on the final state.	result 0.85	0.91	0.41	asserted 0.57
s2	The measurement demonstrates the experimental feasibility of the observable and establishes strategies for controlling associated detector effects, thereby motivating a new program to measure charge-flux observables.	future work 0.65	0.91	0.52	asserted 1.00
s3	This note documents the experimental details supporting the companion experimental paper and the joint theory--experiment Letter.	contribution 0.56	0.24	0.03	asserted 0.96

What kind of paper the classifier reports this is: empirical study 0.99 · evidence from analysis of existing data 0.88.

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sources read

arXiv listing abstract v1

not examined

full text
figures and tables
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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

References

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What this paper does with the arXiv papers it cites

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

The measurement demonstrates the experimental feasibility of the observable and establishes strategies for controlling associated detector effects, paving the way for a new program of charge-flux measurements, both in archival $e^+e^-$ data and at future colliders.

First measurement of the one-point charge correlator in $e^+e^-$ collisions at $\sqrt{s} = 91.2$ GeV with DELPHI Open Data · 0.96

What it cites · 17 sentences without a confident label

Uses the method or tool of 6 papers

The primary MC samples used for correction are generated with PYTHIA 8.3 [ref] with the Monash Tune [ref] , processed through the full DELPHI detector simulation using DELSIM [ref] .

Tuning PYTHIA 8.1: the Monash 2013 Tune · Detector, datasets, simulations, and selections · 1.00
The primary MC samples used for correction are generated with PYTHIA 8.3 [ref] with the Monash Tune [ref] , processed through the full DELPHI detector simulation using DELSIM [ref] .

A comprehensive guide to the physics and usage of PYTHIA 8.3 · Detector, datasets, simulations, and selections · 1.00
The baseline track and event selections follow those established in Refs. [ref] and utilized in Ref. [ref] .

Determination of A_{FB}^b at the Z pole using inclusive charge reconstruction and lifetime tagging · Detector, datasets, simulations, and selections · 1.00

Cites as background 15 papers

Similar to the Feynman-Field definition, charge correlators with an energy weight were introduced in [ref] , and measured in [ref] .

Energy Correlators Taking Charge · Introduction · 0.82
Similar to the Feynman-Field definition, charge correlators with an energy weight were introduced in [ref] , and measured in [ref] .

Joint Track Functions: Expanding the Space of Calculable Correlations at Colliders · Introduction · 0.82
Similar to the Feynman-Field definition, charge correlators with an energy weight were introduced in [ref] , and measured in [ref] .

Probing jet evolution with charged energy correlators in small systems · Introduction · 0.82

Discussion

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