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REVIEW

Precision Measurement of the Weak Mixing Angle in Moller Scattering

High Energy Physics - Experiment · Submitted 26 Apr 2005 · 19 references

Pith's verdict: A solid, well-cross-checked final E158 result; the 6.2σ running claim is a difference of two measured values and does not fold in the theory band on the running itself.

T0 · AI review

How this review was made: An AI referee (selfhosted/deepseek-v4.1-flash) read the paper on October 29, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

  1. T0 AI review An AI read the paper and answered a fixed list of questions.
  2. T1 Audit Automatic checks that the references and files the paper relies on exist and match.
  3. T2 Compute The paper's code or calculations re-run with the same results.
  4. T3 Formal statement The claims written out in a formal math language a computer can read.
  5. T4 Proof Those claims proved, and the proof checked by computer.

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arXiv IDhep-ex/0504049 (version 1)
Pith IDL7IF6PVI, Pith's permanent record of this paper and its review
Citationet al, SLAC E158 Collaboration: P.L. Anthony. "Precision Measurement of the Weak Mixing Angle in Moller Scattering." arXiv:hep-ex/0504049 (2005). https://pith.science/paper/L7IF6PVI
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Referee report
The paper

The paper claims

Electron-electron scattering yields a 17 ppb measurement of the parity-violating asymmetry, giving sin^2 theta_W = 0.2397 at Q^2 = 0.026 GeV^2 and confirming the running of the weak mixing angle at over 6 sigma.

The reading

The weak mixing angle is a fundamental number that sets how the weak and electromagnetic forces mix. The Standard Model predicts it should change with the energy scale at which you measure it, a effect called running. Until this measurement, running had been seen clearly for the electromagnetic and strong couplings but not unambiguously for the weak mixing angle. The E158 experiment at SLAC fired a beam of polarized electrons at a tank of liquid hydrogen and counted how often the electrons scattered off the target electrons differently depending on whether the beam was spinning left or right. That left-right difference, the parity-violating asymmetry, is predicted to be about 320 parts per billion at tree level and is reduced by radiative corrections and the detector acceptance to roughly 130 ppb. The collaboration measured -131 ppb with a total uncertainty near 17 ppb, after correcting for beam jitter, backgrounds from scattering off protons, and beam polarization. From that number they extract the weak mixing angle at low momentum transfer, 0.2397, and compare it to the value measured at the Z boson pole, 0.2315. The two differ by far more than their uncertainties, so the running is seen at over six sigma. Because the measurement is so precise, it also limits possible new heavy particles or contact interactions that would shift the asymmetry, pushing the reach for some new-physics scenarios into the several-TeV range.
Extended reading notes

Core claim

The parity-violating asymmetry in Moller scattering is A_PV = -131 +/- 14 (stat) +/- 10 (syst) ppb, which yields sin^2 theta_W^eff = 0.2397 +/- 0.0010 (stat) +/- 0.0008 (syst) at Q^2 = 0.026 GeV^2, and when combined with the Z-pole value the running of the weak mixing angle is observed with over 6 sigma significance.

Load-bearing premise

The conversion of the measured asymmetry into sin^2 theta_W and into the running claim rests on the background subtraction and dilution model in Table I, especially the inelastic e-(gamma)+p -> e-+X correction of -22 +/- 4 ppb with dilution 0.009, which is about 17% of the signal and is estimated from simulation rather than measured directly. A mis-modeling of this or the elastic ep term (-7 +/- 1 ppb) would shift the extracted angle and hence the significance of the running comparison.

Original abstract

We report on a precision measurement of the parity-violating asymmetry in fixed target electron-electron (Moller) scattering: A_PV = -131 +/- 14 (stat.) +/- 10 (syst.) parts per billion, leading to the determination of the weak mixing angle \sin^2\theta_W^eff = 0.2397 +/- 0.0010 (stat.) +/- 0.0008 (syst.), evaluated at Q^2 = 0.026 GeV^2. Combining this result with the measurements of \sin^2\theta_W^eff at the Z^0 pole, the running of the weak mixing angle is observed with over 6 sigma significance. The measurement sets constraints on new physics effects at the TeV scale.

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, 3,150 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.11 · human participants 0.02 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.99 · compares with prior results 0.95 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We report on a precision measurement of the parity-violating asymmetry in fixed target electron-electron (Moller) scattering: A_PV = -131 +/- 14 (stat.) +/- 10 (syst.) parts per billion, leading to the determination of the weak mixing angle \sin^2\theta_W^eff = 0.2397 +/- 0.0010 (stat.) +/- 0.0008 (syst.), evaluated at Q^2 = 0.026 GeV^2. Combining this result with the measurements of \sin^2\theta_W^eff at the Z^0 pole, the running of the weak mixing angle is observed with over 6 sigma significance. The measurement sets constraints on new physics effects at the TeV scale.

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 We report on a precision measurement of the parity-violating asymmetry in fixed target electron-electron (Moller) scattering: A_PV = -131 +/- 14 (stat.) +/- 10 (syst.) parts per billion, leading to the determination of the weak mixing angle \sin^2\theta_W^eff = 0.2397 +/- 0.0010 (stat.) +/- 0.0008 (syst.), evaluated at Q^2 = 0.026 GeV^2. result 1.00 0.98 0.87 asserted 1.00
s1 Combining this result with the measurements of \sin^2\theta_W^eff at the Z^0 pole, the running of the weak mixing angle is observed with over 6 sigma significance. result 0.51 0.84 0.24 asserted 1.00
s2 The measurement sets constraints on new physics effects at the TeV scale. interpretation 0.98 0.83 0.11 asserted 0.98

What kind of paper the classifier reports this is: empirical study 1.00 · evidence from observation or experiment 1.00.

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
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. shows Aphys for all data, divided into 75 se￾quential samples in Runs I, II (2002), and III (2003). Each Aphys measurement has sign reversals depending on the beam energy and the state of the half-wave plate. AP V is obtained by correcting each result by the appro￾priate sign. The combined result is AP V = −131 ± 14 (stat.) ± 10 (syst.) ppb . TABLE I: Corrections ∆Ai and dilutions fi to Araw and as￾sociated systematic uncertainties. Source ∆A (ppb) f Beam (first order) −10 ± 1 Beam (higher order) 0 ± 3 Transverse polarization −4 ± 2 e − + p → e − + p(+γ) −7 ± 1 0.056 ± 0.007 e −(γ)…
Figure 2. FIG. 2: Predicted variation [18] of sin

Figures reproduced from arXiv:hep-ex/0504049 by the authors.

References
How later papers used it

82 later papers cite it

Evidence: substantial. 82 of the citing papers share no author with it, and 37 of those carry a confident label from Pith's citation classifier.

Pith read 28 of the 106 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 6 of 29 papers with this label
How the literature uses it

74 arXiv papers cite this in 95 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 · 47 sentences without a confident label

Uses its data or values 24 papers
  • According to the latest report given by the E158 Collaboration, Ref. [ref] , the combined result for the parity-violating asymmetry is

    Unparticle Searches Through Low Energy Parity Violating Asymmetry · Results and Discussions · 1.00

  • Moreover, the parity-violating Møller scattering measured at SLAC E158 [ref] has been enforced, which requires $|C_e,V C_e,A| ≲10^-8$ for $M_Z' ≃17$ MeV [ref] , together with the constraints from the anomalous magnetic moment of the electron and the muon [ref] .

    Explanation of the Beryllium Anomaly in a $U(1)'$-Extended 2-Higgs Doublet Model · The Beryllium anomaly in a $U(1)'$-2HDM · 0.93

  • The $A_LR$ asymmetry has been measured at low $Q^2 = 0.026$ GeV$^2$ in the SLAC–E158 experiment [ref] , with the result [equation] leading to a determination of the weak mixing angle of $sin^2 θ_W^eff = 0.2403 ±0.0013$ [ref] , which is $1.25σ$ higher than the SM prediction [ref] , $sin^2 θ^eff_W = 0.23867$.

    Alternative $Z'$ Bosons in $E_6$ · Low Energy Constraints on $E_6$ · 0.93

Compares with it 8 papers
Cites it as background 9 papers

Discussion

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