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
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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
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.
The abstract, sentence by sentence
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
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| 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 was examined, and what was not
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- P abstract
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Figures
Figures reproduced from arXiv:hep-ex/0504049 by the authors.
References
How later papers used it
82 later papers cite it
6 later papers by other authors are listed below: 6 used its data or values.
Uses its data or values 6 of 29 papers with this label
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Used this paper's standard model expectation of sin^2θ_W(Q) = 0.2381 at Q^2 = 0.026 GeV^2, along with low-energy values of G_F and α from other work.
Parity nonconservation induced by spacetime geometry (2024) · 1.00 · paraphrased: the licence does not allow quoting
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Incorporated bounds from low-energy parity-violating asymmetry measurements, including inelastic electron scattering at SLAC E158 from this paper.
Consistent constraints on the Standard Model Effective Field Theory (2015) · 1.00 · paraphrased: the licence does not allow quoting
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Considered observables from three measurements, including Møller scattering from this paper, atomic parity violation, and eN DIS.
Global Analysis of General SU(2) x SU(2) x U(1) Models with Precision Data (2010) · 0.99 · paraphrased: the licence does not allow quoting
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Replaced Λ/√(|g^2_RR-g^2_LL|) by √(|s-M^2_X_i|)/|g^11_i| at low scales to find 90% CL constraints for the E158 experiment of this paper and for MOLLER.
LIght scalars with lepton number to solve the $(g-2)_e$ anomaly (2019) · 0.84 · paraphrased: the licence does not allow quoting
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Likewise, at energies near $m_Z$ and higher the weak angle is taken as $s_W^2≈0.231$ in accordance with results from LHCb $pp$ collisions [ref] , and as $s_W^2≈0.239$ otherwise [ref] .
Production of Magic States via $Z$ Bosons and Dark Photons (2026) · Magic production in EW theory · 0.99
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Included already determined constraints from SLAC in this paper, along with atomic parity violation in Cesium and anticipated QWeak bounds.
Disentangling SMEFT operators with future low-energy PVES experiments (2021) · 0.90 · paraphrased: the licence does not allow quoting
How the literature uses it
74 arXiv papers cite this in 95 sentences
Papers citing it · 47 sentences without a confident label
Uses its data or values 24 papers
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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
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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
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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
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Such a measurement would constitute more than a factor of five improvement in fractional precision over the only other measurement of the same quantity by the E158 experiment at SLAC [ref] .
The MOLLER Experiment: An Ultra-Precise Measurement of the Weak Mixing Angle Using M{\o}ller Scattering · Executive Summary · 0.94
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This is about six standard deviations away from the experimental result [ref] , $Q_W^e = 0.041(5)$.
Tests of non-standard electroweak couplings of right-handed quarks · Parity violation in $e^-e^-$ (Møller) scattering · 0.90
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Other measurements are presented, from APV [ref] , elastic electron-proton scattering (Q$_weak$) [ref] , Moller scattering (SLAC E158) [ref] , electron-deuteron deep inelastic scattering (eDIS) [ref] , neutrino-electron scattering (XENONnT) [ref] , CE$ν$NS from spallation neutron source (COHERENT CsI & LAr) [ref] and from solar neutrinos (PANDAX-4T & XENONnT) [ref] .
Exploring the Standard Model and Beyond from the Evidence of CE$\nu$NS with Reactor Antineutrinos in CONUS+ · The Weak Mixing Angle · 0.88
Cites it as background 9 papers
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Over the decades, $θ_W$ has been measured by many different experiments across various energy scales using different physical processes, such as atomic parity violation (APV) [ref] , electron-deuteron deep inelastic scattering (eDIS) [ref] , polarized Møller scattering (by SLAC E158) [ref] , elastic electron-proton scattering (by Q$_weak$) [ref] , and neutrino scattering (by COHERENT [ref] , Dresden-II [ref] ).
First constraint on the weak mixing angle using direct detection experiments · Introduction · 0.93
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The parity-violating asymmetry $A_PV$ and polarization asymmetry $A_LR$ in t (and u)-channel topology e.g. $e^-e^- →e^-e^-$ (Møller scattering) and $e^- p→e^- p$ determine $s_W^2$ at $≃𝒪(10^2∼4)MeV$ [ref] .
Determining Weak-Mixing Angle at $\mu$TRISTAN · Introduction · 0.89
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For example, Refs. [ref]
Unparticle Searches Through Low Energy Parity Violating Asymmetry · Introduction · 0.93
Discussion
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