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Improved determination of the $\beta$-$\overline{\nu}_e$ angular correlation coefficient $a$ in free neutron decay with the $a$SPECT spectrometer

T0 review · 2 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A 100-day measurement of the proton recoil spectrum in free neutron decay fixes the beta-neutrino angular correlation at -0.10430(84), the most precise value to date.

desk verdict A genuinely new and unusually careful neutron a-coefficient measurement that probably stands, with the main residual worry being the 30 mV work-function transfer uncertainty and the global fit's error scaling. read the letter →

arxiv 1908.04785 v2 pith:YTJCZPN4 submitted 2019-08-13 nucl-ex

M. Beck , F. Ayala Guardia , S. Bae{ss}ler , M. Borg , F. Glück , W. Heil , J. Kahlenberg , M. Klopf
show 10 more authors
G. Konrad R. Maisonobe R. Muñoz Horta C. Schmidt U. Schmidt M. Simson T. Soldner R. Virot A. Wunderle O. Zimmer
This is my paper · ORCID
classification nucl-ex PACS 23.40.-s
keywords neutronbetadecaybeta-neutrinoangularcorrelationacoefficientaxial-vectortovectorcouplingratioMAC-EfilterspectrometerprotonrecoilspectrumStandardModeltestsystematicuncertaintybudget
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Free neutron $\beta$ decay is a direct probe of the charged weak interaction, and its $\beta$-neutrino angular correlation coefficient $a$ determines the ratio of axial-vector to vector weak couplings. This paper reports a measurement of $a$ from the proton recoil spectrum recorded by the aSPECT spectrometer during a 100-day run, giving $a = -0.10430(84)$, a relative precision of $0.8\%$ that improves on the previous world average by a factor of 3.3. From this value the paper derives $|\lambda| = 1.2677(28)$, where $\lambda = g_A/g_V$. The result is consistent with the world average from earlier measurements but disagrees at the 2.8-$\sigma$ level with the most precise $\beta$-asymmetry determination of $\lambda$, an unresolved tension that matters for tests of the Standard Model and for the extraction of $V_{ud}$ from neutron decay.

What carries the argument

The load-bearing object is the MAC-E (magnetic adiabatic collimation with electrostatic filter) spectrometer: decay protons are guided along a magnetic field from a high-field decay volume to a low-field analyzing plane, where an applied retardation voltage $U_{AP}$ acts as a high-pass filter on their longitudinal kinetic energy. The transmission function $F_{\mathrm{tr}}(T,\langle U_A\rangle,\langle r_B\rangle)$ depends on the proton kinetic energy $T$, the average effective retardation voltage $\langle U_A\rangle$, and the average magnetic field ratio $\langle r_B\rangle = B_A/B_0$, so the measured integral count-rate spectrum is a convolution of the theoretical recoil spectrum with this filter. The paper determines $\langle r_B\rangle$ from NMR-validated field simulations and $\langle U_A\rangle$ from work-function maps of the electrode surfaces obtained with a scanning vibrating-capacitor probe, then folds all known systematic effects into a global chi-square fit in which $a$ is one common parameter across detector pads and configurations.

What would settle it

Take a second 100-day dataset with in-situ measurement of the decay-volume/analyzing-plane work-function difference, or with electrode surfaces characterized immediately before and after under the same cold ultra-high-vacuum conditions; if the extracted $a$ moves by more than 0.00084 relative to this run, the 30 mV offset assumption underlying the quoted uncertainty is falsified.

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Extended reading notes

Core claim

The central discovery is a precise value of the $\beta$-neutrino angular correlation coefficient in free neutron decay, $a = -0.10430(84)$, obtained from the shape of the integral recoil-energy spectrum of protons detected in $4\pi$ by a MAC-E filter spectrometer. Using the standard-model relation $a = (1-|\lambda|^2)/(1+3|\lambda|^2)$, the paper obtains $|\lambda| = 1.2677(28)$. The new $a$ agrees with the previous world average of $-0.1059(28)$ but is 3.3 times more precise, and the derived $\lambda$ disagrees with the most precise $\beta$-asymmetry-based value at about 2.8 standard deviations, indicating a possible systematic difference between the two measurement routes.

Load-bearing premise

The result leans on the assumption that the effective retarding voltage felt by the protons can be reconstructed from electrode work-function maps measured after the run with a 30 mV offset allowance; if the surfaces' work functions drifted during the 100-day run, $a$ would shift by about 1\% per 80 mV of unaccounted change.

Editorial extensions

If this is right

  • The beta-neutrino correlation $a$ is now known to 0.8\%, an improvement by a factor of 3.3 over the previous world average, so the Standard-Model prediction can be tested at correspondingly sharper resolution.
  • The derived $|\lambda| = 1.2677(28)$ gives an independent determination of the axial-vector to vector coupling ratio that does not share the beta-asymmetry systematics.
  • Combined with the neutron lifetime, the new $\lambda$ enters the expression for $|V_{ud}|$, feeding the most direct neutron-decay test of CKM unitarity.
  • The 2.8-sigma difference with the beta-asymmetry route means current neutron-decay data do not agree on a single $\lambda$; further measurements at comparable precision are needed to decide whether the discrepancy is a real physics effect or an unaccounted systematic.
  • The paper's upgrade analysis indicates the same technique could reach approximately 0.2\% in $a$ with better work-function control, a larger detector area, and improved beam collimation.

Reading between the lines

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

  • If the 2.8-sigma tension is real rather than a systematic, a combined fit of $a$, the beta-asymmetry $A$, and the neutron lifetime would favor new scalar or tensor contributions; this is a consequence the paper motivates but does not carry out.
  • The load-bearing 30 mV offset for $\langle U_A\rangle$ could be tested directly by an in-situ work-function monitor, or by re-measuring the electrode surfaces immediately before and after a future production run under the same cold, ultra-high-vacuum conditions.
  • The consistency of the edge-effect loss ratio with a simple analytic expression suggests that deliberately shaping the beam profile, not merely collimating it, could turn the edge effect from a 0.15\% correction into a negligible one.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. The paper reports a new measurement of the beta-antineutrino angular correlation coefficient a in free neutron decay using the aSPECT MAC-E filter spectrometer at the ILL PF1b beam line. The analysis is based on a 100-day production run in 2013, in which integral proton recoil spectra were recorded at several retardation voltages and in several detector/configuration setups. The central value is extracted from a global chi-square fit that simultaneously constrains systematic effects with auxiliary measurements and particle-tracking simulations. The authors obtain a = -0.10430(84), which they state is the most precise measurement of the neutron a coefficient to date, and derive |lambda| = 1.2677(28). The result is consistent with the previous PDG value and disagrees with the PERKEO III lambda determination at about 2.8 sigma.

Significance. If the quoted uncertainty is credible, this is a substantial experimental advance: it improves the world knowledge of the neutron a coefficient by roughly a factor of 3.3 and provides an independent constraint on lambda that is complementary to beta-asymmetry measurements. The paper is strong in its detailed systematic accounting: it includes particle-tracking simulations with about 1e10 tracked protons, KEMField/COMSOL cross-checks, proton-NMR field measurements, Kelvin-probe work-function scans, and cross-checks among seven measurement configurations. It also validates the global-fit likelihood with both profiling and MCMC methods and openly discusses the limitations of the work-function transferability. The main risk to the central claim is not the experimental methodology per se but whether the quoted total uncertainty of 0.00084 is robust, given the poor global fit quality and the load-bearing assumption on the effective retardation voltage <UA>.

major comments (2)
  1. [§IV C and Appendix A, Table VI]
  2. [§V, Eqs. (13) and (43), Table VIII]
minor comments (5)
  1. [§III C, Eq. (11)] The notation for the systematic functions f_sys and g_sys is dense and the distinction between fpar and gpar is not always transparent; a table listing each systematic effect, its auxiliary data, and the corresponding polynomial coefficients would improve readability.
  2. [§V, Fig. 28] The exclusion of config 2b is justified by two concrete technical reasons, but the decision is made after inspecting the ideogram. A sentence stating that config 2b was designed as a diagnostic rather than a production configuration, and a statement of the selection criterion before the final fit, would clarify the procedure.
  3. [Appendix D] The text says the classical and Bayesian approaches agree within 2% statistical error; it would be useful to state explicitly whether the comparison is on the central value or on the width of the PDF of a.
  4. [Appendix A, Fig. 34] The caption of Fig. 34 does not state the temperature at which the vacuum Kelvin-probe test was performed; this is relevant because the run conditions are cold UHV conditions, and the temperature should be clearly reported.
  5. [Throughout] There are a number of typographical and notation inconsistencies, e.g., 'Marcov chain' in Appendix D, the title uses beta-nu_e while the text uses beta-nu_e, and some axis labels in Figs. 35 and 36 are incomplete. These do not affect the physics but should be corrected in the final version.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the reported a is a free parameter of a global fit constrained by independent data and simulations.

full rationale

The central value a = -0.10430(84) is obtained as a free fit parameter in a global chi-square minimization (Eqs. (12)-(13)) against measured integral proton count rates. The theoretical recoil spectrum comes from an independent published calculation (Glück, Phys. Rev. D 47, 2840 (1993)), and the main systematic corrections are anchored to separate measurements and simulations: NMR field maps for the magnetic field ratio, Kelvin-probe work-function scans for the retardation-voltage correction, SRIM-based detector response calculations for backscattering and below-threshold losses, and particle-tracking simulations for the edge effect and trapped-proton losses. None of the equations inserts the final a into its own determination; the normalized spectrum in Eq. (8) depends on the fit parameter a, not on the reported result. The reference value a_ref = -0.103 is used only for diagnostic sensitivity studies in Table VII and not as a constraint in the final Global-a fit, which leaves a free and yields a value consistent with, but more precise than, the PDG average. The identified weakness - transferring Kelvin-probe work-function maps measured under ambient conditions after the 2013 run to cold UHV conditions, contributing the 30 mV offset uncertainty in Table VI and Appendix A - is an external-validity or systematic-uncertainty concern, not a circular reduction, because no measured value of a enters the work-function or field simulations. Self-citations to earlier aSPECT papers for the MAC-E filter transmission function and the KASPER simulation framework are normal internal references; the load-bearing physics is independently established or cross-checked against COMSOL and NMR measurements.

Assumptions & free parameters 10 free parameters · 5 assumptions · 0 invented entities

The central claim rests on standard weak interaction theory, the theoretical proton recoil spectrum from Ref. [55], the assumed adiabaticity of the MAC-E filter, and the transferability of post-run Kelvin probe work function measurements to the in-situ UHV conditions. No new particles or forces are introduced. The global fit contains 68 free parameters, most of which describe detector and field systematics and are constrained by auxiliary measurements and simulations. The main free result is a.

free parameters (10)
  • a = -0.10430(84)
    Central angular correlation coefficient extracted from the global chi-square fit.
  • N0 per configuration and pad = Not tabulated individually
    Count rate normalization amplitude of the integral proton spectrum; free fit parameter in Eqs. (6)-(8).
  • c_bg, constant background per configuration and pad = Fit result; cbg approximately 6 cps at 780 V
    Retardation-voltage-independent background offset in the proton region.
  • c_0^rB, offset = Offset prior sigma = 4.8e-6; fit results in Table IV
    Common offset uncertainty in the magnetic field ratio <rB>, from beam position and field mapping, constrained by a Gaussian prior.
  • c_0^UA, c_1^UA = Fit results from global fit, shown as lines in Fig. 14
    Linear model for the deviation <UA> - UAP of the effective retardation voltage.
  • c_bg^0, c_bg^2, R = Fit results for config 1; R = 0.9(1)
    Voltage-dependent background model for config 1, with conversion factor R from the background build-up model.
  • c_ee^0, c_ee^2, c_ee^4 = Fit results from global fit, Fig. 20
    Polynomial coefficients describing edge effect losses for standard and reduced beam profiles.
  • c_blt^0, c_blt^4 = Fit results from global fit, Fig. 22
    Below-threshold proton detection losses as a function of UAP.
  • c_p^0, c_p^2 = Fit results from global fit, Fig. 25
    Pile-up loss rate as a function of the proton count rate.
  • c_tr^{-2}, c_tr^1 = Fit results from global fit, Fig. 26
    Trapped proton loss in the decay volume as a function of UAP.
assumptions (5)
  • domain assumption Standard Model V-A interaction with Fierz interference b = 0
    Eqs. (1) and (2) assume the Standard Model form and neglect scalar and tensor currents when converting a to lambda. A nonzero b would change the extraction.
  • standard math Proton recoil spectrum of Ref. [55], including recoil, Coulomb and order-alpha radiative corrections, is accurate to 0.1%
    Used in the fit function Eqs. (6) and (8) as the theoretical input omega_p(T,a).
  • domain assumption Proton motion through the MAC-E filter is adiabatic to better than 4e-4
    Assumed in the transmission function Eq. (4); the paper cites tracking simulations from Ref. [2] and uses a lower E8 voltage to improve adiabaticity.
  • ad hoc to paper Work function maps measured after the 2013 run under ambient conditions are representative of the in-situ work functions during the run, with a 30 mV offset uncertainty
    Used to compute <UA> in the DV and AP electrodes (Appendix A, Table VI). The transferability to UHV and cold bore conditions is estimated at 10 meV, not directly measured during the run.
  • domain assumption Neutron beam polarization is negligible for the 4pi configurations used in the final fit
    Section V notes that in 4pi detection, the spin-dependent term in Eq. (42) vanishes; only config 2b (2pi) requires polarization knowledge, which is why it is excluded.

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Pith. "Pith review of Improved determination of the $\beta$-$\overline{\nu}_e$ angular correlation coefficient $a$ in free neutron decay with the $a$SPECT spectrometer." pith.science (2026). https://pith.science/paper/YTJCZPN4

@misc{pith2026190804785,
  author       = {Pith},
  title        = {Pith review of: Improved determination of the $\beta$-$\overline\nu_e$ angular correlation coefficient $a$ in free neutron decay with the $a$SPECT spectrometer},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YTJCZPN4}},
  note         = {Machine review of arXiv:1908.04785}
}
abstract

We report on a precise measurement of the electron-antineutrino angular correlation ($a$ coefficient) in free neutron beta-decay from the $a$SPECT experiment. The $a$ coefficient is inferred from the recoil energy spectrum of the protons which are detected in 4$\pi$ by the $a$SPECT spectrometer using magnetic adiabatic collimation with an electrostatic filter. Data are presented from a 100 days run at the Institut Laue Langevin in 2013. The sources of systematic errors are considered and included in the final result. We obtain $a = -0.10430(84)$ which is the most precise measurement of the neutron $a$ coefficient to date. From this, the ratio of axial-vector to vector coupling constants is derived giving $|\lambda| = 1.2677(28)$.

Figures

Figures reproduced from arXiv: 1908.04785 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Expected proton recoil spectrum for [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. The main superconducting coils are operated in persis￾tent mode. Additionally, there are two superconducting correction coils in driven mode to create a small mag￾netic field gradient across the DV, as well as a combina￾tion of external air-cooled coils in Helmholtz and Anti￾Helmholtz configuration in the AP region. For more details regarding the magnetic fields and the aSPECT magnet system, see [1, 2, 37, 39]. The … view at source ↗
Figure 3
Figure 3. FIG. 3. The [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (29 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Fields inside [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Photograph of the DV electrode (left) and the main, [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 7
Figure 7. Figure 7: FIG. 7. The SDD with its three detector pads is mounted [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Measurement sequence of the 2013 beam time which [PITH_FULL_IMAGE:figures/full_fig_p009_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Temporal sequence of 50 V runs for config 1. Plotted [PITH_FULL_IMAGE:figures/full_fig_p013_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11. NMR measurements of the magnetic field on axis [PITH_FULL_IMAGE:figures/full_fig_p014_11.png]
Figure 12
Figure 12. Figure 12: FIG. 12. Simulation of the potential distributions along the [PITH_FULL_IMAGE:figures/full_fig_p016_12.png]
Figure 13
Figure 13. Figure 13: FIG. 13. Simulated potential distribution along the z-axis [PITH_FULL_IMAGE:figures/full_fig_p016_13.png]
Figure 15
Figure 15. Figure 15: FIG. 15. Evolution of the background count rate in the proton [PITH_FULL_IMAGE:figures/full_fig_p018_15.png]
Figure 16
Figure 16. Figure 16: FIG. 16. Temporal sequence of a measurement cycle show [PITH_FULL_IMAGE:figures/full_fig_p018_16.png]
Figure 18
Figure 18. Figure 18: FIG. 18. Measured retardation voltage-dependent back [PITH_FULL_IMAGE:figures/full_fig_p019_18.png]
Figure 19
Figure 19. Figure 19: FIG. 19. (a) Radial spread [PITH_FULL_IMAGE:figures/full_fig_p020_19.png]
Figure 20
Figure 20. Figure 20: FIG. 20. Simulation of the retardation voltage dependence of [PITH_FULL_IMAGE:figures/full_fig_p020_20.png]
Figure 6
Figure 6. Figure 6: From that it results: hεi ≈ 0.94 · |dI/dy| L · hIi · [PITH_FULL_IMAGE:figures/full_fig_p020_6.png]
Figure 22
Figure 22. Figure 22: FIG. 22. Fraction of undetected protons of the integral proton [PITH_FULL_IMAGE:figures/full_fig_p022_22.png]
Figure 23
Figure 23. Figure 23: FIG. 23. Example of two individual proton events within one [PITH_FULL_IMAGE:figures/full_fig_p023_23.png]
Figure 25
Figure 25. Figure 25: FIG. 25. Pile up rate [PITH_FULL_IMAGE:figures/full_fig_p024_25.png]
Figure 24
Figure 24. Figure 24: FIG. 24. Quantitative determination of pile up events (blue [PITH_FULL_IMAGE:figures/full_fig_p024_24.png]
Figure 26
Figure 26. Figure 26: FIG. 26. Relative loss [PITH_FULL_IMAGE:figures/full_fig_p025_26.png]
Figure 27
Figure 27. Figure 27: FIG. 27. Ideogram of [PITH_FULL_IMAGE:figures/full_fig_p027_27.png]
Figure 28
Figure 28. Figure 28: Hereby only the data set of the respective con [PITH_FULL_IMAGE:figures/full_fig_p028_28.png]
Figure 28
Figure 28. Figure 28: FIG. 28. Global fit results on [PITH_FULL_IMAGE:figures/full_fig_p029_28.png]
Figure 29
Figure 29. Figure 29: FIG. 29. Linear relationship (correlation) coefficient of [PITH_FULL_IMAGE:figures/full_fig_p030_29.png]
Figure 30
Figure 30. Figure 30: shows the status of λ measurements (in￾cluding our result) in which the distinction is made be￾tween measurements which determine the λ value from the beta-asymmetry A (blue data points), from the β￾νe angular correlation coefficient a (red data points) and from other…
Figure 32
Figure 32. Figure 32: FIG. 32. Distribution of [PITH_FULL_IMAGE:figures/full_fig_p032_32.png]
Figure 33
Figure 33. Figure 33: FIG. 33. Distribution of the WF differences [PITH_FULL_IMAGE:figures/full_fig_p033_33.png]
Figure 34
Figure 34. Figure 34: FIG. 34. Time sequence of line scans showing the extracted [PITH_FULL_IMAGE:figures/full_fig_p034_34.png]
Figure 36
Figure 36. Figure 36: shows the differential spectra ω ∗ p (T, a) and ω ∗ ps(T, a) for a = aref = −0.103 and a = +0.3. As a test of these equations, we computed with Eqs. (C1 - C7) the integrated proton asymmetry αp defined by Eq. (4.27) in Ref. [99], using the λ = −1.26 value. We got αp =…
Figure 37
Figure 37. Figure 37: FIG. 37. PDF of [PITH_FULL_IMAGE:figures/full_fig_p036_37.png]

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