New result for the neutron $\beta$-asymmetry parameter $A_0$ from UCNA

Background: The neutron $\beta$-decay asymmetry parameter $A_0$ defines the angular correlation between the spin of the neutron and the momentum of the emitted electron. Values for $A_0$ permit an extraction of the ratio of the weak axial-vector to vector coupling constants, $\lambda \equiv g_A/g_V$, which under assumption of the conserved vector current hypothesis ($g_V=1$) determines $g_A$. Precise values for $g_A$ are important as a benchmark for lattice QCD calculations and as a test of the standard model.

Purpose: The UCNA experiment, carried out at the Ultracold Neutron (UCN) source at the Los Alamos Neutron Science Center, was the first measurement of any neutron $\beta$-decay angular correlation performed with UCN. This article reports the most precise result for $A_0$ obtained to date from the UCNA experiment, as a result of higher statistics and reduced key systematic uncertainties, including from the neutron polarization and the characterization of the electron detector response.

Methods: UCN produced via the downscattering of moderated spallation neutrons in a solid deuterium crystal were polarized via transport through a 7 T polarizing magnet and a spin flipper, which permitted selection of either spin state. The UCN were then contained within a 3-m long cylindrical decay volume, situated along the central axis of a superconducting 1 T solenoidal spectrometer. With the neutron spins then oriented parallel or anti-parallel to the solenoidal field, an asymmetry in the numbers of emitted decay electrons detected in two electron detector packages located on both ends of the spectrometer permitted an extraction of $A_0$.

Results: The UCNA experiment reports a new 0.67% precision result for $A_0$ of $A_0=-0.12054{\left(44\right)}_{\mathrm{stat}}{\left(68\right)}_{\mathrm{syst}}$, which yields $\lambda =g_A/g_V=-1.2783\left(22\right)$. Combination with the previous UCNA result and accounting for correlated systematic uncertainties produces $A_0=-0.12015{\left(34\right)}_{\mathrm{stat}}{\left(63\right)}_{\mathrm{syst}}$ and $\lambda =g_A/g_V=-1.2772\left(20\right)$.

Conclusions: This new result for $A_0$ and $g_A/g_V$ from the UCNA experiment has provided confirmation of the shift in values for $g_A/g_V$ that has emerged in the published results from more recent experiments, which are in striking disagreement with the results from older experiments. Individual systematic corrections to the asymmetries in older experiments (published prior to 2002) were $>10$%, whereas those in the more recent ones (published after 2002) have been of the scale of $<2$%. The impact of these older results on the global average will be minimized should future measurements of $A_0$ reach the 0.1% level of precision with central values near the most recent results.

Figure 1

Schematic of the UCNA experimental apparatus. The external muon veto and “backing veto” are not pictured.

Figure 2

Top: Electron energy spectrum from 2011–2013 with background-subtracted data (open circles), geant4 Monte Carlo (solid line), and background (solid circles) included. Residuals between Monte Carlo and data (units of mHz/keV) are below. Bottom: Fully corrected asymmetry as a function of energy for the two separate run periods. The fit is over 190–740 keV, as determined via minimization of the total uncertainty. The errors on the indicated fitted values are purely statistical.

Figure 3

Plot of energy uncertainty vs. reconstructed energy. The points plotted are the mean and $\sigma$ of the residual distributions from reconstructed calibration peaks of Ce, Sn, and the lower and upper Bi peaks in that order. The bands represent the energy uncertainty at any given electron energy for the two data sets.

Figure 4

Total Monte Carlo corrections vs. energy, where ${\mathrm{\Delta }}_{\mathrm{backscatter}}$ and ${\mathrm{\Delta }}_{cos\theta }$ have been combined. The correction has been averaged over 50 keV increments for plotting purposes, while the correction is actually applied on a 10 keV bin basis. The uncertainty band reflects the effective statistical fluctuations on a bin-by-bin basis, as well as the true Monte Carlo statistical uncertainty and the uncertainty on the correction as determined by spectral agreement between data and simulation for each event type.

Figure 5

Corrected and uncorrected asymmetries for various combinations of event types. Only ${\mathrm{\Delta }}_{\mathrm{backscattering}}$ and ${\mathrm{\Delta }}_{cos\theta }$ are applied and error bars are statistical only. The first three combinations include Type 0 events which are identified as having not backscattered and make up roughly $95\%$ of the data. The remaining four asymmetries include only the various backscattering events. The inset shows a closer view of the first three points whose error bars are smaller than the markers in the larger plot. Top: 2011–2012. Bottom: 2012–2013.

Figure 6

Status of $V_{\mathrm{ud}}$, the neutron lifetime, and $\lambda$ measurements. The $\lambda$ result bands (vertical) are divided into pre-2002 [40, 41, 42] and post-2002 [18, 44, 45, 46] results, where the distinction is made using the date of the most recent result from each experiment. The right axis shows publication year for the individual lambda measurements included in the calculation of the $\lambda$ bands (closed markers for post-2002, open markers for pre-2002). Note that the result of this work (Brown et al.) is the combined UCNA result from [18] and the current analysis, and the Mund et al. result is the combined PERKEO II result from [43, 44]. The diagonal bands are derived from neutron lifetime measurements and are separated into neutron beam [31, 32] and UCN bottle experiments, which consist of material bottle storage [34, 35, 36, 37, 38] and magnetic bottle storage [33]. The $V_{\mathrm{ud}}$ band (horizontal) comes from superallowed $0^{+}\to 0^{+}$ nuclear $\beta$-decay measurements [39]. The error bands include scale factors as prescribed by the Particle Data Group [39].

Figure 7

Switcher signal as a function of time, during “D”-type runs: (1) the shutter closes and the switcher state changes, permitting UCN in the guide outside the decay volume to drain to the switcher UCN detector, (2) the AFP spin-flipper changes state, allowing depolarized neutrons in the guides outside the decay volume to drain to the switcher, (3) the shutter opens, permitting depolarized neutrons within the decay volume to drain to the switcher detector, (4) the AFP spin-flipper returns to its initial state, allowing the initially loaded spin state to drain from the decay volume, (5) backgrounds are measured after the UCN population in the decay volume has drained away. The presented data were taken in 2011 and UCN loaded into the decay volume with the spin-flipper off.