Measurement of the neutron decay electron-antineutrino angular correlation by the aCORN experiment

The aCORN experiment measures the neutron-decay electron-antineutrino correlation ($a$ coefficient) using a novel method based on an asymmetry in proton time-of-flight for events where the beta electron and recoil proton are detected in delayed coincidence. We report the data analysis and result from the second run at the NIST Center for Neutron Research, using the high-flux cold neutron beam on the new NG-C neutron guide end position: $a=-0.10758\pm 0.00136\left(\text{stat}\right)\pm 0.00148\left(\text{sys}\right)$. This is consistent within uncertainties with the result from the first aCORN run on the NG-6 cold neutron beam. Combining the two aCORN runs, we obtain $a=-0.10782\pm 0.00124\left(\text{stat}\right)\pm 0.00133\left(\text{sys}\right)$, which has an overall relative standard uncertainty of 1.7%. The corresponding result for the ratio of weak coupling constants $\lambda =G_A/G_V$ is $\lambda =-1.2796\pm 0.0062$.

Figure 1

A summary of experimental constraints on the nucleon weak coupling constants $G_A$ and $G_V$. The purple band is the PDG 2020 [6] recommended value for $\lambda$ from neutron-decay parameters $A$ and $a$, including a scale factor of $\sqrt{{\chi }_{\nu }^2}=2.6$ to account for poor agreement among experiments. The green (no scale factor) and blue (scale factor $\sqrt{{\chi }_{\nu }^2}=1.5$) bands are derived from the neutron lifetime averages for the beam and UCN storage experiments. The brown vertical band shows $G_V$ from superallowed beta decay [10] and the dashed lines indicate the shift due to the calculation of ${\mathrm{\Delta }}_R$ by Seng et al. [11]. The red vertical band shows the CKM matrix unitarity condition using the PDG recommended value of $V_{us}$ [6].

Figure 2

An illustration of the aCORN experimental method. Top: A neutron source, shown as a point source here, lies on axis between a set of proton and electron detectors. A uniform axial magnetic field $\vec{B}$ is present throughout. Electron and proton collimators act to limit the transverse momenta of detected electrons and protons from neutron decay. An electrostatic mirror produces an approximately uniform electric field $\vec{E}$ in the decay region that accelerates and directs all protons toward the proton detector, but beta electrons in the energy range of interest must be emitted into the right hemisphere to be detected. Middle: A momentum space plot showing the cylindrical momentum acceptances of electrons and protons. Bottom: A momentum space construction of the acceptance for antineutrinos from neutron decay, when the detected electron momentum was $\overrightarrow{p_e}$ as shown and the proton was also detected. Conservation of energy and momentum restricts the antineutrino momentum to the shaded regions I and II which have equal solid angle from the source. Region I is correlated with $\overrightarrow{p_e}$ and region II is anticorrelated, so the asymmetry in events associated with each region measures the $a$ coefficient.

Figure 3

A Monte Carlo simulation of aCORN data, proton TOF vs. beta energy for coincidence events. The fast proton branch (group I) is associated with neutron decays where the antineutrino momentum was in region I in Fig. 2. The slow proton branch (group II) is associated with decays where the antineutrino momentum was in region II. The sums $N^I$ and $N^{II}$ are used to compute the wishbone asymmetry for each beta-energy slice.

Figure 4

The dimensionless geometric function $f_a\left(E\right)$, computed numerically from the aCORN geometry and a 36.4-mT uniform magnetic field [see Eqs. (8) and (9)].

Figure 5

A cross-section view of the aCORN tower showing the arrangement of major components. The neutron beam passes through from right to left.

Figure 6

An overhead view of the proton detector assembly showing the positions of the surface barrier detector and focusing electrodes.

Figure 7

An interior cross-section view of the backscatter-suppressed beta spectrometer. Dimensions are in mm.

Figure 8

The redesigned upper end of the electrostatic mirror used in the NG-C run, showing the new square mesh grid and larger open diameter.

Figure 9

The axial (a) and transverse (b) magnetic fields measured by the robotic field mapper on axis. The June 2015 maps were made after reversing and trimming the field. The December 2015 maps were made just prior to the next field reversal. The difference shows typical drift over six months with unchanged trim coil settings. Gray shaded regions in the bottom plot indicate the $<4-\mu \mathrm{T}$ target for the transverse field in the electrostatic mirror and proton collimator.

Figure 10

The transverse field map measured 5.1 cm off axis using the robotic field mapper. At each $z$ position the field is measured at ${30}^{\circ }$ intervals as the mapper rotates. The result is Fourier decomposed into a $cos\theta$ component that gives the uniform transverse field and a $cos2\theta$ that corresponds to a transverse gradient.

Figure 11

A summary of optical insert alignment checks made over the course of the run. Multiple points are independent measurements made by two people.

Figure 12

A typical proton energy singles spectrum. The peak on the right is protons. The noise/background forms a peak on the left due to the soft energy threshold of the PIXIE. The shaded region is the applied proton energy window.

Figure 13

A typical raw wishbone obtained from approximately 100 hours of reduced data, using the proton energy cut shown in Fig. 12.

Figure 14

(a) A 20-keV wide wishbone slice centered at beta energy 100 keV (blue, higher), and the same wishbone slice after subtracting background (green, lower). (b) The same background subtracted slice fit to a horizontal line, excluding the neutron-decay region (3–$4.6\mu \mathrm{s}$). Error bars are statistical.

Figure 15

(a) A 20-keV wide wishbone slice centered at beta energy 380 keV (blue, higher), and the same wishbone slice after subtracting background (green, lower). (b) The same background subtracted slice fit to a horizontal line, excluding the neutron-decay region (3–$4.6\mu \mathrm{s}$). Error bars are statistical.

Figure 16

The 20-keV wide wishbone slices centered at (a) 100 and (b) 380 keV for a data series where the polarity of the electrostatic mirror was reversed, so neutron-decay protons could not be detected. The upper curve (blue) is the raw wishbone and the lower curve (green) is after subtracting background and fitting to a horizontal line. Error bars are statistical.

Figure 17

A background-subtracted wishbone plot (data from Fig. 13). Blue points are positive and red are negative.

Figure 18

(a) The wishbone energy spectrum, i.e., the background subtracted wishbone (Fig. 17) summed over proton TOF and the best fit theoretical spectrum. (b) Fit residuals (data minus fit). Error bars are statistical.

Figure 19

The estimated systematic uncertainty in computing the wishbone asymmetry $X\left(E\right)$ from the data, compared to the Poisson statistical uncertainty.

Figure 20

The wishbone asymmetry $X\left(E\right)$ for the combined $B_{\mathrm{up}}$ data, uncorrected with statistical error bars, and with all corrections.

Figure 21

A COMSOL finite element map of the transverse electric field inside the NG-C electrostatic mirror, in the region near the upper wire grid through which the protons pass.

Figure 22

The electrostatic mirror correction calculated by proton transport Monte Carlo using the 3D COMSOL model of the electric field. The red curve is a smoothed average obtained by fitting the Monte Carlo data to a second-order polynomial. Error bars are statistical.

Figure 23

A combined background-subtracted wishbone plot with all $B_{\mathrm{up}}$ data. The event total in the region outlined in green was used to test for the presence of a low-energy tail in the detected electron response function due to electron scattering. The inset shows the same green-outlined region with an expanded color scale. Blue points are positive counts, red points are negative due to the background subtraction.

Figure 24

A typical proton energy spectrum (blue) fit to a fourth-order polynomial background function plus a Gaussian (red). The resulting Gaussian alone is shown in green. The soft energy threshold of the PIXIE-16 takes effect below channel 27. The slight loss of protons below threshold has a negligible effect on the wishbone asymmetry.

Figure 25

(a) The total $B_{\mathrm{up}}$ wishbone proton TOF spectrum summed from 400 to 600 keV compared to the equivalent Monte Carlo proton TOF spectrum. (b) The same plot with an expanded vertical scale and statistical error bars. The $1\mu \mathrm{s}$ wide regions pre- and postwishbone used to estimate the proton scattering tail are shown in green.

Figure 26

Results from a proton focusing simulation tracking 1 million neutron-decay protons from the proton collimator to the detector. Green and red circles are protons striking the focusing ring and detector inactive region, respectively. The thin black circle indicates the active region of the surface barrier detector.

Figure 27

The corrected $B_{\mathrm{up}}$ wishbone asymmetry (see Fig. 20), divided by the geometric function $f_a\left(E\right)$ (see Fig. 4), giving the measured $a$ coefficient for each beta-energy slice. These were fit to a constant to produce the $a$-coefficient result for the $B_{\mathrm{up}}$ data. Error bars are statistical.

Figure 28

(a) The wishbone asymmetry $X\left(E\right)$ for the combined $B_{\mathrm{down}}$ data, uncorrected with statistical error bars, and with all corrections. (b) The corrected $B_{\mathrm{down}}$ wishbone asymmetry, divided by the geometric function $f_a\left(E\right)$, giving the measured $a$ coefficient for each beta-energy slice. These were fit to a constant to produce the $a$-coefficient result for the $B_{\mathrm{down}}$ data. Error bars are statistical.

Figure 29

A summary of neutron $a$-coefficient measurements from the past 50 years.

Figure 30

An ideogram of precision determinations of the neutron-decay ratio of axial vector to vector coupling ($\lambda$) using the beta asymmetry ($A$ coefficient, blue circles), the electron-antineutrino correlation ($a$ coefficient, red open cirles), and the $A/B$ ratio (green triangle). The distribution features two groups of experimental results and the overall agreement is poor. The weighted average is indicated with the uncertainty expanded by a factor of 2.32.