Measurement of the neutron $\beta$-asymmetry parameter $A_0$ with ultracold neutrons

We present a detailed report of a measurement of the neutron $\beta$-asymmetry parameter $A_0$, the parity-violating angular correlation between the neutron spin and the decay electron momentum, performed with polarized ultracold neutrons (UCN). UCN were extracted from a pulsed spallation solid deuterium source and polarized via transport through a 7-T magnetic field. The polarized UCN were then transported through an adiabatic-fast-passage spin-flipper field region, prior to storage in a cylindrical decay volume situated within a 1-T $2\times 2\pi$ solenoidal spectrometer. The asymmetry was extracted from measurements of the decay electrons in multiwire proportional chamber and plastic scintillator detector packages located on both ends of the spectrometer. From an analysis of data acquired during runs in 2008 and 2009, we report $A_0=-0.11966\pm 0.{00089}_{-0.00140}^{+0.00123}$, from which we extract a value for the ratio of the weak axial-vector and vector coupling constants of the nucleon, $\lambda =g_A/g_V=-1.27590\pm 0.{00239}_{-0.00377}^{+0.00331}$. Complete details of the analysis are presented.

Figure 1

Results from measurements of the $\beta$-asymmetry parameter $A_0$ [38, 39, 40, 41, 42, 43, 44, 45, 46]. The band ($\pm 1\sigma$) indicates the current world average value of $A_0=-0.11846\pm 0.00104$.

Figure 2

Schematic diagram (not to scale) of the primary components of the UCNA Experiment's $\beta$-asymmetry measurement. (a) Layout of the 7.0-T polarizing magnet and AFP spin-flipper, the 1.0-T spectrometer, the decay trap, and the electron detectors. (b) Layout of the UCN source, biological shielding, and UCN transport guides, and the locations of the UCN gate valve, UCN switcher, all of the magnets, and all of the UCN monitor detectors. All of these components are described in detail later in the text. [Note that during our data-taking runs in 2009, the (bare) Cu UCN guides located between the spin-flipper and the entrance to the decay trap [as depicted in panel (a)] were replaced with diamondlike carbon-coated Cu guides; see Sec. 4b for details.]

Figure 3

Schematic diagram (not to scale) of the MWPC and plastic scintillator electron detector package.

Figure 4

Measured SCS field profile during 2008 (circles) and 2009 (squares). The two data sets have been offset for purposes of clarity. The coordinate system is such that the 300-cm long decay trap is centered at $z=0$.

Figure 5

Simplified schematic diagram of the data acquisition event trigger logic.

Figure 6

Arrival time spectra from the switcher UCN monitor detector [panels (a) and (c)] and the SCS monitor detector [inset panel (b)] characteristic of depolarization trapping [DT, panel (a)] and reloaded background [(R), panel (c)] measurements. (The start time $t=0$ corresponds to the start of the load interval or, conceptually, 200 s prior to the end of a $\beta$-decay run.) The states of the gate valve, switcher, and the spin flipper during the load, clean, and unload intervals are indicated schematically. (With the switcher in the “down” state, UCN located between the switcher and the decay trap are transported to the switcher UCN monitor detector; in the opposite state, UCN are transported from the SD${}_2$ source to the electron spectrometer.) The timing and states depicted here are for the case of spin-flipper-off loading. Flipper-on loading measurements reverse the state of the spin flipper.

Figure 7

Schematic diagram of the various event types defined in the text.

Figure 8

Typical scintillator twofold PMT trigger rates during the 0.2 Hz proton pulse repetition cycle. For the clock timing shown here, each of the five beam bursts constituting each proton pulse occur at $t=0$, as the clock was reset to $t=0$ with each beam burst; thus, under this reset scheme, all of the events collected during the five beam bursts appear between 0 and 0.05 s (as noted in Sec. 3b, the time between beam bursts was 0.05 s). The dashed line indicates the cut at 0.05 s.

Figure 9

Typical twofold coincidence trigger relative time-of-flight spectrum for one of the scintillator detectors from a $\beta$-decay run. See text for details.

Figure 10

Typical MWPC anode (a) and summed cathode (b) pulse height spectra from a $\beta$-decay run. The dashed lines indicate the cut positions. The peak in the anode spectrum at channel $\sim 2250$ is overflow. Because the cathode sum is obtained via summation over all of the individual cathode channels, channel overflows are distributed throughout the summed spectrum.

Figure 11

Typical scintillator spectrum for a background run, without (light shaded) and with (dark shaded) the requirement of a MWPC coincidence cut. See the text for a description of the features in the resulting coincidence spectrum.

Figure 12

Distributions of $(x,y)$ position distributions [for the coordinate system choice (4) described in the text] for type 0 neutron $\beta$-decay events from (a) the east detector, and (b) the west detector. The dashed circles denote the nominal 45-mm fiducial volume radius cut. The regularly-spaced “spikes” are an artifact of the position reconstruction algorithm; for events in which two adjacent cathode channels recorded overflow values, the algorithm reconstructed the positions to sharp peaks halfway between the two wires' positions (as discussed in Sec. 5f1).

Figure 13

Calibrated $E_{\text{vis}}$ visible energy spectra (data points with error bars), compared with Monte Carlo calculations (solid lines), for three of the calibration sources: (a) ${}^{139}$Ce, (b) ${}^{113}$Sn, and (c) ${}^{207}$Bi.

Figure 14

Two examples of PMT linearity curves for (a) a PMT exhibiting a nearly linear response, and (b) a PMT exhibiting a highly nonlinear response. The curves are fits to the measured QADC values (horizontal axis) of the peaks for the various calibration sources at different $(x,y)$ positions versus the expected light reaching each PMT. The large nonlinearity observed in some of the PMTs was traced to damaged bases and subsequently repaired for runs after 2009.

Figure 15

Example of a $\eta (x,y)$ light-transport efficiency map for a single PMT, nominally viewing the $(x<0,y>0)$ quadrant of the scintillator disk. By convention, $\eta (0,0)=1$.

Figure 16

Extracted energy response for one of the detectors in photoelectrons per MeV as a function of $(x,y)$ position extracted from (a) one PMT, and (b) the statistically weighted combined response from all four PMTs, thus demonstrating the combined response exhibits a smoother response as a function of the $(x,y)$ position.

Figure 17

The vertical axes appearing at the locations of the expected (i.e., as calculated with Monte Carlo methods) visible energies (on the horizontal axis) for the various calibration sources show histograms of errors (in keV) in the measured visible energies. The dashed lines then show our conservative estimate of an “error envelope” of the total energy calibration uncertainty based on the widths of the error distributions.

Figure 18

Individual PMT trigger efficiencies ${\epsilon }_i$ for the four PMTs (indicated by the different colors) on one of the detectors, as extracted from an analysis of geometry C data.

Figure 19

Baseline calibrated primary MWPC energy spectra for type 0 neutron $\beta$-decay events from geometry B (solid line) compared with Monte Carlo calculations (dotted line). The histograms are normalized to unity.

Figure 20

Calibrated primary and secondary MWPC energy spectra for type 1 and type 2/3 neutron $\beta$-decay events from geometry B compared with Monte Carlo calculations (data: solid lines; Monte Carlo: dotted lines). (a) Primary MWPC energy spectrum for type 1 events, (b) primary MWPC energy spectrum for type 2/3 events, (c) secondary MWPC energy spectrum for type 1 events, and (d) secondary MWPC energy spectrum for type 2/3 events. The histograms are normalized to unity.

Figure 21

$(x,y)$ position maps of the two (west and east) MWPCs' anode PADC channel numbers that correspond to a given calibrated energy (in this case, 4.14 keV).

Figure 22

Efficiency for the identification of charged particle events by the MWPC detectors (for a fixed PADC channel number cut) plotted as a function of the measured MWPC energy deposition. The non-step-function behavior of these efficiency curves is a result of the MWPCs' position-dependent response. Typical results for the east (red circles) and west (blue triangles) detectors from geometries B and D are shown in the left and right panels, respectively.

Figure 23

Reconstructions of $E_{\text{recon}}$ values according to the fit 1 (solid) and fit 2 (dashed) parametrizations for ${}^{113}$Sn source calibration type 0 events from Monte Carlo (thin lines) and experimental data (thick lines). The histograms are normalized to unity.

Figure 24

(a) Monte Carlo calculations of the energy deposition in the primary MWPC for type 2 and type 3 neutron $\beta$-decay events. The histograms are normalized to unity. (b) Monte Carlo calculations of the probability an event identified in data analysis as a type 2/3 event was a type 2 event as a function of the energy deposition in the primary MWPC. The dashed lines indicate the threshold cut of $E_{\text{MWPC}}>4.14$ keV for the assignment of the initial direction to the triggering-scintillator side in analysis choices 3 and 8 for the separation of type 2/3 events. The solid line is a fit to the calculations of the form $\text{Prob}\left(E_{\text{MWPC}}\right)=-p_0\text{erf}(p_1{E}_{\text{MWPC}}-p_2)+p_3$, where $\text{erf}$ denotes the error function and the $p_i$ are fit parameters. This likelihood function was employed for the separation of type 2/3 events in analysis choices 5 and 9.

Figure 25

Comparison between data (red triangles) and Monte Carlo results (filled squares) for primary MWPC energy spectra for geometry A type 2 and type 3 events, after separation of type 2/3 events in data analysis according to the likelihood function Prob($E_{\text{MWPC}}$).

Figure 26

Comparisons of visible energy spectra for the different event types (type 0, type 1, type 2, and type 3 events) extracted from data (black squares) and Monte Carlo (red triangles) for the geometry C configuration. The same selection rules for the event types were applied to both data and Monte Carlo results. See text for details. All error bars shown are statistical; if not visible, the errors are smaller than the marker size.

Figure 27

Fractional residuals for the comparisons between the data and Monte Carlo visible energy spectra for the different event types (type 0, type 1, type 2, and type 3 events) shown in Fig. 26. As can be seen in Fig. 26, there are very few type 2 and type 3 events with visible energies greater than $\sim 500$ keV.

Figure 28

Example of a Kurie fit to the (background-subtracted) reconstructed energy $E_{\text{recon}}$ spectrum for a $\sim 1$-h long $\beta$-decay run. The errors shown are statistical.

Figure 29

Distributions of fitted endpoints for the two detectors, (a) east detector and (b) west detector, averaged over geometries and spin states. The histogram contents were weighted by the inverse square of their uncertainties.

Figure 30

Extracted values for the (blinded) measured asymmetries, $A_{\text{meas}}$, from the geometry B data set obtained under analysis choice 3 for (a) spin-state run pairings, (b) quartet run pairings, and (c) octet run pairings.

Figure 31

Comparison of the scaling of the (blinded) measured asymmetries extracted from the data, $A_{\text{meas}}$, and the Monte-Carlo-calculated asymmetries (from both geant4 and penelope) with the analysis choice for each of the geometries A, B, C, and D. The asymmetries shown here were integrated over an energy window of 225–675 keV. The results from the Monte Carlo calculations were scaled for each geometry in order to match the data at analysis choice 3. All errors are statistical, with the geant4 statistical errors smaller than the symbol size.

Figure 32

Results for the measured background $E_{\text{recon}}$ energy spectra (open circles) and the background-subtracted neutron $\beta$-decay $E_{\text{recon}}$ energy spectra (filled circles) for each of the geometries A, B, C, and D. The spectra shown here were summed over both detectors and then averaged over the two neutron spin states. The resulting measured asymmetries $A_{\text{meas}}$ (filled red squares; see vertical scale on the right) are shown as a function of $E_{\text{recon}}$ for each of the geometries. These are compared with the Monte Carlo calculated values for the measured asymmetries (solid red lines). The energy dependence of the measured asymmetries is primarily due to the $\beta \cos \theta$ dependence of the measured asymmetries [see Eq. (8)]; there are also $\langle \beta \cos \theta \rangle$ acceptance and backscattering effects (e.g., compare geometry B). All errors are statistical.

Figure 33

Results from geant4 Monte Carlo calculations of the energy dependence of the relative sizes of the ${\Delta }_2$ backscattering (thin solid line) and ${\Delta }_3$ angle effect (thick dashed line) systematic corrections for each of the geometries A, B, C, and D. The energy dependence of the relative size of the combined correction $(1+{\Delta }_2)(1+{\Delta }_3)$ is then shown as the thick solid line. The systematic uncertainties in these calculations are discussed in detail later in Sec. 8l.

Figure 34

Results from geant4 Monte Carlo calculations of the relative sizes of the individual ${\Delta }_{2,0}$ (thin solid line), ${\Delta }_{2,1}$ (thick solid line), and ${\Delta }_{2,2}$ (thick dashed line) contributions to the total ${\Delta }_2$ backscattering systematic correction for each of the geometries A, B, C, and D. The systematic uncertainties in these calculations are discussed in detail later in Sec. 8l. [The ${\Delta }_{2,1}$ backscattering correction is non-zero because some small fraction of events will initially backscatter from the decay trap end-cap foils, and then undergo type 1 backscattering (however, the reconstructed initial direction will then be incorrect). The probability for this type of event increases with decreasing energy, and thus the acceptance for this type of events was suppressed in geometries A and B (i.e., thicker MWPC windows).]

Figure 35

Energy dependence of the Standard Model recoil-order correction (calculated according to the formalism of Refs. [21, 22]) for an extraction of $A_0$ from the measured asymmetry $A_3$.

Figure 36

Results for the asymmetries $A_1$ (open circles), $A_2$ (open squares), $A_3$ (filled circles), and $A_0$ (filled squares) for each of the geometries, integrated over the analysis energy window of 275–625 keV. All errors are statistical.

Figure 37

Results for $A_0$ values extracted bin-by-bin from each of the geometries A, B, C, and D. The solid red lines indicate the analysis energy window of 275–625 keV. The quoted errors are statistical.

Figure 38

Schematic diagram of the “beta-blocker” measurement of neutron-generated backgrounds. The dashed lines are meant to indicate the solid angle for production of Compton-scattered electrons in the acrylic at the two different positions.

Figure 39

Results from geant4 Monte Carlo calculations of the relative size of the combined ${\Delta }_2$ backscattering and ${\Delta }_3$ angle effect fractional systematic correction (thick solid lines) and the total fractional systematic uncertainty assigned to these corrections (gray bands) for each of the geometries A, B, C, and D.

Figure 40

(a) Final results for the measured background $E_{\text{recon}}$ energy spectrum (open circles) and the background-subtracted neutron $\beta$-decay $E_{\text{recon}}$ energy spectrum (filled circles) summed over both detectors, averaged over the two neutron spin states, and then averaged over all four geometries. The Monte Carlo prediction for the $E_{\text{recon}}$ spectrum is shown as the solid line. (b) Final results for $A_0$ extracted bin by bin and then averaged over all four geometries. The solid red line indicates the analysis energy window of 275–625 keV. The quoted error is statistical.

Figure 41

Ideogram of values for $g_A/g_V$ extracted from measurements of the neutron $\beta$-asymmetry parameter $A_0$ (this work [39], filled red square; all other measurements of $A_0$ [40, 42, 44, 47], open red squares), a simultaneous measurement of $A_0$ and $B_0$ (black triangle [75]), the current average value of $g_A/g_V=-1.2726\pm 0.0024$ from these measurements (gray band; note that the current 2012 Particle Data Group average value for $g_A/g_V$ has not yet incorporated the result of Ref. [47]), measurements of the neutron lifetime ${\tau }_n$ (blue circles [76, 77, 78, 79, 80, 81, 82]) assuming the superallowed $0^{+}\to 0^{+}$ value for $V_{ud}$ [35], and the current 2012 Particle Data Group average value for the neutron lifetime of $880.1\pm 1.1$ s [34] (between dashed lines).