Introduction
The Neutron
The quarks are bound together by the strong force to make up the neutron. We highlight the contrast between the neutron and the proton, both of which are called "nucleons".
Ultracold Neutrons
- Definition
- Properties
- Production
In fact, the proton is the lightest baryon which implies that the free proton is a stable particle (assuming conservation of Baryon number). This is called superthermal production - when UCNs are produced out of thermal equilibrium with the production material and is conceptually the same as the method in LANL.
Neutron Beta Decay
- The Weak Interaction in the Neutron
- Neutron Beta Decay and Correlation Coefficients
- The Asymmetry Term, 𝐴
- The Fierz Interference Term, 𝑏
- The Neutron Lifetime, 𝜏
The mediators of the weak interaction (𝑊± and𝑍) are enormous and have a mass given by [Gri08]. In the low momentum limit (𝑄 𝑚𝑊), the propagator term of the decay can be approximated as.
Neutron Electric Dipole Moments
- nEDM Experiments: Past, Present, Projected
- Beyond Standard Model Searches
- CP Violation
- Baryon Asymmetry
In this section, we discuss the sequence of data collection in the operation of the UCNA experiment. Remember that our tolerances when assembling the magnet were approx.
The UCNA experiment
Overview of Experiment
The UCNA experiment in Area B at LANL was part of the Los Alamos Neutron Science Center (LANSCE). At the end of the 2013 data collection, the UCNA experiment completed its final run.
UCN Polarization and Transport: From Source to Experiment
- UCN Production at LANL
- Exiting the UCN Source Volume
- Gate Valve and Pre-Polarizing Magnet
- Switcher for UCN Measurements
- Neutron Polarization
The purpose of the gate valve is to separate the UCNA apparatus volume from the source volume while the proton beam is on (and therefore produce UCNs). This asymmetry exists along the magnetic moment of the neutron and the resulting direction of the 𝛽 decay electron.
The UCNA Spectrometer
- Decay Trap
- Multi-Wire Proportional Chamber (MWPC)
- Plastic Scintillator
- Magnetic Field
- Calibration Sources
- Xenon Mapping
- Supplemental Components
On the east and west sides of the decay trap, thin foils are designed to contain the neutrons in the central volume (while allowing 𝛽 decay electrons to pass). This magnetic field was 1𝑇 in magnitude and oriented along the axis of the decay trap.
Data-Taking Runs
- Event Types
- Octet Structure
This is a key functionality of the simulation used in the analyzes described in Chapters 4 and 5. The position of the particles can be extracted from the information tracked in the GEANT4 geometry.
UCNA Simulations
GEANT4: A Particle Tracking Software Package
In this work, the main application of the GEANT4 simulation was to recreate an accurate representation of the UCNA apparatus and track the decay electrons inside the apparatus. The results of the GEANT4 simulation and the PENELOPE simulation were compared with each other and were consistent.
ROOT: A Data Analysis Software Package
The relevant properties of the particle change based on what physics processes occur, secondary particles are created and tracked, and the primary particle moves to the next step in the simulated volume. At Caltech, the main effort (and expertise) was on the GEANT4 simulation, and therefore the GEANT4 simulation was retained and used in this work.
The UCNA Apparatus in Simulation
- Detector Construction Class
- Decay Trap
- Wirechamber (MWPC)
- Plastic Scintillators
- Detector Package Frame
- E&M Fields
- Physics List Class
- Primary Generator Action Class
- Initial Kinematics Generation
- Particle Tracking Classes
- Run Action
- Event Action
- Tracker
The multiwire proportional chamber (MWPC) used in the UCNA experiment was discussed in Section 2.3.2. The calibration was generated separately in the asymmetry analysis [Bro18] and ultimately this component of the simulation was not used. In the original run of the simulation, only the first term on the right was accessible.
Within the GEANT4 simulation, the best grain resolution in the simulation comes from the TrackerHit class and the TrackerSD class.
Post-Processing: Applying the Detector Response Model
- Position Map Corrections
- Finite PMT Resolution
- Energy Calibration Distortions
- Trigger Function
- Creating a Reconstructed Energy
Here we provide a brief overview of the various effects considered in the detector response model. Another effect that the detector response model applies to the simulation output is the smearing of the energy resolution due to the finite resolution of the PMT in the hardware. This produces eight quenched energies, one for each PMT in the UCNA apparatus, smeared by the effects of PMT resolution and position map.
This results in a weighted average of the quenched energy deposited in the East and West detectors respectively.
Motivation for Using Simulation
- Event Types Identification
- Energy and Timing Spectra Reconstruction
Polynomial variations were chosen due to the polynomial nature of the energy nonlinearity in the PMTs used in the experiment (Hamamatsu R7725 PMTs with custom bases, more details in [Hic13]). However, the distribution of the 𝑏 values was not the dominant source of uncertainty in the spectral extraction. Thus, in the spectral extraction of the Fierz interference in section 4.2 we did not separately account for these energy-dependent effects.
Time spectra are overlaid for events generated in the center of the UCNA decay trap (green) and uniformly populated throughout the decay trap (black).
UCNA: Fierz Interference Analysis
The Fierz Interference Term
- UCNA Sensitivity to Fierz
Due to the nature of the asymmetry measurement, UCNA has recorded several important kinematic observables that allow a direct extraction of a Fierz interference term—in particular, a robust energy measurement of the neutron𝛽 decay electron spectrum that is directly related to 𝑏 compared 1.12. As an overview, the spectral extraction involves fitting an energy spectrum to identify a small energy distortion of the form 𝑚𝐸𝑒𝑒, while the asymmetry extraction involves fitting the 𝐴. 0, fits over our energy window in the asymmetry analysis and it is a simple matter to introduce an energy dependence of the form for non-zero𝑏 to the fit.
0 coefficient with uncertainties (mainly statistical, as we will see in section 4.3) as a function of energy, provided by the asymmetry analysis.
The Spectral Extraction Method
- The Super-Sum Spectrum
- Motivation and Definition
- Fitting the Energy Spectra
- Blinding the Spectral Extraction
- Dominant Systematic Uncertainty: Energy Calibration
- Calibration Variation Selection Procedure
- Other Systematic Effects
- Background Subtraction
- Energy Resolution
- Backscattering
- Detector Inefficiency
- Other Spectral Systematic Studies
- End Point Correction Studies
- LED Studies
- Summary of Spectral Extraction Method
In the procedure in the previous section, we discussed applying energy calibration variations to the processed event energy to study the effects of the energy calibration uncertainty (interchangeably called the error envelope). This is the estimate of the systematic uncertainty in 𝑏due to the energy calibration uncertainty and it is the dominant source of uncertainty in the spectral extraction method as we will see in later sections. In some cases the spread was narrower than the value of the error envelope at the calibration source peak.
In this section, we quantitatively describe and investigate some other sources of potential systematic errors in the spectral extraction of the Fierz interference term.
The Asymmetry Extraction Method
- The Asymmetry Definition
- Constructing an Asymmetry
- Asymmetry with Fierz Interference
- Blinding the Asymmetry Extraction
- The Fierz Interference from Asymmetry Extraction
- Statistical Uncertainty
- Systematic Studies
- Energy Response Systematic Uncertainty
- Electron Backscattering
- cos 𝜃
- Background Subtraction
- Detector Trigger Efficiency
- Energy Resolution
- Inner Bremsstrahlung
- Summary of Asymmetry Extraction Method
We highlight the bias and spread as estimators of the error associated with the energy calibration variations on asymmetry extraction of Fierz interference. We remind the reader of the form of the asymmetry due to a non-zero𝑏, Equation 4.23. In the asymmetry analysis, however, these dispersion effects are persistent to the final asymmetry and actually constitute a large part of the systematic error budget (see error decomposition in [Pla+19]).
A summary of the statistical and systematic errors from the Fierz interference asymmetry derivation can be found in Table 4.2.
Combining the Extraction Methods
- Energy Fit Window Study
- Position Fit Window Study
- Discussion on Unblinding Criteria
- Weighted Averages
We kept either the super-sum or super-ratio fitting windows fixed and first varied the low-energy threshold of the other data set, for the 2011–2012 and 2012–2013 data sets. Due to the uncertainty induced by the Fierz extraction asymmetry statistics, these figures only show the robustness of the fit with respect to different choices of energy regions. An additional study in the combination of Fierz's derived interference results was the dependence of the position on the face of the scintillator and how it contributed to the systematic error.
However, during the position dependence studies, it was decided to primarily use the asymmetry-extracted Fierz interference.
Results and Discussion
Our results provide constraints on a direct measurement of the neutron dark matter decay channel in equation 5.9. One of the decay channels in the theory was the neutron in dark matter plus a positron-electron pair. The specific design of the 𝐵0 magnet coil is further optimized for the specifications of the nEDM@SNS experiment.
We then applied fixed offsets to the size of the ROMER handle tip (a 6 mm diameter ruby ball was attached to the tip of the ROMER handle to ensure that it would always contact the surface perpendicularly).
UCNA: Dark Matter Decay Analysis
The Neutron Lifetime Anomaly
- The Neutron Lifetime
- Experimental Methods: Bottle Experiments
- Experimental Methods: Beam Experiments
- The Anomaly
We then present two classes of experiments that have different central values of the neutron lifetime. Historically, there have been two categories of experiments aimed at measuring neutron lifetimes. Bottle experiments measuring neutron lifetimes can be understood simply from a conceptual point of view.
More details on the extraction of neutron lifetimes from beam measurements can be found in the latest results publication [Yue+13], and updates on the follow-up experiment can be found in [Hoo+19].
A Dark Matter Decay Channel
Other early universe elemental abundance calculations are based on the 4𝐻 𝑒 abundance given in equation 5.4 and thus the neutron lifetime and associated uncertainty enter these estimates explicitly (see [Ioc+09] for a review of these abundance calculations). With the neutron mass as𝑚𝑛=939.565 𝑀 𝑒𝑉, the electron and positron masses as 𝑚𝑒+/𝑒− =0.511 𝑀 𝑒𝑉, and the mass constraints of 5.7 available in equation 5.7. . In equation 5.13, we only measure the Γ𝛽−𝑑𝑒 𝑐𝑎 𝑦 in beam experiments, while in bottle experiments we would measure Γ𝑡 𝑜𝑡 𝑎𝑙.
Thus, through this analysis, we attempt to place limits on the branching ratio of equation 5.9 with an overarching eye toward a 1% branching ratio.
UCNA Analysis of Dark Matter Decay
- Overview of UCNA Sensitivity to Decay
- Event Classification
- Coincidence Time Calibration
- The TDC Data
- Simulations of the Timing Spectrum
- Discussion on Background Subtraction
- Detection Efficiency Estimates
- Kinematic Acceptance
- Timing Window Acceptance
- Trigger Function Efficiency
- Electron-Positron Detector Response
- Final Total Acceptance
We ultimately chose not to use any of the 2011–2012 data set in the dark matter decay analysis because of this unreliability in the timing data. This is because the conversion factor is set in the electronics so that the center of the STP can be converted to a physically relevant time. We set the center of STP to 140𝑛𝑠, which corresponded to 44 𝑝 𝑠/𝑐 ℎ as in the above wire length discussion.
However, in the course of the asymmetry analysis, a global driving function is derived in units of the reconstructed energy.
UCNA Extracted Limits
- Bin Aliasing Study
- Look-Elsewhere Effect Correction
- Final Exclusion Limits
- Discussion
This correction is applied to the cumulative distribution function (CDF) of the single-bin confidence levels. This electric dipole moment of the neutron is what the nEDM@SNS experiment aims to measure. The coordinate axes are defined relative to the position of the ROMER arm base mounted on the UVT.
After installation, the ROMER arm was mounted on the UVT, calibrated, and used to measure the inner radius of the gage plates.
The Neutron Electric Dipole Moment
- Overview of nEDM@SNS Experiment
- Introduction
- Experimental Highlights
- Two Complementary Measurements
0magnet as a component of the nEDM@SNS apparatus and provide further details in later sections of this chapter. To achieve the sensitivities of the previously described targets, nEDM@SNS has made considerable efforts to reduce the predicted systematic uncertainty below that of the statistical uncertainty. 0 is the zero-order Bessel function of the first kind, and the index 𝑖 ends with 𝑛,3 for the neutron and 3𝐻 𝑒respectively.
In other words, the rate of change of the angle between the neutron and.
The 𝐵
- Constructing the 𝐵
- UVT: A Vacuum Lamination Table
- Inner Core Hoops
- Lead End Caps (LECs)
- Superior Lead End Caps (SLECs)
- Boss Rings
- Story Sticks
- Stiffening Gussets
- Wire Tensioners
- Final Assembly of 𝐵
- Covid-19 Considerations
- Testing the Assembly Components
- The ROMER Arm
- Calibrating the ROMER Arm
- UVT Surface Measurements
- Gauge Plates Inner Circumference Measurements . 169
- Liquid Nitrogen Cold Tests
- Testing the 𝐵
- Room Temperature Field Measurements
- Results and Comparison to Free Space Model
This was because the positional tolerances on the SLECs are more forgiving than the magnet's other components. In Figure 6.11b we highlight the arrangement of the wire tensions and note that this is characteristic of a cos𝜃 magnet coil. There was a small ring holder mounted in the center of the UVT which would allow the ROMER to connect to the UVT.
We couldn't trust that the ROMER arm could hook and grip the back of the wire slot reliably every time.
- The Polarization Transmission Measurement
- The nEDM Measurement
Conclusion
Where Are We Now?
- Fierz Interference Measurements
- Dark Matter Decay Limits
- 𝐵
What’s Next?
- UCNA+
- nEDM@SNS
