Chapter IV: UCNA: Fierz Interference Analysis
4.2 The Spectral Extraction Method
4.2.3 Other Systematic Effects
act as a Monte Carlo study on this effect. Internally, this was called “tin stitching”
and the prescription is described by
𝐸𝑠𝑡𝑖𝑡 𝑐 ℎ =
364
368.5𝐸𝑒 0< 𝐸𝑒 < 368.5 ( 782
773.58 −8.51)𝐸𝑒 368.5< 𝐸𝑒 < 1000
(4.19) where the numbers are expressed in keV and chosen such that the end point energies match at 782 keV (see section 4.2.4.1 for more details) and that a correct 113𝑆𝑛 calibration energy peak at 368.5 kEv is reconstructed to the 364 keV that the 2012- 2013 calibration produced. We note that we chose to perform an “inverse” stitching by making the properly calibrated 2011-2012 spectrum resemble the incorrectly calibrated 2012-2013 spectrum. This was chosen to simplify the comparisons in code but ultimately does represent the magnitude of the𝑏shift — the true shift would be the negative of the extracted value due to this stitching procedure. The value of𝑏 extracted after this procedure is applied on a sample 2011-2012 spectrum can be compared with the same spectrum without the energy modifications in equation 4.19 and the magnitude of theΔ𝑏can be found.
The Fierz interference extractions differed by about≈0.17 when extracted from the 𝑏 =0 Monte Carlo, detector-processed simulations using the 2011-2012 vs the 2012- 2013 energy reconstruction. In particular, the 2011-2012 reconstruction produced an output𝑏 ≈0 which was consistent with the𝑏input value. After applying the energy modification in equation 4.19, the extracted𝑏value was≈ −0.17. This shows that the discrepancies introduced by the shift due to the113𝑆𝑛source energy reconstruction could be potentially substantial and cover a lot of the range of systematic shifts in the Fierz interference extraction. Unfortunately, at this stage, we did not have other energy benchmarks that could be used to reliably override the 113𝑆𝑛 calibration source peak. As a result, we accepted a larger uncertainty in the energy calibration (and potential offsets), particularly in the 2012-2013 energy calibration compared to the 2011-2012 calibration. Ultimately, this provided a qualitative justification for not relying principally on the spectral extraction method, particularly in 2012-2013, because we could not fully correct our energy calibration discrepancies.
to the energy calibration uncertainty when performing a spectral extraction on the Fierz interference term.
This analysis was initially completed via toy Monte Carlo studies in [Hic13]. Con- currently with the 2010 UCNA dataset extraction, the other systematic effects were quantified using the full UCNA 2010 geometry GEANT4 simulation (topic of Chap- ter 3) whenever possible as an independent check. A table of the systematic effects and their final quantitative contributions can be found in table 4.1. Each effect is described in more detail below. We note that this is only presenting the 2010 UCNA dataset systematics but that minor changes in detector geometry, negligible improvements in energy calibration, and the subdominant nature of these systematic effects imply that they are approximately adaptable to the 2011-2012 and 2012-2013 dataset spectral analyses. Indeed, for completeness these effects were calculated for the 2011-2012, 2012-2013 datasets and shown to be subdominant but ultimately not included explicitly in our final publication (see [Sun+20]) since they were not relevant to the overall spectral extracted Fierz interference values.
Contribution 𝜎𝑏
Background Subtraction ±0.005 Energy Resolution ±0.01 Electron Backscattering ±0.005 Detector Inefficiency ±0.02 Energy Response +0.087/−0.056
Table 4.1: Summary of 1𝜎 systematic uncertainties on the 2010 UCNA dataset extraction of Fierz interference [Hic+17]. These uncertainties are generally extracted from simplistic Monte Carlo studies except for the “Energy Response”, which is studied using the full GEANT4 simulation.
4.2.3.1 Background Subtraction
This effect refers to the error in the background model potentially propagating into the final energy reconstruction. In particular, underlying structures in the background model shape would influence the resulting shape of the𝛽-decay electron spectrum. Monte Carlo studies on background rate fluctuations were compared against the overall high statistics of the UCNA electron detection and resulted in subdominant error due to this effect.
4.2.3.2 Energy Resolution
Energy resolution refers to the finite resolution of the PMTs, expressed in units of the reconstructed energy. Since each energy bin “smears” to both higher and lower energies, the 𝛽-decay electron energy spectrum lowers the decay rate at the neutron 𝛽-decay energy spectrum peak and pushes the decay rates in each bin above the peak to higher energies. We note that low-energy events that get pushed to lower energies are removed due to the trigger acceptance characterized by a trigger function (see below). Ultimately, the shift in spectral shape due to energy resolution is again subdominant because this overall shift does not produce a polynomial signal that would be detectable as a non-zero 𝑏, as noted when studies were performed by introducing a secondary Gaussian energy resolution with characteristic width of several energy bins.
4.2.3.3 Backscattering
Electron backscattering refers to an uncertainty associated with the events that are not classified as “Type 0” (see figure 2.7 for a reminder of event types). These additional event classifications have their own separate energy reconstruction that was less precise due to significantly fewer events. The spectral analyses avoid any complications with multi-scattering event types by simply excluding them. In contrast to the asymmetry analysis, we are able to do this because our uncertainty is not limited by statistics for the Fierz interference analysis. Thus, this systematic error in relation to 𝑏 solely refers to the number of incorrectly identified Type 0 events compared to non Type 0 events. This is a quantity that was extracted from the GEANT4 simulation, as discussed in section 3.5. We set a limit on a Fierz interference systematic error by allocating the fractions of misidentified Type 0 events and performing a spectral extraction.
4.2.3.4 Detector Inefficiency
The detector inefficiency refers to the trigger function — a function describing the number of events not detected due to their energy being insufficient to trigger the electronic hardware (see section 3.4.4 for more details). It is an energy dependent probability that, in principle, is calculated for both East and West detector. In order to estimate this effect, the detector inefficiency, which is the probability that the event does not trigger our apparatus, was varied by a large ±20% factor in order to conservatively estimate this effect. The resulting spectra are fit and a 𝑏 value is
extracted. We note due to the chosen low energy cut-off, the majority of effects due to the trigger function are excluded and hence why a large variation of 20% leads to subdominant systematic uncertainties.
4.2.4 Other Spectral Systematic Studies