Chapter III: UCNA Simulations
3.4 Post-Processing: Applying the Detector Response Model
8. Incident momentum - the momentum the particle had when entering the volume.
9. Exit momentum - the momentum the particle had when exiting the volume.
10. Particle species ID - a flag that indicated 𝛽-decay electrons as opposed to photons or other particles.
11. Process name - the name of the physics process which created this track. In certain physical processes, a cascade of tracks can be created and GEANT4 records each one and resolves those secondary particles automatically.
12. Volume name - the name of the volume where the track is located.
13. Creator volume name - the name of the volume where the track was created.
Within TrackerSD, a collection of tracker hits is created and stored for each SD. In the original asymmetry simulation, there were≈ 12 SDs for use in calibration and analysis. For the Fierz analysis, only four SDs were used: the East and West plastic scintillators and the East and West MWPCs. This was due to the simplified analysis requirements of the Fierz interference extraction and studying the UCNA detector response after one analysis had already been completed (publication [Men+13]).
After the hits collection is created, each tracker hit associated with a SD is stored within the hits collection. Then, once a particle is completed within a SD volume, a final function is called that accumulates all the kinematics from all the tracker hits within the SD. This, for example, sets the track ID, gets the particle ID, adds up all the energy deposited within the SD of this name, applies a quenching factor, and so on. The integrated kinematic parameters stored in the SDs are then accessible and printed out at the end of an event in the Event Action (discussed above in section 3.3.4.2).
Figure 3.5: Example 𝐸𝑟 𝑒 𝑐𝑜𝑛 spectra from combined PMT response for simulation (red) and data (blue) for all conversion electron source data (137𝐶 𝑒,113𝑆𝑛,207𝐵𝑖) after application of the calibration. This is for a random run that included all three sources within the fiducial volume at the same time. Figure from [Bro18] and the individual PMT comparisons between simulation and data prior to being combined into𝐸𝑟 𝑒 𝑐𝑜𝑛are also given there.
a simulation output that is data-like, and then combines those quantities into a final reconstructed energy.
The real detector response model used in the work in this dissertation is taken from the 2011-2013 asymmetry analysis and is described in detail in Chapter 4.2 of [Bro18]. Here, we provide a brief overview of the various effects accounted for in the detector response model. Figure 3.5 gives a comparison of this detector model applied to calibration data and calibration simulations. We note that these compar- isons were generated with the old GEANT4 simulations however the comparison is valid for our recreated simulation described in this chapter. The subsequent sections describe briefly the different analysis procedures in the detector response model that go into generating the comparison in figure 3.5. These effects are applied to simu- lated initial𝛽-decay electron kinematic spectra (as shown in figure 3.2) in order to illustrate what must be accounted for when converting pure Monte Carlo simulated spectra into “data-like” simulated spectra.
After settling on an analysis procedure for the Fierz interference, we then went back and applied our procedure to the integrated 2010 dataset. As a result, we used octet- by-octet or calibration period-by-calibration period measured detector responses for the 2011-2012, 2012-2013 datasets while for the 2010 dataset we used the entire year’s integrated data and calibration together. The following effects are described to provide additional context for how the simulation output is modified. We will see later in Chapters 4 and 5 how these different detector effects also become relevant in the UCNA dataset analyses.
3.4.1 Position Map Corrections
The first effect that the detector response model applies to the simulation output is the position map corrections. The analyzer (interchangeably called the “Simulation Processor” or simply the “processor”) takes as input the geometry that the GEANT4 simulation was executed with. It then loads the corresponding position maps as determined in [Men14; Bro18]. Throughout the analysis, there was a flag to process the simulations like the individual octets: we would either process simulation events on an event-by-event basis until we reached the same number of events as the desired octet, or we would process 16× the number of events (in order to create a “high statistics” Monte Carlo so the statistical error would be dominated by the real data in any comparison). The octets had different position maps associated with their activated Xenon position mapping run. Further details of the activated Xenon position map extraction on the 2011-2013 UCNA datasets can be found in [Bro18].
The position of the particle can be extracted from the tracked information in the GEANT4 geometry. Specifically, at the end of the event, the variable “Hit Position”
is used to determine where the particle was located on the face of the plastic scintillator. This position is then compared with the proper position map to extract a correction factor for this event’s light yield.
3.4.2 Finite PMT Resolution
The second effect that the detector response model applies to the simulation output is the smearing of the energy resolution due to the finite PMT resolution in the hardware. For each geometry, there is a calibration on each of the four East PMTs and the four West PMTs energy resolutions. This is reported in the form of nPE/keV, otherwise known as the “number of photo-electrons” per keV deposited and is unique to each geometry and PMT. For each scintillators quenched energy,𝐸𝑄, a Gaussian with mean𝐸𝑄and standard deviation of𝛼𝑖𝜂(𝑥 , 𝑦)where𝜂is the position map factor
discussed above (section 3.4.1), and𝛼𝑖is a resolution factor for PMT𝑖4. This creates eight quenched energies, one for each PMT in the UCNA apparatus, smeared with the PMT resolution and position map effects.
After the four smeared quenched energies for each detector are calculated, they are combined using their sampled photo-electron statistics as weights. This results in a weighted average of quenched energy deposited in the East and West detectors respectively.
3.4.3 Energy Calibration Distortions
In principle, the next processor effect to be applied is a modification for energy non- linearities. Energy calibration variation polynomials up to cubic order in averaged quenched energies5 are used to modify the energy response of the East and West detectors. This is discussed extensively in the Fierz interference spectral extraction, section 4.2. However, in a nominal simulation processor run, there are no energy calibration variations applied and this step is skipped.
3.4.4 Trigger Function
The fourth simulation processor effect applied is the trigger function. The trigger function is loaded depending on the calibration period used since there is a trigger function of the East and West detectors for each calibration period. Additional details on the trigger logic and extraction methodology is given in [Bro18].
The trigger threshold is then sampled to determine if there was a trigger in either the East or West detectors. Trigger flags are set based on this probabilistic sampling.
Afterwards, the event type classification is assigned based on the triggers in the East, West detectors and MWPCs and the simulation’s time flag for which SD triggered first.
We highlight the presence of this trigger function because it is a hardware-based effect. In the GEANT4 simulation, any amount of energy can be lost by our simulated particle in the scintillator SD and hence when we interrogate that SD we can extract any amount of energy deposited. The real experiment does not work the same way.
4The actual calculations of𝛼𝑖is non-trivial and detailed extensively in [Bro18]. The results of those𝛼𝑖extractions are loaded directly into the Simulation Processor and applied to the simulation data.
5From this point onwards, this weighted average of smeared quenched energies per detector side is called the visible energy,𝐸𝑣 𝑖 𝑠. We take care not to confuse with the actual data𝐸𝑣 𝑖 𝑠which is the final weighted signals in East and West plastic scintillators. However, since the simulation processor is intended to make simulations look “data-like”, this is similar to a data𝐸𝑣 𝑖 𝑠.
There is a minimum required energy for the 𝛽-decay electron to produce enough light in the scintillator such that it can be transported out towards the PMTs and generate a detectable signal. This is characterized extensively in [Bro18] and forms an important component of the UCNA detector response at low energies (where the trigger function dominates).
3.4.5 Creating a Reconstructed Energy
The final process applied by the simulation processor is to convert the “data-like”
quenched energies in the East and West detectors into a reconstructed energy. The details of this conversion formula for the 2011-2013 UCNA datasets is given in [Bro18]. After this final processor stage, the simulation output quenched energy deposition has been converted into a reconstructed energy that mimics the hardware effects of the detector.