Timing Window Acceptance

Chapter V: UCNA: Dark Matter Decay Analysis

5.3 UCNA Analysis of Dark Matter Decay

5.3.4 Detection Efficiency Estimates

5.3.4.2 Timing Window Acceptance

The second acceptance that gets included in the detection efficiency is the timing window acceptance. This represents the amount of candidate dark matter decays in equation 5.9 that we could detect in a given time window. When we simulate the

Figure 5.11: Monte Carlo simulation of arrival times in the detectors for a three- body decay where𝑚_𝜒 is a minimum and hence there is maximum available kinetic energy to the 𝑒⁺𝑒⁻ of 644 𝑘 𝑒𝑉. Timing spectra are overlaid for events generated in the center of the UCNA decay trap (green) and uniformly populated throughout the decay trap (black). The large bin at 100 𝑛𝑠 represents an “over-fill” bin — a bin where all the events beyond are contained as well. In reality, there would be an arbitrarily long tail to the spectrum that extends>100𝑛𝑠.

kinematic decay of equation 5.9 within the decay trap volume of UCNA, we obtain a spectrum of arrival times (shown in figure 5.11 for one value of 𝑚_𝜒). Due to the helical nature of the electron (or positron) trajectory, there are potentially long time delays between coincidence triggers. We simulate this by populating decays via equation 5.9 within the UCNA trap and performing a phase space three-body kinematic decay where we vary the mass of the 𝜒 particle and hence the available kinetic energy for the𝑒⁺𝑒⁻ pair.

We reproduced these simulations for different values of potential 𝑚_𝜒, consistent with the energy resolutions of our final energy bin widths. Over the range of masses for candidate 𝜒particles, the acceptance probability ranges from≈ 20−40% when using aΔ𝑡 = 12𝑛𝑠timing window cut. The choice of timing window was studied and is discussed below.

At this stage, we remind the reader of a few points discussed throughout the course

of this section. First, the minimum transit time for a 𝛽-decay electron across the 4.4 𝑚 scintillator-to-scintillator distance is ≈ 15 𝑛𝑠. Second, we have 𝜎_𝑡 ≈ 2𝑛𝑠, as ascertained by the width of the STPs and corroborated by a GEANT4 timing spectrum simulation. Third, there is≈1.7𝑛𝑠deadtime in the beginning of the West TDC associated with longer cable lengths when compared with the East TDC and hence the initial 1.7𝑛𝑠is cut from the physically relevant timing region.

With these considerations in mind, we analyzed several choices of timing windows to see what background-subtracted events survived our cuts. In particular, we want to minimize any events from the true Type 1 backscatter signal. Some sample timing windows can be seen in figure 5.12. From this, we clearly see how, as the time window is opened up, there is a clear structure of Type 1 backscatter neutron𝛽-decay events entering in the spectrum. It is interesting to note that even in the background only runs (see figure 5.12a) this peak still begins to enter in the spectrum shape.

these could have originated from electrons produced from Compton scattering by background photons interacting with the plastic scintillator. These electrons could pass through the apparatus and trigger the opposite side detector.

We studied which timing window would be best to balance cutting out noise while optimizing our acceptance window and general robustness of results. For instance, a short time acceptance window would leave us with very few events and a stronger limit. However, we also wanted to be robust against systematic shifts in TDC channels from run-to-run or octet-to-octet and hence would like a larger time accep- tance window. Furthermore, we wanted to avoid choosing a narrow time range and weaken the confidence in our studies on underlying systematic shifts in the timing data. Throughout the analysis, we kept in mind the overarching < 15𝑛𝑠 limit as the minimum transit time for a speed-of-light particle (noting that for typical Type 1 𝛽-decay electron energies, the fastest transit time would be≈ 16𝑛𝑠). We wanted to be (1−2)𝜎𝑡 ,𝑟 𝑒 𝑠𝑜𝑙 𝑢𝑡𝑖 𝑜𝑛 within the kinematically forbidden region and include as much of the timing window as possible. Ultimately, we settled on a timing window from 0−12𝑛𝑠where the first ≈ 2𝑛𝑠of the West TDC values were cut out due to additional deadtime (this was adjusted for in our final acceptance). We varied this time window to study the effect of choosing different West TDC time cuts (and later East TDC) on the total number of events in the kinematically forbidden region. The results are shown in figure 5.13. We use the resulting count numbers in the figure to estimate our uncertainty in the timing window acceptance at≈15%.

We note that this analysis was unblinded, in contrast to the Fierz interference

Figure 5.12: Energy spectrum of (a) background and (b) foreground runs, for three separate time-windows. We note that there is factor ≈ 5 difference between live times for the foreground and background runs, hence the differences in total count numbers. Clear structure of a neutron 𝛽-decay backscattering peak at 300 keV is visible for time-windows > 12 ns in the foreground runs. Dashed lines at 0 keV, 800 keV indicate the energy region of interest used for the present analysis. Figure first published in [Sun+18].

Figure 5.13: Number of background-subtracted events accepted within our chosen timing window as a function of the high time cut off. Three different low time cut offs are used: −2 𝑛𝑠 (black), 0 𝑛𝑠 (red), 2 𝑛𝑠 (green). We note that the −2 𝑛𝑠 is unphysical unless there was systematic electronic jitter in the TDCs. Verical error bars are set by

√

𝑁of the total number of counts and horizontal error bars are set to 1𝑛𝑠arbitrarily. The final chosen timing window for the West TDC was[2𝑛𝑠,12𝑛𝑠] in order to cut out the additional dead-time from wire length differences (see text).

For the East TDC, we used[0,12𝑛𝑠]. Efficiencies were adjusted for these East/West time window discrepancies.

extraction discussed in Chapter 4 using the same datasets. This was primarily due to the fact that the signal of a𝑒⁺𝑒⁻ appearing at the 1% branching level would be so significant (see, for example, figure 5.8) it would be unrealistic to blind. Hence we were not concerned about making analysis cuts that would mildly bias our upper limits (we note that a 1% branch corresponds to 100×our upper limit).

After choosing our final timing window, we make an energy cut at 644𝑘 𝑒𝑉 which is the maximum allowable summed kinetic energy of the𝑒⁺𝑒⁻ pair. This introduces another efficiency in the form of the energy resolution. Namely, decays with 𝑚_𝜒 resulting in 𝐸_{𝐾 ,𝑒}+𝑒⁻ = 644 𝑘 𝑒𝑉 would be smeared by the energy resolution and hence the peaks would be centered at 644𝑘 𝑒𝑉 with some characteristic width. An energy cut at 644 𝑘 𝑒𝑉 would in principle miss half the events. We adjust for this

Figure 5.14: Background-subtracted𝑒⁺𝑒⁻ pair kinetic energy spectra for events in the chosen analysis time-window. For comparison, simulated positive dark matter decay signals at summed 𝑒⁺𝑒⁻ kinetic energies of 322𝑘 𝑒𝑉, 644 𝑘 𝑒𝑉 are overlaid, assuming 1% branching ratio. Bin widths of 25 𝑘 𝑒𝑉. Figure first published in [Sun+18; Sun+19].

efficiency as well in the final acceptance. In figure 5.14 we show the resulting events that pass our timing window cut from background-subtracted UCNA 2012-2013 data, restricted by our energy cut to 𝐸_{𝐾 ,𝑒}+𝑒⁻ ∈ [0,644 𝑘 𝑒𝑉]. This data is overlaid with 1% branching ratio signals, simulated in GEANT4, as described in Chapter 3, at the endpoint energy and half the endpoint energy. As in figure 5.8, these overlaid signals are to give a qualitative impression of the relative signal strengths and are not propagated in quantitative limits discussed below.

At this stage, we have the final data with an acceptance time window of 0−12𝑛𝑠 and binned in 25𝑘 𝑒𝑉 bins (comparable to energy resolution). We have determined the kinematic and timing window efficiencies. Next we determine the efficiency factors for the UCNA detector response.