The TDC Data

Chapter V: UCNA: Dark Matter Decay Analysis

5.3 UCNA Analysis of Dark Matter Decay

5.3.3 Coincidence Time Calibration

5.3.3.1 The TDC Data

As discussed in the analysis overview above (section 5.3), the timing of coincidence trigger events in the UCNA detector was crucial to the overall sensitivity of this measurement in order to differentiate between our candidate dark matter decay events and our original foreground events from conventional neutron 𝛽-decay. The UCNA experiment used CAEN V775AA 32-input, 12-bit, 1200-ns range time-to- digital converters (TDCs).

The TDCs used in the UCNA experiment used a “common-stop” signal. This meant that each individual subsystem start a “stopwatch” at each individual trigger and stop their measurement at a global trigger plus a fixed delay5^,6. For the UCNA apparatus and a Type 1 event where both scintillators see only a single decay event each within the common stop time, this means the first triggered TDC has a large peak at the endpoint of the TDC, corresponding to the global trigger plus fixed delay time. This

5The fixed delay is composed of two components: a known electronic delay set in the instru- mentation, and an unknown (detector-specific) cable length delay.

6The electronic trigger logic is presented in [Men14] and described in detail in [Bro18]. As a brief overview, for an event to register a global trigger in one detector, that detector must have a two-fold PMT trigger. That is, at least two of the four PMTs in that detector must have triggered above a pre-set threshold. In addition, a software MWPC threshold is applied to reject gammas, and a software muon veto coincidence is checked to reject cosmic muons.

is called the self-timing peak (STP). However, the opposite side TDC produces a standard Type 1 timing spectrum (relative to the STP) because its stopwatch started later relative to the global trigger plus fixed delay. So, for half the Type 1 events in each detector’s timing spectrum, we would see the timing structure of a neutron 𝛽-decay electron traversing the detector, and for the other half of Type 1 events we would see a STP.

For the 2010-2012 UCNA datasets, the TDC data was noisy. While clear coincidence signals were identified (which was needed for the 𝐴

0analysis), the spectra were not stable. The STPs of each TDC showed large electronic jitter and, in some octets, had up to three separate STPs of characteristic width 2 𝑛𝑠(similar to the properly calibration TDC data), peaked at three locations separated by upwards of ≈ 6𝑛𝑠. Hence, the actual TDC data was not reliable to within > 6 𝑛𝑠 unless there were separate calibrations for each type of TDC jitter. In addition, there were further complications with the quality of the remaining TDC data and concerns whether certain runs had the TDCs powered on. We ultimately chose not to use any of the 2011-2012 dataset in the dark matter decay analysis due to this unreliability in timing data.

During the beam shut down between the 2011-2012 and 2012-2013 data-taking runs, several components of UCNA were upgraded. We discussed some of the geometry changes in section 2.4. One additional upgrade was fixing the TDCs so that they operated reliably. In the 2012-2013 data-taking run, the TDCs were operating correctly and had standard TDC timing structures in their readouts. In particular, we could identify a clear STP and a signature timing spectrum for Type 1 backscatter events, both of which are shown in Figure 5.5 for East and West TDCs.

We note a few features. The large peaks at channel number 3100 (East) and 3250 (West) are the STPs. The peak structure at channel 2600 (both) is the 𝛽-decay electron timing spectrum from Type 1 events (we note this data is taken with a Type 1 event cut). A flat 150 channel shift was applied to the East TDC to get the Type 1 backscatter peak to align since this was our physically relevant check point. This shift in channels is likely due to different cable lengths for each TDC which are discussed below. We do note that the actual channel-to-time conversion is dependent on the center of the STP. 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. By shifting the East TDC spectrum up, we “compress” the resulting timing spectrum and conservatively ensure we capture as many events in a chosen analysis

Figure 5.5: Timing spectra taken from East (red) and West (blue) TDCs in raw channel count, operated in a “common stop” mode, for Type 1 backscatter events.

Self-timing peaks are seen centered around channel 3150 (red) and 3250 (blue).

Significantly more electronic jitter is seen in the West TDC. A flat 150 channel offset has been applied in order to align the Type 1 backscatter peak at channel 2600. A conversion of 44𝑝 𝑠/𝑐 ℎwas applied. Figure first published in [Sun+19].

time window as possible, within noise (see discussion on the timing window in section 5.3.4.2).

Throughout the course of the initial time analysis, we noticed that the backscatter and self-timing peaks did not align in the East and West TDCs. This hinted towards systematic offsets in the TDC data. Dr. Brad Filippone identified that this may be due to mis-matched wire lengths between the TDCs and the trigger logic that connected them. A simple diagram of the wire set-up is shown in figure 5.6 and it was used to guide the estimation of the wire length induced timing delay. In order

Figure 5.6: A simple diagram of wire connections between the TDCs and the UCNA detector [Fil18]. This was used as a guide to estimate the time delays due to potentially mismatched cable lengths (see text).

to perform this estimation, we identify that for the West TDC:

start=𝑡_𝑊 +Δ𝑡 stop=𝑡_𝐸+𝑡^𝑊

𝐷

and𝑡^𝑊

BSP =stop−start=𝑡_𝐸+𝑡^𝑊

𝐷 −𝑡_𝑊−Δ𝑡 . Similarly, for the East TDC we have𝑡^𝐸

BSP =𝑡_𝑊 +𝑡^𝐸

𝐷 −𝑡_𝐸 −Δ𝑡 with, additionally,𝑡^𝑊

STP =𝑡^𝑊

𝐷

and𝑡^𝐸

STP =𝑡^𝐸

𝐷

(5.15)

where BSP stands for backscatter peak, STP stands for self-timing peak as described earlier, E and W are East and West respectively, and D stands for delay. The “start”

and “stop” represent the commands for the TDCs. From the TDC data, we have 𝑡^𝑊

𝑆𝑇 𝑃=𝑡^𝑊

𝐷 =3138𝑐 ℎ𝑎𝑛𝑛𝑒𝑙 𝑠 (5.16)

𝑡^𝐸

𝑆𝑇 𝑃 =𝑡^𝐸

𝐷 =2917𝑐 ℎ𝑎𝑛𝑛𝑒𝑙 𝑠 (5.17)

𝑡^𝑊

𝐵𝑆 𝑃−𝑡^𝐸

𝐵𝑆 𝑃 =145𝑐 ℎ𝑎𝑛𝑛𝑒𝑙 𝑠 (5.18) where the units are in TDC channels and we note that within the electronics there was a channels-to-time conversion setting of 180𝑛𝑠=4096𝑐 ℎ𝑎𝑛𝑛𝑒𝑙 𝑠 →44𝑝 𝑠/𝑐 ℎ.

From equation 5.18, we get

2(𝑡_𝐸 −𝑡_𝑊) + (𝑡^𝑊

𝐷 −𝑡^𝐸

𝐷)=145𝑐 ℎ𝑎𝑛𝑛𝑒𝑙 𝑠 (5.19) 2(𝑡_𝐸 −𝑡_𝑊) +221𝑐 ℎ𝑎𝑛𝑛𝑒𝑙 𝑠=145𝑐 ℎ𝑎𝑛𝑛𝑒𝑙 𝑠 (5.20)

=⇒ Δ𝑡 =𝑡_𝑊−𝑡_𝐸 =38𝑐 ℎ𝑎𝑛𝑛𝑒𝑙 𝑠≈ 1.7𝑛𝑠 (5.21) Hence, the time delay in our wire length differences was≈1.7𝑛𝑠. This was adjusted for by applying a flat channel shift in downstream timing window analysis.

We take the characteristic TDC spectrum shown in Figure 5.5 for all the 2012-2013 data and convert to a physical time. We set the center of the STP at 140𝑛𝑠which corresponded to 44 𝑝 𝑠/𝑐 ℎ as in the above wire length discussion. We show the negative difference of each point from the center of the STP7to turn our “common- stop” into a common zero and produce a conventionally understood timing spectrum.

The resulting spectra for East and West TDCs are shown in Figure 5.7. Again, we note a few features here. The vertical dotted lines represent the nominal chosen timing window for the candidate dark matter decay events, discussed further below in section 5.3.4.2. The red overlaid timing spectrum is a simulated spectrum of Type 1 back scatter events with a 2𝑛𝑠timing resolution applied. This is described in more detail in the following subsection below.