The goodness of the OF fit can be quantified with the Chisq quantity. This is calculated between the measured pulse and scaled fit template in the frequency domain. There are 2 relevant rqs for PT, PTOFchisq, which calculates the total chisq, and PTOFchisqLF which calculates the total chisq below a frequency cutoff, set in the config files at 10kHz for this processing. Figure 1 shows the ratio of these two quantities as a function of OFamps after most of the other quality cuts have been applied. At energies above ~5keV, the two quantities are proportional, but below 5keV the full chisq stays proportionally larger than chisqLF. This could be because the smaller pulses will have relatively more signal at higher frequencies, so at low amplitudes, the chisq is mostly measuring the noise chisq, and may be missing the pulse. Because we are particularly interested in low energy events, we decide to use the full PTOFchisq as the goodness of fit quantity.

Figure 1: Chisq/ChisqLF ratio

The cut was set by eye to include the main band of events in all 3 datasets. The cut was also chosen to have the same definition across datasets because there should be a consistent definition for a “good fit”, regardless of how often this occurs in different datasets. I.e. it is more correct to have a single cut definition with differing passage fractions than different cuts with the same passage fraction. The cut is defined as follows:

TCut cchit = "PTOFchisq<(PTOFamps>6e-6)*((PTOFamps-6e-6)/3e-8)**2+PTOFamps/2e-9+5e3"

In the Figure 2, all events above the red line are discarded. Note that the chisq is calculated in frequency space, so noise events will fail this cut if their spectrum is too different from that of the template (weighted by the average PSD). Note also that the best fit is at low energies in all data types. There, the chisq value approaches the expected value for a good fit of Chisq=Nsamples=4096. This is an indication that the template is dong a good job of representing the average pulse shape in this area. At higher energies, saturation starts to change the pulse shape and Chisq diverges quadratically as expected.

Figure 2: Cut line
	~1 keV	~30 keV
Bkg
Na
PuBe

Figure 3 below shows 3 example Na events which fell just outside of the cut area. They seem to all have sloped baselines, but are otherwise good traces. These sloped baselines are presumably the main reason for the degraded fits.

Figure 3: Example failed events.
~1 keV	~4 keV	~ 10 keV

In fact, there is a noticeable correlation between the baseline slope and chisq. Figure 4 shows the distribution of PTOFchisq versus PTdbs, the average channel baseline shift calculated from weighted individual baseline changes. The plot includes events from 1-15 keV. This plot was made without any chisq cuts. It is clear that more steeply sloped baselines (more negative PTdbs) generally results in a higher chisq value. However, it can also be seen that the cut removes much of this effect. It would be an interesting study to look at how the OF values (amplitude, t0, chisq) are biased with a sloped pulse baseline. For present purposes, it is sufficient to notice that the chisq cut seems to be removing those events which are good triggers without pileup, but have a degraded fit due to sloping baseline. This is encouraging in that it indicates the earlier cuts are catching most pileup events since they do not appear here.

Figure 4: Chisq vs. PTdbs