HIGH-THRESHOLD ANALYSIS: PARAMETRIC FIDUCIALIZATION
4.3 Model dataset Construction
4.3.3 Background Model: Gamma sourced events
4.3.3.1 Systematic gamma correction
Qualitatively, the first two steps of the systematic correction outlined above can be summed up by:
Xw(~x)= XW I MP(~x)
Xcalib(~x) (4.10)
where XW I MP, andXcalib are the marginal density estimate of RRQ ~x for the wimp search and calibration data sets respectively andXwis the resulting weight distribu- tion. For the gamma model, Xcalib is constructed from the sideband, single-scatter,
133Ba data that falls inside the fiducial blinding region. XWimp is constructed from similarly selected WIMP-search data. We restrict ourselves to the fiducial blinded region to ensure we do not contaminate our gamma model with large amounts of
210Pb. Inside this fiducial blinded region we have no access to NR band single- scatter events in the WIMP-search data, so we utilize the NR-band sideband as a proxy. As a demonstration of how this works here is our re-weighing machinery acting on a contrived RRQ (that is just the sum of some Gaussian). Using the fol- lowing fake RRQ definition:
~xcalib= N(0.5,2,1e5)+N(−1,1,1e4)+N(0,0.3,1e5) (4.11)
~
xW I MP = N(1,1,1e4)+N(−2,0.5,1e4)+N(0.3,0.04,1e3) (4.12) WhereN(µ, σ,N) is a vector ofN samples from a normal distribution with mean µand standard deviationσ. The resulting RRQ and weight density estimation can be seen in figure 4.2. We have implemented many different estimation methods,
(a) (b)
(c)
Figure 4.2: Overview of our systematic correction using the data from equa- tion 4.11. The calibration data (a) is a high statistics dataset that extends into the blinded region. We want to use it to model a particular distribution in the WIMP- search data (b), but as we can see they are systematically different distributions. To correct this we divide the two and form the weight distribution (c). This can be used to sample weights for the points in (a). As can be seen here a number of density estimation methods were examined, but in the end a simple histogram (blue) was chosen.
but have settled on the histogram as the best preforming. At this point the actual per-event weights can be found for this RRQ, by sampling the weight distribution at each of the calibration dataset’s points or:
~
xw= Xw(xcalib~ ) (4.13)
This process are repeated for the discriminating parameters described in section 2.4, and the results can be multiplied event-by-event. The result is the un-normalized weight vector. Although it is lower in statistics and less clear than the fake example shown in figure 4.2, this process is plotted in figure 4.3.
(a) (b)
Figure 4.3: An example ofγ-sourced weight vector construction for detector IT3Z1.
This particular example corrects the recoil-energy distribution, and an identical pro- cess is carried out for all discriminating parameters. On the left are theprecoiltNF distributions for133Ba-sourced (blue) as well as our WS sideband data (orange). On the right is the resulting weight distribution.
4.3.3.2 Gamma normalization
For our gamma model, we want to model the number of gamma events that are misidentified as signal by our detectors (obviously as a function of all other RRQs).
To this end, we want:
kw~ik1 =X
k
wik = NiNRS S (4.14)
WhereNNRS Si is the number of single scatter events that fall inside the NR band from our WIMP-search dataset in detectori. How do we measure NNRS Si ? Outside the fiducial blinding region, this measurement is easy. We simply count the number of single scatter events in the NR band from our WIMP-search dataset. These events are mostly going to be at high Z and R positions (The fiducial blinding cut is defined in terms of charge symmetry (cQsym_blind) as well as radial partition (cQin1_blind and cQin2_blind) amongst other things). The number of NR single scatter events
NNRS Sblind = NNRS SBa NS BS SW I MP
NS BS SBa (4.16)
whereNNRS SBa is the number of 133Ba NR-band single scatters in the fiducial blind- ing region (shown as the dark blue points in figure 4.4), NS BS SW I MP is the number of WIMP-search sideband (out of NR band) single scatters in the blinding region, and NS BS SBa is the number of133Ba sideband single scatters in the fiducial blinding region (dark red in figure 4.4). There was initially some interest in allowing our prese-
(a) (b)
Figure 4.4: Ionization yield vs recoil energy depicting a portion of our preselected region. Both the 133Ba-calibration (a) as well as the WIMP-search data (b) are shown. The events are colored based on various preselection criteria. Importantly to estimate the total number of single-scatter NR-band, gamma-sourced events that fall inside our blinding region for WIMP-search data (which would be colored dark blue but have been blinded) we start with the dark blue events in (a) and correct by the ratio of dark red events between (a) and (b).
lection region to include the fiducial unblinded region, which would set the total γ-sourced background model normalization to NNRS S. This was to provide more statistics for our gamma model. This would rely either on our optimizer cutting out all fiducial unblinded events on its own (as they are not candidates for our signal
region) or instituting a post-optimization cut to remove them. The former event did not come to pass (our optimizer was never so accommodating) and instituting a post-optimization further-fiducializing cut calls the entire purpose of optimization into question. As a result we restricted our preselection conditions to only include events inside of the fiducial blinding region, and the total γ-sourced background model normalization isNblindNRS S.