Further Information

For a description of the standard parameters used in the network classifier (harmonic, residual and residual-harmonic) along with more background information on the use of neural network analysis in SNO see the reports by Steve Brice [26,27].

The ACF code computes two angular correlation functions for each event, without and with application of a "residual time cut" (RTC). As used here, the angular correlation function is simply the normalized distribution of the cosines of the separation angles for all pairs of hit PMTs. The event correlation functions are compared to standard functions for the same $N_{hit}$ value, calculated previously from electron-initiated or NC-in-salt Monte Carlo events. (Standard functions are provided for $N_{hit}$ between lower and upper limits of 20 and 150 for electron events and 20 and 85 for NC events.) Several measures of the difference between the event functions and the standard functions are calculated. The average pair separation angle is calculated (identical to $\theta_{ij}$ except for the PMTs selected for the calculation). Finally, the event correlation function is compared to two other functions by calculating ``correlation function inner products''

The PMT pair separation angles are calculated using the fitted event location as the vertex. To apply the residual time cut, a time residual is calculated for each hit PMT, given by

$$t_{res} = t_{hit} - t_{fit} - d_{fit}/v ,$$ (18.3)

where

$t_{hit}$ = PMT hit time;
$t_{fit}$ = fitted event time;
$d_{fit}$ = distance between fitted event position and the PMT;
$v$ = speed of light (21.75 cm/ns).

An 8 ns sliding window is imposed on the residual times, positioned to include the greatest number of PMT hits. PMT hits that fall outside the window are excluded.

The fourteen ACF output parameters are:

1. Mean pair separation angle, in degrees, without RTC
2. Mean pair separation angle, in degrees, with RTC

3. Chi-square of event correlation function relative to the electron standard correlation function, without RTC
4. Natural logarithm of the determinant of the electron standard function covariance matrix, without RTC
5. Greatest difference between the cumulative event correlation function and the cumulative electron standard function, without RTC

6. Same as item 3, using the electron standard function with RTC
7. Same as item 4, using the electron standard function with RTC
8. Same as item 5, using the electron standard function with RTC

9. Same as item 3, using the NC-salt standard function without RTC
10. Same as item 4, using the NC-salt standard function without RTC
11. Same as item 5, using the NC-salt standard function without RTC

12. Same as item 3, using the NC-salt standard function with RTC
13. Same as item 4, using the NC-salt standard function with RTC
14. Same as item 5, using the NC-salt standard function with RTC

15. Number of PMTs passing RTC
16. Inner product of event correlation function with that of an ideal ring
17. Inner product of event correlation function with normalized difference of CC and NC average correlation functions

The ACF code also produces diagnostic histograms for the complete sample of events processed if the user has enabled them. These are

1. No. of PMT Pairs vs. $\eta$ (degrees, no time window cut)
2. No. of PMT Pairs vs. $\eta$ (degrees, with time window cut)
3. Average Correlation Function vs. $\cos \eta$ (no time window cut)
4. Average Correlation Function vs. $\cos \eta$ (with time window cut)

($\eta$ is the pair separation angle.) The histograms are numbered beginning at one plus the offset given in control titles bank TCLN 1.

A discussion of the angular correlation function is given in SNO-STR-2000-032 ("Use of the Angular Correlation Function to Identify Background SNO Events", by W. Heintzelman).

When the ACF routines are called through the classifier, the calculations are done using the event positions determined by the fitter specified. A user writing his own usr_exe routine or defining his own DQFs to extract data can instead call subroutine acf_angcormain independently of the classifier, in which case he can specify which fitter is to be used and he can make several calls for each event with a different fitter each time. In that case, he must also call acf_trm or AngCorTrm from usr_trm to terminate the ACF routines properly and generate the histogram output, which is written into FILE USR 1 instead of FILE CLN 1.

The ITR (In-Time Ratio) parameter gives the fraction of hits in a user-defined prompt time window. Only tubes with valid calibrations are included in this numerator and denominator of the fraction. The lower and upper limits of the in-time window cut are given in words 8 and 9 of bank TCLN 1. The lower limit should always be negative, and the upper limit positive.