1. Localization of a Neutrino Interaction Vertex in the OPERA Experiment
Dubna, February 8, 2006
Localization of a Neutrino Interaction Vertex in the OPERA Experiment
S.Dmitrievsky, Yu.Gornushkin, G.Ososkov

2. Outline: Brief description of the OPERA detector.
Short review of previous studies.
Our BF algorithm description.
Comparison of two neural networks.
Preliminary results.
Conclusion and outlook.

3. The OPERA Detector
The OPERA experiment is designed for a direct observation of appearance in the CNGS long baseline beam (from CERN to Gran Sasso Laboratory) as a result of oscillation.
OPERA exploits nuclear emulsions as very high resolution tracking
devices for the direct detection of leptons produced in the
charge current (CC) interaction of the with matter of the detector.
The target part of the detector consists of 62 target brick walls (photoemulsion layers, interlaced with led layers, are organized in bricks). Each wall consists of ~3300 bricks. It is accompanied by two planes (X-Y) of electronic Target Tracker (TT) detectors. The TT planes consist of 256 scintillator strips, each is ~7 m long. The strips are read out by WLS fibers optically coupled to photodetectors on both ends of a strip.

4. The TT mainly serves for a location of the event vertex's position, i
The TT mainly serves for a location of the event vertex's position, i.e. for a Brick Finding (BF) - a procedure of a target brick identifying where a neutrino interaction occurred.

5. JINR’s group is deeply involved in the TT detector construction.
Now we started to work on TT software development as well.
The goal of our work was to develop a BF program based on some data handling algorithms developed at the JINR and used in other experiments.
As a first step of validation of our BF approach we tried in particular to reproduce the results of the previous studies:
I.Laktineh, Brick Finding Efficiency in Muonic Decay Tau Neutrino Events. OPERA Internal note,
21 January, 2002.
I.Laktineh, Brick Finding Efficiency of No-Muon Tau Neutrino Events in OPERA. OPERA Internal note,
18 November, 2002.
C.Heritier, D.Autiero, Status of Brickfinding, OPERA Meeting, Napoli, October 23-25, 2003.

6. The brick finding problem
The main obstacle of BF is back-scattered particles (BSP):
Vertex
Beam Z
In the previous studies the search of the vertex brick is performed as follows:
-The Hough transform (HT) is used to get rid of BSP and “background” hits;
-Events are classified by their topology in the TT;
-Neural networks are used to select the vertex wall;
-Tracks are fitted to HT selected points to find x-y vertex coordinates and indicate the vertex brick.
BF efficiency obtained for events:
72.5% for electronic, 68.1% for hadronic, and 72.4% for muonic -decay mode

7. Our BF algorithm:
1. Event cleaning using a cellular automaton approach;
2. Event classification by its topology in the TT;
3. Muon track recognition applying the Hough transform;
4. Principal shower axis reconstruction using a robust fitting method;
5. Vertex wall determination using a neural network;
6. Vertex brick determination by crossing of the found axis with the selected wall.

8. Event Cleaning on the basis of the Cellular Automaton Approach
The ideal event would be the tracks coming out of the same point allowing us to find a vertex directly. Unfortunately, we have the BS, neutron or gammas interaction with the detectors, natural radioactivity background, PMT noise, etc., which produce isolated hits that are misleading in the most of cases.
We use the cellular automaton approach for preliminary event cleaning in order to efficiently eliminate disconnected hits that can distort the topology of the events.
We have tested a set of different ’survival rules’ and, finally, our cleaning method consists in removing of each hit that has none of 14 nearest neighbors in two adjacent TT walls.
Neighboring hits
Beam Z

9. Choice of the CA ‘survival’ rule
case:

10. Event Classification by their topology in the TT
The neutrino interaction events can be separated in few classes according to their topology in the TT detector. The BF procedure can be optimized differently for those classes depending on presence of a muon track or hadronic showers.
Events are separated in 3 classes depending on the number of the hit walls and on the mean number of hits per TT plane. This separation is motivated by the fact that the NN performance used to locate the vertex wall is improved by separating QE-like from DIS-like events and also by separating events with small shower development from those of important ones. The three classes of events are defined as follows:
1. Events with one or two hit TT walls;
(A TT wall is defined here as a composition of X and Y TT planes)
2. Events with more than two hit walls and a mean number
of hits/plane less than 2.5;
3. Events with more than two hit walls and a mean number
of hits/plane more than 2.5.

11. Muon track recognition using the VSH method
The Method of Variable Slope Histograms (VSH) is a particular case of the Hough transform for straight lines revealing.
The idea of the method consists in fragmentation of an inspected region by narrow parallel bands in every of which the number of hits is calculated. A slope of bands is gradually changed. When one of such slopes coincides with some of tracks, it would produce the maximum in a histogram corresponding to this slope.
In a case of the muonic events we use the VSH method for a muon track finding. The criterion of the muon track definition is that a bin of histogram with the maximum value must contain at least 10 counts.

12. Robust Fitting Method for a shower axis reconstruction
The TT detector has a pitch of 26 mm and it is difficult to single out distinct tracks near the vertex of the event. In that case the reconstruction of a shower axis can be more useful for finding a general direction to the vertex.
Two simple examples, when Least Square Method (LSM) does not work: ε
a) point - outlier
b) uniform contamination
In both cases the crucial LSM assumption of residual normality is violated
so we propose to replace the Least Square functional Σi εi2 by the other one L(p,σ)=Σi ρ(εi ) (1)
where εi are residuals and ρ(ε) is a compact contribution function.
This functional gives a weight to each hit depending on its distance ε from the fitted line. The weights quickly decrease with growing the residuals εi.

13. Weight function
Amplitude of hits
To determine a principal shower axis we use the robust fit of a straight line to all hits excluding the hits of the found muon track.
Initial approach:
- The robust fitting procedure starts from the initial approach, which is a line passing through the center of gravity of all hits and parallel to Z axis.
- wi (0) Ξ 1, i.e. usual LSM solution (the worst for heavy contamination).
A robust weight of each hit is recalculated on each step of an iterative procedure taking into account the hit amplitude, and its distance from the fitted line.

14. Vertex Wall Determination using a NN
For the purpose of the vertex wall determination we use the Neural
Network (NN) approach on the basis of a multilayer perceptron (MLP) with standard back propagation training algorithm. The energy functional minimization of the network is performed by the method of conjugate gradients (CG).
Our first goal was to reproduce the results of the previous studies making use of our own NN code and we started with about the same input parameters.
The numbers of neurons in the input and hidden layers were equal to 14. The input variables were the follows:
for the first 3 hit TT walls:
 Number of the hits in a particular wall;
 Total amplitude of hits in the wall;
 Dispersion of the hits in the wall;
 The mean distance of the hits in the wall with respect to the event shower axis.
In addition to those 12 variables, ratios of energy in the next wall with respect to the previous one, E2/E1 and E3/E2, were also included to the input parameters to train the NN.

15. Distributions of the energy ratios in the first three hit walls.
1 BS hit wall in front of a vertex
No BS
E3/E2
E3/E2
1 BS hit wall in front of a vertex
2 BS hit walls in front of a vertex

16. Relative weights of the input parameters for different types of events

17. MLP(CG) vs SNNS
OCT MC
MLP(CG)
SNNS
Efficiency
MSE
8000 ep.
40000 ep.
2 cl.
84.4  2.9
0.249
84.8  3.5
0.247
0.234
3 cl.
84.1  3.4
0.199
84.9  3.1
0.189
85.2  3.6
0.224
85.8  3.2
0.228
0.212
84.9  2.6
0.207
85.0  2.6
0.209
0.196
79.9  4.6
0.269
78.9  3.8
0.285
0.271
83.2  3.5
0.226
83.6  2.9
0.225
0.217
89.5  3.6
0.178
90.2  3.8
0.174
0.165
84.4  3.1
0.197
86.5  2.4
0.187
The MLP(CG) was elaborated especially for the OPERA data analysis, therefore it is simple, compact and can be directly built in OPERA software.
The comparative study of MLP(CG) used by us and SNNS with analogous training and minimization algorithm shows that corresponding mean square errors (MSE) after 8000 epochs are approximately equal to each other.

18. Vertex residual distributions in X and Y planes

19. Available Monte-Carlo statistics:
Preliminary results
Available Monte-Carlo statistics:
OCT MC
DATA
2 class
3 class
train
test
9000
1000 *
6000
7000
4000
Necessary statistics should be at least events!
* Statistics is insufficient
Wall Finding (NN), Brick Identification, and total BF efficiency achieved so far:
Corresponding efficiency obtained in the previous studies:

20. As the next steps we plan:
1. to work on further algorithm optimization:
Now we find a muon track as a straight line in the front part of an event (10 first walls). In a case of strong hadronic shower presence the VSH method may not determine true MT direction. Moreover because of multiple scattering a MT in event is not represented by a straight line, so it was proposed to begin search of a MT from the back part of an event (using some other method, for example, Kalman Filter) and then extrapolate the MT through a shower.
2. to make better separation of neutrino events to classes:
Now we know the event type beforehand from the MC and use corresponding NN for the WF. In real life the type of a neutrino interaction for given event is unknown, so it is necessary at first to determine this type. Another way is to train NN on mixed types of events using some new classification rule.

21. The first obtained efficiencies for different types of events.
3. to implement the BF strategy with identification not just one but few most probable vertex bricks:
Using the vertex residual distributions we can determine relative probabilities of several bricks (in the found vertex region) to be a vertex brick.
The first obtained efficiencies for different types of events.
4. to generate sufficient statistics of realistic MC events making use of the information of calibration and commissioning of the TT.
The C++ code of the wall finding part of our algorithm is now included in the official OPERA CVS repository (WallFinder package).
BF eff-cy
1 brick
2 bricks
3 bricks
68.6
87.2
93.5
70.5
89.8
94.7
59.2
79.7
86.4