1. Localization of a Neutrino Interaction Vertex in the OPERA Experiment S.Dmitrievsky, Yu.Gornushkin, G.Ososkov (JINR, Dubna) Gran Sasso, Italy, November 23, 2005

2. Our group from the Joint Institute for Nuclear Research (JINR) in Dubna is deeply involved in the TT detector construction. Now we started to work on TT software development as well. My talk is devoted to our studies of the problem of brick-finding (BF).

3. An essential issue in OPERA is the finding of the brick where the neutrino interaction takes place.

4. Outline: 1.Short review of the previous studies. 2.Our BF algorithm description. 3.Comparison of two neural networks. 4.Preliminary results. 5.Conclusion and outlook.

5. The goal of our work is 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. 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” counts; -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: Non-muonic events: – 72.5% for electronic and 68.1% for hadronic -decay Muonic events: -72.4% The brick finding problem The main obstacle of BF is back-scattered particles (BSP): Vertex Z Beam

7. Our BF algorithm: 1. Event cleaning using the cellular automaton approach; 2. Event classification by their topology in the TT; 3. Muon track recognition applying the Hough transform; 4. Principal shower axis reconstruction using a line-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 Z Beam

9. 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 three classes depending on the number of the hitted 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 hitted TT walls; ( A TT wall is defined here as a composition of X and Y TT planes ) 2. Events with more than two hitted walls and a mean number of hits/plane less than 2.5; 3. Events with more than two hitted walls and a mean number of hits/plane more than 2.5.

10. 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. X-Z projectionY-Z projection Muon Identification 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.

11. Robust Fitting Method for a shower axis reconstruction Two simple examples, when Least Square Method (LSM) does not work: a) point - outlierb) uniform contamination In both cases the crucial assumption of residual normality is violated so we propose to replace the Least Square functional Σ i ε i 2 by the other one L(p,σ)=Σ i ρ(ε i ) (1) where ε i 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 ε i. ε 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.

12. 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. - w i (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. 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. Weight function Amplitude of hits X-Z projectionY-Z projection

13. 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 are equal to 14. The input variables are the follows: for the first 3 hitted TT walls:  Total amplitude of hits in a particular wall;  Number of the 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, are also included to the input parameters to train the NN.

14. Distributions of the energy ratios in the first three hitted walls. E2/E1 E3/E2 E2/E1 No BS 1 BS wall in front of a vertex 2 BS walls in front of a vertex

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

16. MLP(CG) vs SNNS OCT MCMLP(CG)SNNS EfficiencyMSEEfficiencyMSE 8000 ep. 40000 ep. 2 cl. 84.4  2.9 0.249 84.8  3.5 0.2470.234 3 cl. 84.1  3.4 0.199 84.9  3.1 0.1990.189 2 cl. 85.2  3.6 0.224 85.8  3.2 0.2280.212 3 cl. 84.9  2.6 0.207 85.0  2.6 0.2090.196 2 cl. 79.9  4.6 0.269 78.9  3.8 0.2850.271 3 cl. 83.2  3.5 0.226 83.6  2.9 0.2250.217 3 cl. 89.5  3.6 0.178 90.2  3.8 0.1740.165 3 cl. 84.4  3.1 0.197 86.5  2.4 0.1870.178 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.

17. Vertex residual distributions in X and Y planes

18. Preliminary results Available October Monte-Carlo statistics: Wall Finding, Brick Identification, and total BF efficiency achieved so far: * Statistics is insufficient Corresponding efficiency obtained in the previous studies: Necessary statistics should be at least 20000 events! OCT MC DATA 2 class3 class traintesttraintest 9000100090001000 **60001000 **70001000 9000100090001000 4000100090001000

19. As the next steps we plan:  to work on further algorithm optimization;  to implement the BF strategy with identification not just one but few most probable vertex bricks;  to make better separation of neutrino events to classes;  to generate sufficient statistics of realistic MC events making use of the information of calibration and commissioning of the TT. Conclusion and outlook Though the wall finding efficiency for the studied neutrino reactions is the same as in the previous works, our current BF efficiency is lower. It may be because of lack of MC statistics, of some difference in MC samples, not optimal algorithms, etc.