1. Measurement of through-going particle momentum by means of Multiple Scattering with the T600 TPC Talk given by Antonio Jesús Melgarejo (Universidad de Granada) On behalf of the ICARUS Collaboration Cryogenic Liquid Detectors for Future Particle Physics L’Aquila, 13 March 2006

2. A.J.Melgarejo (U.Granada) Why Multiple Scattering Methods?  The momentum of partially contained events can not be measured by calorimetry  However multiple scattering based techniques can be used  We explore two techniques to measure the momentum using multiple scattering:  Classical Method  Kalman Filter  As we will show, by taking into acount energy losses and correlation between measurements in adition to multiple scattering we are able to improve our resolution in momentum measurement

3. A.J.Melgarejo (U.Granada) The Classical Multiple Scattering Method  A particle traversing a medium is deflected through many small angle scatterings.  The resulting angle distribution follows the equation where p is the particle momentum and we are considering detector noise  By splitting a track in segments of a given length and measuring the RMS of the angle distribution it is possible to make an estimation of the particle momentum

4. T600 Event Reconstruction Decay Electron hits Muon Hits delta rays

5. A.J.Melgarejo (U.Granada) The Kalman Filter Technique  Kalman Filter is a technique to deal with noises that affect signals  It can distinguish multiple scattering effects from those asocciated to detector errors  It provides the best estimator for a state of a system after some steps in its propagation.  Energy losses and correlation effects can be included when computing the propagation  As far as we know Kalman Filter has never before been used in an homogeneous non magnetized medium

6. A.J.Melgarejo (U.Granada) Predicted Position Measured Position Filtered Position Smoothed Position Practical Case: Particle Traversing a Medium Final Prediction of Kalman Filter Predicted Trajectory Smoothed Trajectory Filtered Trajectory

7. The Kalman Filter Technique State vector evolution Measurement vector Noise in the system Noise in the measurement Angle between segments in the present step. Related with momentum through Multiple Scattering formula Positions Slopes Measurement Matrix Multiple Scattering Noise in the detector Transportation Matrix Incorporates energy losses The complete set of used formulas can be found on R.Fruhwirth, Nucl. Instrum. Meth A 262 444 (1987)

8. A.J.Melgarejo (U.Granada) MonteCarlo Simulation  We make a full simulation using the FLUKA package  Electronics and detector noise are simulated with ICARUS collaboration software  We generate samples of 1000 muons with initial momenta in the range 0.25-3 GeV  Momentum is measured independently for every muon

9. MonteCarlo Results Classical Method needs offline corrections to take into account energy losses

10. MonteCarlo Results Resolution 20 % 10 %

11. A.J.Melgarejo (U.Granada) Real Data Analysis  MonteCarlo analysis shows that Kalman filter is an optimal method for momentum measurement  To confirm this fact we will study a real data sample  We use a set of 1009 stopping muons whose momentum, known by calorimetry, is below 1 GeV  This range is not optimal for Kalman Filter but if agreement between MonteCarlo and real data occurs it is straifghtforward to extrapolate this result to higher energies

12. A.J.Melgarejo (U.Granada) Momentum measurement using calorimetry  Measured energy is related to deposited energy by the formula: Measured and published by ICARUS Collaboration Measured individually for every event This will be our reference momentum

13. Results (I)  Distribution of the computed momenta Momentum measured using calorimetry Momentum measured using Kalman Filter

14. Results (II) Kalman Filter results are in good agreement with calorimetry Momentum measured using calorimetry Momentum measured using Kalman Filter  Profile of the measurements

15. Results (III)  At last, we split our sample using the calorimetry measured momentum on 100 MeV intervals  For each event on each interval we compute the relative error between Kalman Filter and calorimetry momenta  We plot for each interval the mean and the RMS of this magnitude distribution On average Kalman Filter and Calorimetry differences are very low Errors decrease with increasing momentum and values are in agreement with MC simulations

16. A.J.Melgarejo (U.Granada) Conclusions  The MonteCarlo analysis shows that Kalman Filter is a good tool for momentum measurement of partially-contained particles in liquid argon TPCs  The real data analysis shows that momentum can be measured with an error of the order of 15% being optimal in the range of a few GeV  This tool is optimal to study non contained atmospheric neutrino events  Kalman Filter based techniques will be a powerful tool for momentum measurement in future liquid argon neutrino detectors

17. The End