Measurement of throughgoing particle momentum by means of

Measurement of through-going particle momentum by means of Multiple Scattering with the T 600 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

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 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 A. J. Melgarejo (U. Granada)

T 600 Event Reconstruction Muon Hits delta rays Decay Electron hits

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 A. J. Melgarejo (U. Granada)

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

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

Monte. Carlo 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 Ge. V § Momentum is measured independently for every muon A. J. Melgarejo (U. Granada)

Monte. Carlo Results Classical Method needs offline corrections to take into account energy losses

Monte. Carlo Results Resolution 20 % 10 %

Real Data Analysis § Monte. Carlo 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 Ge. V § This range is not optimal for Kalman Filter but if agreement between Monte. Carlo and real data occurs it is straifghtforward to extrapolate this result to higher energies A. J. Melgarejo (U. Granada)

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

Results (I) § Distribution of the computed momenta Momentum measured using Kalman Filter Momentum measured using calorimetry

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

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

Conclusions § The Monte. Carlo 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 Ge. V § 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 A. J. Melgarejo (U. Granada)

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