[en] Large angle two-body hadronic scattering was studied between 3 and 12 GeV/c by the WA 13 experiment at C.E.R.N. (Omega Spectrometer), with a negative RF separated beam, on a hydrogen target. The cross sections of these reactions, at fixed c.m. angle, decrease very rapidly with the energy; then high beam intensities were required together with high selectivity, obtained thanks to a multilevel triggering system, including a coplanarity chamber associated to a fast logic. This thesis describes the reactions with two charged final particles (π^-p, K^-p, antipp elastic scattering and antipp annihilation into two mesons). The kinematical reconstruction eliminates the background almost completely. More over a special vertex fitting method improves the reconstruction of the tracks, using their convergence at the same point to increase the geometrical information. Neglecting fixed t structures, the differential cross sections are compatible with the dimensional counting laws (however elastic antipp seems to decrease less rapidly than expected). Different models are compared with the results: no one agrees with the whole set of available data. This work emphasizes the handling of error matrices and the use of optimal estimation. It proposes a recursive track fitting method, optimized with respect to the multiple scattering

[en] A direct numerical algorithm (without Monte-Carlo evaluation) is proposed to compute the error matrices on optimal estimator of trajectory parameters in a track detector, assuming gaussian errors on the raw measurements, and including, if needed, the effect of multiple scattering. Approximations are given for the case of helix trajectories

[en] A least squares method is proposed to fit the geometrical parameters of a set of curved tracks assumed to originate in a common vertex: the parameters measured independently for each track are first extrapolated with their weight matrix to a point close to the expected vertex position; then a local parabolic parametrization of the trajectories is used in a fast fitting procedure, where all parameters (vertex coordinates and track parameters) are modified at each iteration: the global amount of computation is roughly proportional to the number of tracks. Moreover this formalism is well suited to add a track to an existing vertex, or to remove a track from it

[en] In some problems one has to perform a least squares fit on a large sample of data, with few general parameters and other ones particular to small data subsets. Examples are given, and a method is proposed to vary all parameters at each iteration (ensuring optimal convergence) while keeping the amount of calculation roughly proportional to the number of parameters

[en] A trajectometer is made of layers of charged particle detectors which measure successive positions along the trajectories; it is generally immersed in a magnetic field, so the curvature of the trajectory provides a measurement of the momentum. A method to perform a progressive fitting of the trajectory (Kalman Filter formalism), incorporating the measurements one after one, with an optimal account for the perturbations (multiple scattering, energy loss), is described with some indications for practical implementations in realistic detector layouts. Useful byproducts of the method and tests of validity are discussed. The procedure appears to be a combination ad libitum of elementary operations on vectors and matrices of fixed dimension (the number of parameters needed to define the trajectory), affording very flexible strategies, including a coupling of the pattern recognition of tracks with the fit of the trajectory, and combination with calorimetric or timing measurements. Extension to non-gaussian errors is discussed. Once the trajectories of an event are independently reconstructed, they may be extrapolated back to the region of production of the particles (target, or zone of intersection of the beams in a collider) and associated to one or several vertices (primary interaction, and possible secondary interactions or decays): a fast and flexible method is described to perform these operations and improve the geometrical reconstruction, hence the kinematical one, by the constraint of a common origin; additional constraints may be added. Here again, the elementary steps consist in linear operations on vector and matrices of fixed dimension, allowing the user to easily proceed by successive trials and to optimize the strategy. (authors)

[en] An analytical calculation of the variance is performed, in some simple cases, for standard least-squares estimators of track parameters (accounting for independent measurement errors only); comparison is made with optimal estimators (accounting also for scattering errors, correlated between one point and the following ones). A new method is proposed for optimal estimation: the points measured on the track are included backwards, one by one, in the fitting algorithm, and the scattering is handled locally at each step. The feasibility of the method is shown on real events, for which the geometrical resolution is improved. The algorithm is very flexible and allows fast programmation; moreover the computation time is merely proportional to the number of measured points, contrary to the other optimal estimators. (orig.)

[en] A progressive recognition of charged particle trajectories is proposed: starting from a small segment, the tracks are extended by adding points one after another; the fitted parameters of the trajectory are updated at the same time (using a Kalman-like formalism), thus giving an increasing precision on the prediction to the next point. This method was implemented in the DELPHI TPC off-line analysis: a flexible strategy is associated with this general principle in order to cope with specific problems (overlap and edge effects, error tails, etc). A generalization of the method to more general configurations of tracking devices is proposed. (orig.)

[en] A brief summary is presented of the results obtained so far from a K^-p formation experiment carried out in the 200 HBC at CERN. It provides new data at a level of approximately 10 events/μb in the mass region 2200 MeV to 2450 MeV which covers the resonant peaks found by counter experiments in the I = 1 at 2250 MeV and I = 0 at 2350 MeV and its main motivation is to study in detail the Jsub(P) structure of these peaks. A discussion is given in some detail of the quasi two body reaction K^-p→Λω and the two body reactions K^-p →Σ^-+π^+- and K^-p→ antiKN. In the last section however, for completeness a summary is given of all the results on the new resonances parameters, including the channels Λπ⁰ and Ψ*⁰K⁰ already published. For the other quasi two body channels Y*π and K*N a complete amplitude analysis of the type carried out for the reaction Ψ*K is in progress. (author)

[en] A progressive track finding algorithm based on the Kalman filtering method has been proposed and tested for the track reconstruction in high energy physics experiment. The algorithm starts from small track segments with fitted track parameters and weight matrices or from fitted tracks of a neighboring detector, then extends the candidate tracks by adding measured points one by one. The track parametes and weight matrices of the candidate tracks are updated at the same time of each point addition. Therefore at the end of the track finding, the track fitting is accomplished simultaneously. The main procedures and its advantages of the algorithm are presented. Its performance is briefed

[en] A fast vertex fitting algorithm has been tested, which uses a local parametrization of tracks around a fixed point. This point is chosen to be close to the primary and short-lived secondary vertices, or to the decay vertex of a long-lived particle; hence useful approximations may be utilised. The extrapolation of the trajectory and its error matrix to the vertex region is performed once per track, even if the track association procedure needs to be iterated. The time spent on the computation of the fitting procedure is proportional to the number of tracks (n) instead of n³ as in a standard least-squares method where the parameters of all tracks are fitted together at their common vertex. The method is used in the LEP experiment DELPHI at CERN. The Monte Carlo test has been made for the ZEUS experiment at DESY. The vertex fitting quality and the time consumption etc. have been examined. (orig.)