IMPLEMENTACIÓN DE LA SOLUCIÓN ALTERNATIVA EN TERRENO

The generators use an occupation grid for generating hits. Each bit in the grid represents a small volume in 3-_d space. The grid is used to avoid generating multiple hits with similar coordinates and takes into account that hits cannot overlap in the emulsion. The hits, like in real data, can still be spaced arbitrarily close, because the position of a hit inside a grid cell is random. The occupation-grid’s cell size reflects the scanning microscope’s resolving power for neighbouring grains (xy). The spacing in depth (z) is set either to a fixed layer spacing or to the microscope’s depth of field, depending on whether the generators are setup for fixed layers or for real 3-d hit positions. When hits are generated for fixedz-layers, the generated 3-d hit positions are projected onto the layer. For hits on a track, the slope of the track is thus not taken into account, in accordance with the grains seen by the microscope. Any grain detected in the depth of field of the microscope is assigned az-coordinate at the center of that layer.

142 track finding in emulsion

Background generator

The background generator is rather straightforward. It generates uniformly distributed random positions for a requested number of hits. The hits are marked as background to distinguish them from hits belonging to tracks. Track-correlated background hits (like delta-rays) can be important in the real data. However, this is not simulated.

Track generators

The track generator is chosen at run-time. The simplest track generator creates straight tracks. An extended version, used in the results presented in section 4.4.4, distorts the tracks using a simple distortion model explained below. The basic track generator is set up with the following parameters: fixed layers or free 3-_dcoordinates; a variable number of tracks originating from a common vertex; the range in z where tracks can start and end; a minimum track length in case a track leaves the volume; and a distribution for the track slope (θ) with respect to the z-axis. Another set of parameters determines the distribution of hits along a track: the hit residual, defined as the sigma of a normal distribution modelling the perpendicular distance to the track; the probability of having a hit on a layer in the case of discrete layers, or the parameters of a Poisson distribution for free hit positions. In the chorus experiment, the number of hits per unit track length for a fixed number of layers is accurately described by a binomial distribution. This binomial distribution is the cumulative effect of, among others: intrinsic emulsion sensitivity, blind spots in the emulsion, microscope depth of field, layer spacing, image filtering, and grain detection. The use of a constant hit probability per layer is justified because it also leads to a binomial distribution for a fixed number of layers. When using free hit positions, the response of a uniform emulsion to a traversing particle is modelled. The model uses a fixed probability per unit length of having a developed emulsion grain. This also leads to a Poisson distribution for the number of grains on a fixed length of track.

For the distorted-track generator, only the most common form of distortion is mod- elled. One end of the tracks (atz= 0) is shifted by a random distanceδfrom its original starting point. The shiftδ(z) is a quadratic function of z, such that the original track’s direction is preserved atz = 0, dδ(z)/dz = 0|z=0, and the track’s position at the other

end is fixed,δ(zmax) = 0.

In the results presented here, no vertices were generated. Hits close to the vertex can usually be assigned to multiple tracks, an effect which requires a study by itself, but is not relevant to the track-finding efficiency discussed here. The other settings were chosen to reflect the typical _chorusemulsion scanning values: 25 fixed layers of 4µm thickness; tracks enter from the bottom at z = 0 and exit via the top or sides of the volume; minimum track length for detection is 14 layers; and a±300 mrad wide uniform distribution of track slopes. The hit residual is set to 0.38µm and the probability of detecting a hit on a layer is set to 75 %, lower than that of the real data which has 86 % hit efficieny per layer. The goal of this study is to estimate the track-finding efficiency for recognizable tracks, therefore tracks which have not enough hits to pass the final acceptance criteria of the criterion class (see section 4.4.2) are discarded. Distortion parameters were set according to a normal distribition with a mean shift of 0µm and a sigma of 5µm for all tracks in a single set. Each track has an additional random shift with a sigma of 0.63µm, 1.7 times the assumed track residual.

The track hits are merged with the generated background. In order to compare recon- structed tracks on a hit-by-hit basis with the generated tracks, the track to which each hit belongs is recorded. In the analysis of reconstructed tracks, the Monte-Carlo track with the largest number of hits in a reconstructed track is considered to be the matching Monte-Carlo track. A reconstructed track with only background hits is considered a fake track.