Simulation - Particle Tracking - Calibration and Performance of the MICE Scintillating

Chapter 3 Calibration and Performance of the MICE Scintillating

3.7 Particle Tracking

3.7.1 Simulation

The simulation of the MICE trackers is achieved with a Geant4 based package, where the materials and geometry of the tracker and solenoid are accurately represented. The solenoid and other MICE magnets are modelled based on their current and coil configurations. The field maps for the magnets are generated at the start of the simulation run. A number of different algorithms can be used to generate the map from geometry, or an externally generated or measured field map can be used. The electronics is modelled with a simple approximation to the relationship between light yield and ADC counts, depending on general values for the fibre attenuation, quantum efficiency, gain and other parameters. Once the light yield in the fibre has been estimated from the energy deposition, it is converted into an ADC count and smeared with a Gaussian distribution.

3.7.2 Reconstruction

The simulation and reconstruction framework for the trackers, G4MICE, arranges this reconstruction process in layers. The initial state involves unpacking the data into a primary hit class which stores the raw information obtained from the AFE boards, called a VLPCHit. The hit stores the electronics channel information, along with the data obtained from the front end (ADC, TDC, discriminator). The equiv- alent step in simulation is handled by a SciFiHit which stores the Geant step energy deposition along with time, momentum, position and detector information such as the fibre through which the particle passed.

Digits

Reconstruction of digits from raw AFE information is performed with the DigitRec function. In order to ascertain which channels observed a large enough light yield to be considered as signal candidates, their numbers of photo-electrons must be calculated. To convert the recorded ADC count for this channel into photo-electrons,

the pedestal and gain for this channel are retrieved from a calibration class. The method of obtaining these calibration values was described earlier in Section 3.6.4. Once the number of photo-electrons in a channel has been calculated, a cut is made on it. This is an arbitrary cut designed purely to limit the presence of noise and was initially implemented in the absence of zero suppression. With the discriminators calibrated and active, such a cut may no longer be required.

The mapping of the electronics channel to the physical fibre is also performed at this stage. There is a direct correspondence between a single electronics channel, which is defined by three integers signifying the AFE board, VLSB bank and DF- PGA channel number, and the fibre which is also defined by three integers signifying the station, plane and fibre number. The mapping of electronics channel to physical channel is stored externally and retrieved with a cabling class. The resulting SciFiDigit therefore records the physical channel, time and light yield for a given event, and is kept if its light yield is above threshold.

Clusters

Given the overlap between fibre ribbons it is possible that a single particle can pass through two channels, generating two separate signal hits. In order to avoid this degeneracy, any two digits which are adjacent, above threshold and in the same event are combined into a cluster. Any remaining digits without a neighbour are also converted into clusters. The initial implementation of this process did not consider the possibility of electronic or optical cross-talk, and therefore only a maximum of two adjacent clusters were ever combined. An investigation into cross-talk at the reconstructed level is presented in Section 3.8.3.

Next, the physical position of the cluster centre is calculated and stored in

the SciFiDoubletCluster object. With the central fibre number being a defined

parameter at x = y = 0, and the width of each channel and its orientation also

defined, the position of the centre of the cluster is calculated by its deviation from the central channel and a coordinate transformation from the orientation of the plane.

Space Points

The overlapping of clusters in different planes provides a 2D region through which a particle may have passed. The triplet active regions for each station in tracker one can be seen in Figure 3.22, where the positions have been found by Monte Carlo and cut for one half of the active region. The three planes within each station provide a

number of combinations in which clusters can overlap; in the instance in which all three possible clusters produce a signal above threshold, and all three are combined to form a space point, this type of point is labelled a triplet. In the event of only two clusters overlapping, the space point is termed a doublet.

The clusters are iterated over and possible combinations are passed to an algorithm which decides whether the clusters should form a triplet or doublet, and keeps or rejects the candidate space points based on the sum of the triplet’s constituent channel numbers. Beginning with all possible triplets, defined by clusters in the same station but different planes, the channel numbers are added and tested to see if they fall within a certain range.

The channels within each plane are numbered in such a way that if a point is taken anywhere in the active region of a station, the sum of the channel numbers covering that region will equal the sum of the central channel numbers. The vector

sum of this addition is given in Equation 3.7, whereui, vi and wi are the channel

numbers of the clusters in the triplet, andu0, v0 andw0 are the channel numbers at

the centre of the plane, as shown in Figure 3.21. This is well proven from data from the first cosmic ray test, where this algorithm was not used (a cut on the internal residual, or separation of the clusters, in combination with higher light yield cuts was used instead).

x u

v w

Figure 3.21: Station plane channel ordering, with a constant vector sum of 0 for triplet points.

tri= (ui+vi+wi)−(u0+v0+w0) = 0 (3.7)

Once this conjecture had been proven from data (as shown in Section 3.8), it could be used as a method of verifying the quality of a space point made from three clusters. In this way, it forms the major component of the space point pattern recognition. All clusters are sorted into station and plane and ordered by their light yields (low light yield clusters had a detrimental effect on the space point finding, as is discussed later). Clusters in the same station but different planes are then combined to form triplets and tested to see whether the sum of their channel numbers lies within an acceptable range; if so, the point is kept and the constituent clusters removed from the list.

Once all possible combinations of triplets have been considered, the remaining clusters are formed into doublets and tested to see whether the resulting space point lies within the tracker active volume; if so, the point is kept but the clusters remain within the search.

The intrinsic error on each space point depends on the physical area covered

by the overlapping fibres. Since the tracker stations contain three planes at 120◦

to each other, the active region can take many shapes, and hence the errors will differ depending on these shapes. In order to fully test the treatment of the fibre combination in the reconstruction and simulation, a high statistics simulation was performed without multiple Coulomb scattering or energy loss considered in the physics list. This allowed an investigation into the effects of the tracker geometry on the space point error without other effects. Using the results of the MC residual

with the position of the space point, thex−yerrors of each type could be considered,

albeit without the added complication of the overlapping regions. A full treatment would ideally consider all possible combination of overlapping regions, or ideally

keep the unbiasedu−v−wreference frame and perform a track fit with the original

clusters.

By plotting the MC position of a particle in each station, and making re- quirements on the sum of the channel numbers, the effect of this requirement and the overlapping region for a triplet space point can be seen. This is shown for tracker 1 in Figure 3.22.

Pattern Recognition

The set of accepted space points is then used by the track reconstruction for pattern recognition and fitting. The pattern recognition algorithm finds sets of points likely