The charge measurement is performed using pixel clusters. Pixel clusters are groups of hits from neighbouring pixels. The charge is the sum of charge of each pixel in the cluster. Only clusters in the barrel, containing no ganged pixels, are studied. In addition, clusters with a pixel in either the row or column adjacent to the module edge are discarded, as well as clusters containing more than one pixel in the long pixel direction. Clusters are required to be associated with a reconstructed track, and hence termedclusters on track, to remove any clusters from noise. Tracks are required to have at least two hits in the Pixel Detector barrel and a significant number of hits in the remaining inner detectors: 5·SCT Barrel Hits + TRT Barrel Hits>= 30[84].
The track propagation distance in the sensor is related geometrically to the track incidence angle: l=t/cosα, wheretis the sensor thickness. During module production, the average sensor tile thickness was measured to be253.7±0.7µm [85]. However,∼3.6µm of this thickness is inactive because it consists of inactive metallisation layers and depositions of silicon-oxide and silicon-nitride on the sensor surface. Therefore the average active thickness is 250.1µm. The simulation used a constant sensor thickness of 250µm.
Thetotaltrack incidence angle,α, is defined relative to the normal vector to the module surface.
It is calculated from the two component track angles as tanα = ptan2θ+ tan2φ. The angle θ is directed in the long pixel direction andφin the short pixel direction. For barrel modules, θ is the angle in thez-direction and φcircles around the barrel. Figure 5.13 clarifies the relationship between the three incidence angles.
Asαincreases, the total amount of deposited charge increases. Using Eq. 5.3 a 15% increase in the MPV of the deposited charge is expected (from 19.0 ke to 21.8 ke), whenαincreases from 0 to 0.5 radians. This variation must be taken into account in finding the MPV. Fits are made in bins of the track propagation distance. The fits are also performed separately on clusters containing either one, two or three pixels in theφdirection.
At largeα, despite the large cluster charge, the charge per pixel is small because the cluster size is also large. If the charge per pixel is near threshold, the cluster can split and be reconstructed as multiple clusters. This effect, which occurs at largeα, biases the charge to low values. Therefore clusters are vetoed if an additional cluster is reconstructed within the same module. As cosmic-ray
α= atan( tan ( ) + tan ( ) )2φ 2θ x φ l = t tan( ). y θ l = t tan( ). l = t/cos( )α normal to module plane θ φ t
Figure 5.13: Calculation of the total track incidence angle,α, from the component track incidence angles. The angles are shown with the module orientated horizontally and the normal to the module surface vertical. The labellxis the track propagation distance in the short pixel direction andly is the propagation in the long pixel direction[68].
events typically contain a single track and a noise rate of10−10 hits/bunch crossing/pixel [1], the number of clusters lost due to an additional track or a noise hit in the same module is negligible [36]. When the magnetic field is on, the electrons produced in the module by a traversing particle drift at an angle known as the Lorentz angle (see [43]). For the barrel modules, the drift is in the positiveφdirection. For track angles&0.1rad, the cluster size is smaller for the magnetic field on than off. For angles.0.1 rad, the opposite is true, i.e. the cluster size is larger for field on than off. See [36] for further discussion on cluster properties with and without the magnetic field.
The particle momentum can only be measured for the field on data. Ideally, only tracks with
p > 50 GeV would be used to match the particle momenta used in the theoretical calculation, but as the cosmic ray spectrum decreases rapidly with momentum, this would retain insufficient statistics for the measurement. Therefore a cut ofp >5GeV is implemented to limit the bias from low momentum tracks. This results in a measured energy loss corresponding closely to that of a muon withp= 5GeV because the number of tracks decreases rapidly with momentum. The field off measurement is expected to be slightly biased to low values, because no cut on momentum can be applied.
Table 5.1: The number of tracks and clusters of cosmic-ray data and cosmic-ray simulation samples.
Data Simulation
Field Off On Off On
Tracks 131338 126017 178070 184646
Clusters 1234663 1302766 2112396 2111490
Clusters On Track 586853 576687 817280 816519
Good Clusters 443026 437027 661509 657044
is defined as a cluster passing all cuts used for the charge scale measurement.