Going beyond the cell level

The ECAL-standalone Charge Estimator (EQE)

Ce chapitre conclut l’étude des performances du calorimètre électromagnétique

par la construction d’un estimateur de charge nucléaire utilisant uniquement

ce sous-détecteur. Une étude est menée afin de déterminer la pertinence

d’aller en-deçà de l’unité simple de la cellule, utilisée jusqu’ici, pour descendre

au niveau des fibres. Une modélisation tridimensionnelle du calorimètre

est réalisée, et ses résultats analysés sur des simulations et des données

faisceaux. Un estimateur est enfin construit grâce à une méthode de maximum

de vraisemblance utilisant l’énergie déposée dans les couches au MIP. Ses

performances, en fonction du nombre de couches touchées et de la charge des

particules incidentes, sont précisées. Des corrections pour les charges au-delà

de l’oxygène sont enfin appliquées.

—

6.1. Going beyond the cell level

6.1.1. Cell position correction

Until now, the best level of precision reached when computing MIP, for example, was

the cell. While it is sufficient for the purposes exposed, like monitoring the MIP on a

day-to-day basis, for which the main uncertainty sources come from other parameters

(low statistics, accuracy of the fit), our goal is to know whether it is possible, or not,

138 Chapter 6. The ECAL-standalone Charge Estimator (EQE)

to go beyond this level. In fact, in the energy reconstruction from ADC hits, besides

attenuation and equalization, another correction is applied. The Figure 6.1a recalls the

structure of a single PMT. We can see that four light guides are used to collect the light.

The shape is such that, between the guides, in the middle and on the edges of each

PMT, the light can not be collected. It reflects in the signal collected, as can be seen in

Figure 6.1b, taken during the scan of fibers in the BT 2007 campaign, which shows S

,

the energy in the most hit cell, with respect to the position of the beam, in cell units, 36

being the center of each layer.

(a)PMT along with 4 light guides (b) Signal collected by scanning position of a

PMT [GR08]

Figure 6.1.: Structure of the light guides inside a PMT. We can see small dead zones in the

middle and edges of the PMT, which reflects on S1, the signal of the most hit

cell.

A correction is applied in the official software (see [GR08]), but to take precise

measurements in the high-gain channel using ADC hits, this is the first (and main) effect

which has to be taken into account. The goal of this subsection is to know whether it is

necessary for our purposes to go beyond that level.

6.1.2. Fibers

The light guides mentioned in the previous Section collect the light from fibers, which are

enclosed in a lead sandwich whose role is to trigger the shower, as can be schematically

seen in Figure 6.2a. The optimal configuration to get an homogeneous response would

be one with a maximum compacity (the center of fibers making “equilateral” triangles),

which is not the case (two adjacent fibers of the same layer in the lead are closer than

6.1. Going beyond the cell level 139

the closest fiber of any other layer). The question is to know if this has an impact on the

energy reconstruction.

(a) 3D representation (b)Dimensions of the fibers and lead

Figure 6.2.: Representations of fibers enclosed in the lead of the ECAL

The signal deposited in the ECAL is proportional to the length of fiber crossed, known

as path length. This Section will try to estimate it the most accurately possible.

6.1.3. First 2D model

The first efforts to motivate the need of this path length measurement and estimation

were triggered in [Oli11]. The path length was computed using the simple 2D model

shown in Figure 6.3.

Figure 6.3.: 2D model of path length in the calorimeter [Oli11]

We keep theX coordinate from the Figure and its origin (distance in centimeter from

the edge of a PMT, along the layer), but, for the other axis, following the conventions

for the AMS coordinates, define the Z axis going down. The path length is computed

140 Chapter 6. The ECAL-standalone Charge Estimator (EQE)

by scanning the layer in two dimensions. By noting xind0the X coordinate of the edge

between the two first layers (x

= 0.92cm), the first scanning parameter is theX axis,

where the range goes from x

to 2x

. The other dimension is the angle θ

such that

tan(θ

)≡(x

−x

)/z

, where x

and z

are the coordinates of the impact point at the

bottom of the layer.

The results, expressed in units of crossed diameters, are shown in Figure 6.4. In this

basic model, the path length crosses a wide range going from 0 to 5; the white areas are

the ones for which the particle crosses only the lead between the fibers. It appears that,

for certain angles (where tan(θ

) ≈ ±0.4), by moving to a 0.5cm distance in the X

coordinate, a path length of 0 or 5 fiber diameters can be crossed. Therefore the need to

compute a more sophisticated model to see if those effects remain.

Figure 6.4.: Path length results from the 2D model

6.1.4. Drawbacks of the 2D model

The previous two-dimensional model suffers several drawbacks.

The unit of the result is unpractical Of course, it could easily be transposed from

fiber diameter to centimeters.

A single layer was taken into account A complete model, using both unequally spaced

layer in the dimension at stake, and the path length in the perpendicular layers, could

average the inhomogeneities observed.