Finding charged tracks with silicon tracker in a high density environment is rather difficult in terms of efficiency and fake rate. Track fitting uses hits associated by the previous track finding phase, thus the proper functioning of this latter is essential.

In the actual track finding method seeding starts from pixels. Seeds are produced by combining pixel hits from the two innermost layers. If they are compatible, a further check is made on the existence of another compatible hit in the third pixel layer. Due to the combinatorical nature of the process, the number of possible combinations grows with track multiplicity N as N2.

The incoming charged particle leaves energy, charge in the channels (pixels or strips) of the detector. Neighboring channels are composed to form a cluster. The reconstructed cluster is regarded as a single hit. Up to know only the position of a hit, a kind of center of gravity for the cluster, has been used for track finding and fitting. It turns out that the length, direction and the average deposited energy of the cluster contain valuable information, as well.

This report consist of two parts. The first part explains how to extract the parameters of a cluster. They can be easily transformed to track parameters. The second part will discuss the possible applications of the obtained track parameters, such as:

  • fast vertex finding with clusters only, before track finding
  • reduction of compatible cluster seeds, resulting in faster tracking, higher efficiency and lower fake rate; in fact, track finding in track parameter space becomes possible
  • V0 finding
  • determination of the average energy loss of a particle (dE/dx)

Of course these advantages come at a price: a proper modelling of the detector is necessary with the use of some powerful tools from numerical analysis.

At the moment this study deals with barrel clusters only, but looks at both pixels and strips. The plots accompanying this study have been made for 1000 minimum bias p+p events and a single central Pb+Pb event.

Coordinate systems

In the global coordinate system the z-axis is along the beam direction. Both x- and y-axes are in the bending plane, they can also be decomposed to radial (e.g. pT) and azimuthal components. The electric field E is radial, the magnetic field B is in beam direction, the Lorentz-shift due to ExB is azimuthal.

The local coordinate system is attached to detector units. The x-axis is along azimuthal direction, y-axis is parallel with the beam direction, z-axis is radial. The relations of local axes to global directions and fields are summarized in table below.

Local axis Local direction Global direction Field direction
x width azimuthal Lorentz-shift ExB
y height beam Magnetic B
z thickness radial Electric E

For the sake of full use of space some of the detector units are "flipped". In case of un-flipped units the local z-axis points outwards in radial direction, while for flipped ones it points inwards. The direction of the electric field E is always in local z direction. As a result, the measured Lorentz-shift is always in positive azimuthal direction.


The parameters of a cluster can be transformed to track level. A charged particle at creation point can be described by four geometrical parameters:

  • polar angle θ, which is connected to pseudo-rapidity by cotθ ≡ sinhη
  • creation point along the beam line z0
  • initial azimuthal angle φ
  • signed curvature qκ, related to pT = 0.3 B / qκ

If the detector unit was segmented along the beam direction the parameters cotθ and z0 can be extracted. If the detector unit was segmented in the azimuthal angle the parameters φ and qκ can be obtained.

Barrel strips mostly lie in beam direction (segmented in azimuthal angle), thus they allow to measure φ and qκ. (In case of double strip layers the stereo part is rotated by 5 degrees, so those strips will not be perfectly aligned with the beam direction.) Barrel pixels are segmented in both directions, they allow to measure cotθ, z0, φ and qκ.

Relation between the average energy loss and particle momentum exists, based on an energy loss model ("Bethe-Bloch" curve), but only if the particle type, its mass, is assumed. Since it would introduce bias in track finding, it was kept to be a free parameter. As a result of this choice, the projection of the path of particle onto the plane of the detector unit is well-defined only if the size of the cluster is greater than or equal to three channels. In other words, the box containing the cluster has to be at least three channels wide in the desired direction. Still, even with box size of one or two channels the estimation of cluster parameter intervals is possible.

-- FerencSikler - 11 Jan 2006

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Topic revision: r5 - 2007-11-11 - FerencSikler
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