The Pattern Recognition issuefor the

Mu2e experiment

Giovanni F. Tassielli - giovanni.tassielli@le.infn.itG. Marconi University

FNAL

INFN Lecce

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The issue of the track reconstruction

Due to the Lorentz force :

a charged particle that is moving inside a Magnetic field deviates by its original trajectory.

p: particle momentum;q: particle charge;m: particle mass;B: magnetic field.

Bpm

q

dt

pd

By the equation we have that only the transverse (to the magnetic field) part of the particle motion is deflected. Therefore if B is a constant uniform magnetic field the particle will move with a circular uniform motion in the plane transverse to axis of the field and with a constant linear motion in the direction parallel to the magnetic field axis. This means that the particle will follow an helicoid path.

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The issue of the track reconstruction

Using some algebra it is possible to define some sets of equations that relate the parameters of the equation of the helix to the quantities that describe the particle(the equation on the right are form the BaBar experiment).

From these consideration we can conclude that the problem of measuring the charge, the momentum and the direction of a charged particle by using a tracking detector is analog to reconstruct an helicoid path into the space.

Now we have defined a strategy on how to measure what we need, but now we have some open questions:

How can we find an helix?And if will be there more tracks or we will have not only the proper points of the helix?

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The issue of the track reconstruction

The answer to this question seems simple, using a least square method we can fit the points to an helix and we can estimate its parameters. But in the real life the particles interact with the matter of the detector and they can be deflected by the ideal path, nevertheless we can assume that we are able to take into account these kinds of effects.

In this case we should fit all the potential helix, that means that we will take all the combinations of group of point and fit them. Like an example, if we have 60 point we have to fit all the combination of point by grouping them in group with more than 5 points (5 are the parameter of the helix):

How can we find an helix?

And if will be more tracks or we will have not only the proper points of the helix?

N comb= ∑k=6

k=60

60k ≈ 1.5•1018 ≈ 4 years (@ 10 GHz)

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The issue of the track reconstruction

The previous rough calculation tells us that we need a strategy to recognize which group of point must be fitted, we need a Pattern Recognition, so we can tell that the Pattern Recognition is a crucial issue for the success of a modern experiment of particle physic.

Roughly speaking, we can tell that a Pattern Recognition is a set of procedures and algorithms that can raise some peculiar aspect that are embedded inside the distribution of the points that were released by a particle track.

The Pattern Recognition task is more important for the Mu2e experiment too, look next slide. Despite to the fact that the Mu2e experiment will not be expected a large number of signal track to be reconstructed it will work in a very high noisy environment and so it will have to be able to recognize a track on a huge amount of other hit that will come from noise.

The G. Marconi group at FNAL is actively working on the Pattern Recognition for the Mu2e experiment.

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Example of what we will expect at Mu2e

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Example of the Patten Recognition that is under development

By using some ad hoc mapping algorithms, we are identifying the signal electron track over some noise.

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Thanks