AndrewSpano
commented
3 years ago -
For the second bullet:
Plotted the number of hits for of every particle for a specific event. Made some observations regarding the "most common" number of hits, which is 14. I wanted to see if this holds for most (if not all) the events. So I computed the number of hits of every particle for all the events:
which suggests that our initial thought was correct.
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For the third bullet:
I started by plotting all the tracks for one event:
Of course, this does not provide much insight. Let's take the hits for one particle only:
We would like to fit a circle in this track (since ideally the particle follows a circular trajectory). Effectively, we want to learn a radius and a center. Since a function must have only one output (and in the Cartesian circle, any "x coordinate" may correspond to 2 "y coordinates"), we can use a transformation to the polar coordinates system. This will transform the circle into a straight line, which will allow us to use linear regression to fit it. The coordinates in the polar plane will look like this:
Since we only have a few datapoints (on average 14 hits) we should make sure not to overfit the given data. That's why we will use Ridge Regression, a Linear Regression algorithm that uses regularization. The polar coordinates will be fit like so:
which will translate in the following curve in the Cartesian plane:
After having computed this chord of the circle, we can sample any 3 points from it in order to recreate the actual circle. Note that those 3 points are not from the given dataset, they are estimations that the regressor has made. The circle we will find is:
Using the radius we found from the circle, we can compute the estimated transverse momentum and compare it to the ground truth like so:
which yields quite accurate results.
asalzburger
noemina
In
data/pdg13-n25-0.5to10GeV-0.5etathere are more complicated input files. The simulation is now done withInfo: curvature, magnetic field, particle mass.