Charge Sharing & Hit Identification & Cluster Information

Charge Sharing ● Whenever a strip is hit by a particle, the adjacent strips will share some of the deposited charge? ● For the strips with a small pitch, can the same particle cross 2, 3 or even 4 strips? ● How big is this “charge sharing” effect? ● How to distinguish these two phenomena? ● Using a chi² probability cut of 1e-6 we get the following histogram of signal distribution:

What do we gain? ● As we can see from the previous histogram, the adjacent strips have an average of over 50% signal of the strip with the hit. ● This happens because of the cases where a particle originates a signal on two neighbor strips. ● As it turns out, almost all hits have a simliar (smaller) identic signal shape on (at least) one of the adjacent strips and sometimes there are clusters of 3 or 4 strips with the same signal shape ● This can may be used to get a better spacial resolution, deposited charge, but maybe, also, to improve the hit detection method

Charge Sharing and Multi-Strip Hit ● How to tell apart these two efffects? ● Can both these cases occur? If so, we would see smiliar signals: BeamBeam Charge Sharing Multi-Strip Hit

● Here we can see two adjacent strips with similar (tipical) pulse shape ● Here we can see three adjacent strips with similar (tipical) pulse shape. The leftmost is much smaller than the others, but the pattern is still visible

● Here we can see four adjacent strips with similar (tipical) pulse shape. The leftmost one (strip -2) might not be from the same particle ● Another set of four adjacent strips

● This can happen even for “non standard” pulse shapes, has we can see in this hit and it's left neighbor ● Here is something that is detected as a hit but is most likely a fake, because the even though the signal is high, the neighbor strips have a completely different pattern!

How to use charge-sharing to help in hit identification? ● There is a small probability of having a noise pattern that looks like a signal, but the probability of having two adjacent identical noise patterns is much much smaller. And so the search for a good pattern matching method begun! ● 1 st method was a simple “Dot Product” ● 2 nd method was a “Chi² Test” ● 3 rd method was a “Linear Fit” with a Chi² cut ● 4 th method was the “Entropy Distance”

What is Relative Entropy ? ● Let a discrete distribution have probability function pk, and let a second discrete distribution have a probability function qk. Then the relative entropy of p with respect to q, also called the Kullback-Leibler distance, is defined by: ● Although relative entropy does not satisfy the triangle inequality and is therefore not a true metric, it satisfies many important mathematical properties. For example, it is a convex function of pk, is always nonnegative, and equals zero only if pk = qk.

How can we use it? ● We used a more “simmetric” formula to determine the “distance”: ● It is a great way to measure the distance between two discrete distributions! ● Next we can see two plots. One for the lowest entropy distance and one for the highest one

Practic use of the Entropy Cut ● We can now use an “Entropy Cut” to help determine adjacent hits and get a better idea of the hit proportion ● Using an entropy cut of at 0.7, we are able to detect new adjacent hits and we obtain the following results for cluster ratios

Cluster Ratio ● Cluster ratio for background probability cut of 0.02 ● Cluster ratio for background probability cut of 1e- 6

Some estimates of the hit proportion ● 30% of the hits generate a pattern on 3 adjacent strips ● 40% generate a pattern on 2 adjacent strips ● 30% only have a signal shape on the strip with hit TODO: Cluster ratio for different sensor zones to see how the cluster size changes with strip pitch and length

Conclusions ● The Entropy Distance is a great method for finding adjacent hits to already identified hits, and therefore, increase the cluster size and its information, (hopefully) providing a better spacial and energy resolution. ● The next step is to extrapolate tracks from the pixel telescope and see if they coincide with strip hits, and if not, what is the ADC pattern in the strips where the track goes by and how can we improve/change the current hit detection method in order to detect these hits.

End

Hit Detection with Entropy Distance Cut ● The Entropy Distance Cut can also be used to help detect hits and remove fakes, the problem is that it requires pre-defined patterns which we know to be hits! ● Back to the beginning: What is a hit? ● TODO: Use a pedestal run to discover what is NOT supposed to be the pattern of an hit ● And how about pile up? Do we want “pile-up hits”?

1 st step ● Search for something that looks like a hit

2 nd step ● Search for something that looks like a hit ● Normalize the adjacent strips to the highest time sample of the strip with the hit

3 rd step ● Search for something that looks like a hit ● Normalize the adjacent strips to the highest time sample of the stirp with the hit ● Perform a Chi Square test for the left and right strip, assuming the center one is the “correct pattern”

4 th step ● Search for something that looks like a hit ● Normalize the adjacent strips to the highest time sample of the stirp with the hit ● Perform a Chi Square test for the left and right strip, assuming the center one is the “correct pattern” ● Select the smallest chi2 and do a cut