FINAL+EXAM

=Final Project:= To sum up the semester, I feel that it is appropriate to put forth the work that we have done in identifying and isolating cosmic rays in our data set from CERN. As we know, cosmic rays originate from space and penetrate the CMS detector, resulting in muons that appear to have originated from inside the detector, when in reality, they simply penetrate the detector and give unwanted data. As I have researched this topic, I have come upon a multitude of ways we can identify and isolate cosmic rays in the data. This can be done by looking at the phi, eta, Q1*Q2, Esum/M, and mass values of the particles. For each of the mentioned parameters in the data set, cosmic rays contain unique characteristics that separate them from other particles inside the detector. Thus, for this final exam, I will be explaining and showing these characteristics of the parameters by isolating the cosmic rays in the data set of 100,000 recorded events.

(E1 + E2)/M
In our data set, the first cut I will perform is the cut containing of E/M. The logic behind this parameter deals with the nature of the detector's recording system. As a cosmic ray is just a single particle that moves straight through the detector, the detector is fooled into thinking that it is instead a dimuon decay event taking place with two daughter particles moving away from each other in exact opposite directions. In this case, that would mean that the particle has zero momentum, as can be assumed by the equation E^2 = M^2 + P^2. Because momentum must be conserved, the detector believes that the momentum of the alleged "parent" particle is 0, as the "daughter particles" resulted in opposite and equal directions. Thus, for cosmic rays, we can assert that a value of E/M should be 1. From here, I cut all the data from the spreadsheet that did not have this characteristic in order to separate the cosmic rays. Here is what I am left with: I have made the first cut of the data, and find that I am left with 1198 events that have E/M = 1. To do this, I had to make a histogram of the E/M column, and when done, I found that at my final point, a distinct break occurred, pointing me to cut the data at this specific instance, which happened to occur at 1.003835. From this, the first cut is finished. Here is the break in the graph of E/M: As can be seen, the break is quite noticeable at the 1198 range.

Q1 * Q2
This particular cut was not performed until recently. We have found that cosmic rays will result in a negative value when we multiply Q1 * Q2. As the machine interprets the cosmic rays to be the result of a dimuon decay event, one particle must be positive, the other negative. This is an example of conservation of charge. With two oppositely charged particles, the Q1*Q2 must be negative. I have uploaded the current set of data into Many Eyes, then decided to analyze Q1*Q2 vs event #. I have found that a decently good size of low-massed particles are present, and all have positive values, while the bulk of the events are clearly negative. In doing this, I feel that it is parallel to theory and the data to cut these values that are positive. Here is the result: Because Ibelieve there to be a malfunction with the display in ManyEyes, I have displayed a random graph that shows the spread of the particles, and by the color of each particle, it shows that the cut was successful. They all have a negative value. After making this cut, I am left off with 1134 events in the spreadsheet, which is still a greater number than I had hoped, as I will explain next.

Phi, Eta, and Mass
Phi, Eta, and Mass are all parameters that can show signs consistent with cosmic rays, however, it is very difficult to successfully make an accurate cut of these parameters as it is a gradual change in data by matters of just .0001, which makes it impossible to know where to draw the line in cutting the data. In previous analyses of Mass, however, we noticed a clear break in the presence of particles with a mass of 40 and above. It seems that suddenly these cosmic rays just appear at this point, and can be seen in this graph of all events: As can be seen, the linear arrangement begins at a mass of 40 along the line of E=M. Because of this, we wonder why there are particles still remaining in the data that have masses lower than 40, but E/M = 1, and Q1* Q2 = -1. Without scientific reasoning to support a theory of having cosmic rays have a mass below 40 GeV, I cannot yet make that cut out of the data, but until then, I am pleased with the progress that has been made. I have cut out thousands of particles in the data set, leaving me with just cosmic rays along with a small cluster of a few particles of mass below 20. My best conclusion that I can come up with at this point is that those extraneous particles with masses below 40 GeV are simply errors in the detector. There is great evidence for this, as it seems that the equation E^2 = M^2 + P^2 does not hold true for those particles. Graphs of momentum show that some particles have momentum values greater than 0, which simply means that they have to be errors in data collection, causing this equation to not hold true. In conclusion, I am very pleased with the progress that has been made in the search for cosmic rays. I have been able to create and analyze many parameters that has allowed me to learn and research the properties that cosmic rays have, as well as given me the necessary skills to manipulate data in Excel and Many Eyes. In the coming term, I am hopeful to further realize the causes of these discrepancies in the data, as well as look for more conclusive black/white ways to separate cosmic rays.