Week+of+10-29+to+11-4

October 29th
Today Grace, Jeremiah, and I arrived at QuarkNet at 3:35. Today is a day for analyzing graphs. The first graph I looked at was py1 parent rest frame vs. phi1. The graph is below. This graph shows that sinusoidal pattern that seems to be popping up every time we look at a graph that involves phi and px or py. Here's why: the momentum values are separated into components. Phi is measured on a circular plane, similarly to measurements in radians on the unit circle. The x and y momentums line up in a similar way to the x and y components of a point on the unit circle. So, as the phi measurements rotate around the circle, the x and y momentums should follow sinusoidal patterns as cosine and sine, respectively. This graph shows the pattern of the sine function because they both pass through the origin and have a maximum at pi/2 (about 1.57) and a minimum at -pi/2 (about -1.57). This makes sense because sine is the y-component, and we are looking at the y-component of momentum. The other interesting thing about this graph is that the sinusoid has a much greater amplitude for the particles of higher mass. This is likely the case because cosmic rays and other high-mass particles are also high-energy particles, and thus travel faster. The next graph I chose to break down was E sum vs. p 3d resultant, shown below. The thing that catches the eye on this graph is that nothing is below the line y=x (or E sum=p 3d resultant). The reason this occurs is because p is a component of energy (recall the equation E^2=m^2+p^2). So, E could never be less than p 3d resultant because p 3d resultant is the entirety of p and mass cannot be negative. The other interesting phenomenon in this graph is, once again, the different pattern exhibited by particles of high mass. They frequently have E sum > p 3d resultant, which makes sense because they are high-mass particles, so their mass would definitely play a part in their energy. The other clear pattern is the group of particles at p 3d resultant of 0. These are likely the cosmic rays, because each cosmic ray is one particle which the detector treats as two different particles. So, the momentums of "particle 1" and "particle 2" would be exact opposites because they are actually the same particle measured in two different places. Next I set out to tackle the graph of E1 parent rest frame vs. pz1 parent rest frame, shown below. This graph has an interesting limit - E1 parent rest frame is never less than the absolute value of pz1 parent rest frame. This relates to the graph above where I explained why E sum was never lower than p 3d resultant. Sometimes, the entirety of the velocity vector's magnitude comes from one component. The points on this graph that lie on the line E1 parent rest frame = abs(pz1 parent rest frame) are cases in which the particle probably traveled entirely in the z direction, so z was the only contributor to the total. The energy of the first product will never be greater than any of the momentum components, as shown by this graph. Once again, the cosmic rays are set apart from the other data. This time, it is merely that the particles of highest mass are of a far higher energy in relation to pz1 than the rest of the particles, which makes sense because if the mass component of energy is larger given that momentum is consistent, the energy will be larger (once again referring to E^2=m^2+p^2). Next I attempted to decipher the graph of pt1 parent rest frame vs. px sum. It is shown below. This graph has a line of symmetry at px sum=0,all the points of small mass are concentrated around the origin, and the points of high mass are concentrated heavily around px sum=0. First, to explain the particles of high mass. If the particles of high mass are generally cosmic rays, and cosmic rays generally fly in vertically, they wouldn't have any momentum in the x-direction, only in the y-direction. Additionally, I explained earlier the way that the momentums for the two "different particles" measured by the detector when a cosmic ray goes through tend to cancel each other out, since they are actually opposite measurements of the same particle. So, this is another reason that the px sum of a cosmic ray would be 0. Pt1 parent rest frame can't be negative because is is a two dimensional magnitude; only the components (px1 parent rest frame and py1 parent rest frame) would be negative. That is why none of the pt1 parent rest frame values are below 0. As for the data's almost-circular concentration around the origin, my best explanation comes from the relationship of these values to the unit circle. The squares of px and py add together to get pt squared. This would be the explanation of the circular relationship. px^2 + py^2 = pt^2 is very reminiscent of the equation of a circle. It appears that this graph draws from that kind of circular relationship, but applies a "less than or equal to" idea. I cannot go too far into depth, because not only is this graph crossing between rest frames, it is comparing the sum of one value to a component of another, so although this graph looks interesting, it is vexing to fully explain its patterns. I left QuarkNet today at 5:35