The data for this hack can be downloaded from the CMS public data website. We use the file, dimuon.csv, which is pre-selected events which have two well-identified muons.
What is a muon?
A muon is a subatomic particle, related to the electron, but 200 times more heavy!
It possesses either a positive or negative charge.
Muons do not interact very often with atomic nuclei that make up the CMS detector, and so they travel through much of the material and are relatively easy to detect.
Where are these muons coming from?
When the protons collide in the LHC they produce many other particles. Some of these particles decay very, very quickly and produce a spray of other particles that are then detected in CMS.
Sometimes one of these particles decays to two muons.
Sometimes the muons are coming from two different parent particles.
The goal of this exercise is to figure out when the muons are coming from the same parent. To do this, we calculate the invariant mass of the two-muon system. If there is a preference for certain values of this mass, we may be seeing signs of the common parent particles!
To calculate the mass, we have two choices:
- Classical physics, which relates momentum, energy and mass from the equations of Newton.
- Special relativity, which relates momentum, energy and mass from the equations of Einstein.
We use the following variables for these values:
- m: mass
- v: velocity
- KE/E: kinetic energy/total energy
- p: momentum
- c: the speed of light (300,000,000 meters per second)
Calculating the mass from Classical Physics
p = mv
KE = 1/2 m v^2
KE = p^2 / (2 * m)
Calculating the mass from Special Relativity
E^2 = (p*c)^2 + (m*c^2)^2
(m*c^2)^2 = E^2 - (p*c)^2
With the data we are using, the units have taken into account the factors of c, so that we do not need to include it in our calculations (c=1).