Week of November 13

Today, I continued my work on radioactive decay and calculating branching fractions. Using the Review of Particle Physics, I found the five most common decays for the D meson, and I calculated the branching fractions for each of those decays. I spent the majority of my time today working on my Python skills, however.

Today, I reviewed writing functions, using the range function, and writing if-else statements. Dr. Bellis gave me the task of writing a Python program that calculates if a number is prime or not and returns all of the prime numbers under 100. Although the part of the program that returned all of the prime numbers under 100 was fairly simple, I couldn't write that section until I wrote the first one. I knew that to calculate if a number was prime or not, I first had to define a range for the computer to calculate from. I defined the range as all the numbers between 2 (since 1 isn't a prime) and 1 + the square root of the number, since there aren't any new factors of a number after its square root. This is what that section looked like:

I had to use the integer function int() which converts all numbers into integers since the range function only works with integers. The if statement "if number % x == 0" basically says "if the number entered is divided by any number in the defined range, and the answer is equal to 0, then return 'False.' If the answer isn't equal to 0, then return 'True.'"

I wrote the section of the program that checks if the number entered by the user is prime, but there were too many bugs for the program to run successfully. Next time I have my internship, I will continue writing and debugging the program.

Week of November 6

Today, Dr. Bellis and I continued our discussion of radioactive decay, with a particular focus on the decay modes for the B meson and for the J/psi particle.

There are several different decay possibilities for any single particle. For example, two possible decay modes for J/psi are J/psi --> e+ e- and J/psi --> μ+ μ-. So, how does one know what a certain particle will decay to? All of a particle's decay modes, the probabilities of these decays, and everything else you could possibly need to know about a particle are published in the wonderful 2012 Review of Particle Physics (which has 1526 pages and a size 10 font).

One important piece of information to know about a decay mode for a particle is its branching fraction. Basically, a branching fraction is the number of particles that decay a certain way over the total number of particles that decay. The Review of Particle Physics publishes the branching fraction for each decay.

Here is a crazy looking graph for the branching fractions of the famous Higgs boson particles, which has many decay channels. This graph shows the branching fraction of the Higgs boson as a function of its mass. Source: Higgs Physics Group at Imperial College London. 

If you have two steps in the decay process, how do you calculate the total possibility of that decay? For example, suppose you want to find the proportion of particles that decay from a B neutral meson to a positive and negative pion. A B neutral meson first decays to a K neutral meson, which then decays into the two pions. You can find the total probability of the decay from a B neutral meson to a positive or negative pion using a simple rule of probability: if two events are independent, then the probability of them both occurring is the product of the probabilities of each occurring. Therefore, to find the total branching fraction for the decay of a B neutral meson to a charged pion, you have to multiply the branching fractions for each separate decay together.

Using this information, I calculated the branching fractions for three different situations. Unfortunately, I had to spend over an hour today in the IT office at Siena since my computer wouldn't connect to the network, so I didn't have much time to do anything else.