Measuring the Strong Coupling Constant, Alpha_s

The Theory of Everything (ToE), which seeks to unify the four fundamental forces, is one of the hottest topics in modern physics. High energy physicists have combined the electromagnetic force and the weak force into the electro-weak force, but unifying these with gravity and the strong force still eludes scientists, primarily because of the enormous amount of energy required to achieve recombination. All forces have coupling constants which are dependent on energy. The strong force coupling constant, a_s, is somewhat similar to other familiar force constants such as G is to the gravitational force and k is to the electromagnetic force. a_s, like the other coupling constants, is dependent on energy, hence there is nothing constant about it! Shown below is a plot of known a_s values vs. energy. In order to gain a deeper understanding of how the strong force varies with energy, we need to measure a_s at a range of energies. Calculations of a_s have been performed at high and medium energies, but lower energies have not been explored as much. BaBar is particularly good for calculating a_s because of the relatively low energy and the large amount of data available for analysis. It is important to get an accurate measurement of a_s at lower energies in order to get a good idea of how a_s changes with energy. This will help theorists determine if the four fundamental forces converge to a single point at a higher energy There are many methods for calculating alpha_s. In this study we investigate a jet ratio method for calculating the strong coupling constant. A jet is a large amount of hadronic energy within a small angular distribution. How a jet is determined depends on the combination algorithm that is used to analyze the given data. This method compares the ratios of 2, 3 and 4 jet events to the total number of events and sees how this ratio changes with different threshold values (ycut). We use a jet finder package to assemble jets from a billion events and use mn_fit to further analyze the resulting histograms

2.The Jet Finder Algorithm

Each event generates particles that are detected by the BaBar detector. Software traces the path of these particles and their decay products through the detector. Because of the nature of the strong force, events generating quarks result in jets. The number of jets in the reconstructed event is determined by the Jet Finder algorithm. The Jet Finder attempts to find two particles that both decayed from the same parent particle. It does this by calculating a metric yij related to the probability that two particles came from the same parent particle. The pair with the smallest yij value most likely came from the same parent. The Jet Finder combines these two and repeats the process with the parent particle in their place. It continues combining until all the remaining particles have metrics greater than the threshold value, ycut. :

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3. Results and Future Work

This histogram is a plot of the ratio of evens with 2, 3, and 4 jet events vs. ycut. The black represents 2-jet , red represents 3-jet, and blue represents 4-jet events. As ycut increases, the Jet Finder algorithm is more likely to construct 2-jet events instead of 3 or 4. The probability of the jet finder algorithm finding two-jet line approaches 100% as ycut increases.

We have performed the Jet Finder algorithm on generated data. We will run on real data to get a measurement of the running couplding constant. We will also soon run on more data, looking at over a billion events. We will also use different metrics, which will change the criteria that the Jet Finder uses to pair decay products with parent particles. By doing this we will get several different measures for the strong coupling constant and be able to compare their accuracy. We find that the Jet Finder algorithm is an easy and effective method for calculating the strong coupling constant