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Lorayna Hinton

Interpreting Particle Interactions
December 6th 2016

Math 89S Mathematics of the Universe

Hubert Bray

Duke University

Abstract:

This paper should serve as an introduction to particle interactions. To begin, the concept of particle decay and the standard model of particle physics’ prediction for particle decay will be introduced.Following, the LHC and its role in high energy particle collisions and interactions will be discussed. Next, the types of data collected/methods of data collection from the LHC will be explored as well as this data’s potential significance. Towards the end of the paper, there will be a short problem set in which the reader is directed through an application of basic mathematics and logic to the collected data. These problems are geared towards creating anability for the reader to draw conclusions about data collected from the LHC and create their own predictions for particle interaction."

Particle Decay

Introduction: To best understand this text, background knowledge in elementary particle decay and interactions is essential. For this, I will explain the basic principles of particle decay, and introduce Feynman diagrams to represent these interactions.

Elementary Particle Decayis the process by which particles of a certain energy fall into more desirable states. This may include forming five different particles and energy from a single quark, or perhaps particles come together to form a more massive particle. These interactions between particles are commonly expressed in Feynman Diagrams. An example and description of a Feynman diagram will be presented below.

This diagram shows a particular interaction known as electron-positron annihilation. This shows the electron (e-) and positron, the antimatter variant of the electron, (e+) coming together to form two photons (Y). In text, this diagram is represented as e- e+  YY. The straight unbroken line you see almost always represents any matter (leptons, quarks, protons etc.). The sinusoidal line represents an interaction with the electromagnetic force, a photon (Y).

In these diagrams, the symbols and variants of connecting lines are held constant, creating a simple way to visualize interactions between particles. Note that any Feynman diagram is reversible, that is, if I say the interaction e- e+  YY is valid, this means the interaction YY e- e+ is also valid. This is true for any interaction. To best understand these diagrams for more than a single case, knowing the representations for all forces is necessary.

[Y is the photon, the force carrier for the electromagnetic force. Z is a Z boson, and W+. W- is the W+,- boson, the force carriers for the weak force. g is the gluon, the force carrier for the strong force, and h is the Higgs boson, not exactly a force carrier, but the specifics of the Higgs boson are unimportant for simply understanding its notation.]

As shown from above, one can see how useful this diagram is for its ability to graphically visualize and standardize a graphic for particle interactions. However, for the best understanding of these diagrams, one must know the symbols for the particles represented on these diagrams. Below will be a comprehensive chart of common particles the reader can refer to as this text moves forward.

Standard Model of Physics’ Table of Particle Decay

Introduction: Now that the reader has an idea about what particle decay is and how to read them, the common patterns associated with various forms of matter will be discussed, going into detail about particular highlighted phenomena in physics research such as the Higgs boson.

When trying to construct a Feynman diagram for particle interaction, one must realize there is a set of rules set by the Standard Model of Physics. This includes conservation of energy, charge, spin, lepton number, and baryon number. The specific meaning of these quantities will not be described in this text, just note that the sum of these values for the start of one interaction must be the same for the resulting particles after the interaction. Any interaction that follows these rules CAN happen.

For example, say we want to make an environment (an interaction) for a Higgs boson to be created. First, we must know a string of data quantities about this particle including its rest mass, predicted velocity at time of interaction, spin, and other values to conserve these values set by the SM. Once we have these quantities, we know anycombination of particles that follow the rules set by the SM could create the Higgs boson.

[The diagram above shows a few interactions that could lead to the creation of a Higgs boson.]

Thinking of a perfect setup to create a particular particle is much different from creating this environment however, which is where a great deal of the difficulty comes in creating such a particle. The upside to this however, is if you can see the ‘before’ parts of an interaction that you are looking for, and the reaction only has one possibility, you can know with a certainty that the ‘after’ part is what you were looking for. So if one were to see one of the environments for a particle as data in the LHC, one could predict by looking at this data if the particle sought after did actually exist—especially if the decay products of that particular particle are found as well

Data Collected from LHC

Introduction: The LHC is a particle accelerator that can bring particles to velocities to over 0.999999c. This creates an environment in which the accelerated particles, when brought to collide, release all of the kinetic energy in the form of high energy particles, photons, gluons etc. These particles quickly decay into large ranges of other particles, letting physicists observe the kinds of particles that can exist (like trying to discover the Higgs boson), and understand how these particles interact with other particles. The detectors filter out events that may not relate to what is being sought after at that time. For example, perhaps the detector will only show me events of g+g interactions if this is what I am trying to study.

[ This is an example of an isolated collision that was picked up by detectors at the LHC. This image was then reconstructed by the detectors to give a visual of the collision. Each block of different colors represents a resulting particle from the collision with green being the path. The stream of red coming from the top and bottom are neutrinos.]

The graphic shown on the previous page is definitely interesting, but without actual labels and information about timing and energy, we cannot directly make predictions about what happened in this collision, or what the initial objects were that collided (most of the time this would be protons, but we would not know just by looking at this graphic). It is for this reason we need more descriptive data with information about the specifics of the collision.

Data from these collisions are stored very selectively. If CERN were to store all information collected, they would be taking in 40TB (40 standard computers) of raw data every second of collisions. As previously stated, one uses the detector as a filter to only capture data that relates to what said person is studying.

Once the raw data is collected, scientists can begin to analyze the data. This analyzing includes figuring out which particles formed where in a reaction, and the consequences under which this decay interaction occurred.

Problem Set/ Examples

Introduction: The purpose of this set is to show the reader the possibilities of understanding these interactions. A question will be proposed, and will be solved in general terms.

  1. The mass of an unknown neutrally charged particle H is W MeV. Particle H2 appeared as the only other particle in the system, the detector tells us that this is an electron with W2 mass.Both are X distance from the known collision site, and have a velocity of Y. It has appeared at your detectors V time after the collision. What is this particle?

The first thing to look for in solving this problem is the mass W. Because a desirable energy state does not combine energy with mass to create a more massive particle, we know that the mass of its particles that decayed into H were less than the sum of the mass W and W2. Also because charge needs to be conserved, we know H and H2 decayed from a negatively charged particle. To finish solving this problem we must look for possibilities of what decays into and electron and one other particle, that has a charge of -1 and conserves all other laws of conservation. We can do this by looking at a chart of particles, as well as their decay times, since we know distances and speeds of the particles. If no known particle matches the description, we can conclude the SM is wrong if the results are statistically significant (if it happens enough times). We may also suppose H is a new particle!

  1. Using the charts below, please describe the circumstances under which a particle with a mass of .511 MeV could be created.

We can see from the chart that the electron or positron has the desired mass of .511 Mev, so we can suppose a situation where one of these would be created. Let us chose a positron. For the positron to be created, a particle with a mass greater than .511 MeV must decay into the positron and another particle (we do not often see a particle decaying into just one other particle). The other particles that are created alongside the positron have to conserve spin and charge, so with a positron’s spin of ½ perhaps this particle would have a spin of -1/2 or whatever value necessary to conserve spin. Any condition that satisfies these laws of the SM could create a positron.

Conclusion

Since the discovery of elementary particles, scientists have given definition to every aspect of each particle and force carrier. Our technologies for measuring these defining traits are getting better, our particle accelerators are getting faster. It can only be imagined as to what will be discovered next with higher energies! Now that the reader has more information about these defining traits, and has the tools to make predictions for interactions, perhaps,when these truly amazing advances come in the decades to come, there will be a greater intuition of the reader to understand these results. Arguably the best of all, is to be the one that finds these results. One must just wait and see.

References:

  1. Gaillard, Mary. "The Standard Model of Particle Physics." ArXiv (1998): n. pag. Web. Dec. 2016.
  2. Nolan, Peter. (2016). Fundamentals of The Theory of Modern Physics.Chapter 6.
  3. Mouth, L. (2016, September). Particle physics- Feynman diagrams. Retrieved December, 2016.Pictures and Information.
  4. Wikipedia contributors. "Higgs boson." Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 25 Nov. 2016. Web. 25 Nov. 2016. Pictures and Information.
  5. Nave, R. “Allowed and Forbidden Particle Decays.” hyperphysics.phy-astr.gsu.edu/hbase/Particles/allfor.html#c1.
  6. Alex, F. P. “Particle Accelerators.” Four Peaks Technologies, 2012,
  7. Strassler, Matt. “Decays of the Standard Model Higgs.” Dec. 2011, profmattstrassler.com/articles-and-posts/the-higgs-particle/the-standard-model-higgs/decays-of-the-standard-model-higgs/.
  8. Wikipedia contributors. "Particle decay." Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 8 Dec. 2016. Web. 8 Dec. 2016. Picture for problem set.