Feynman Diagram Assignments in ASTR/PHYS 109people.physics.tamu.edu/toback/109/Diagrams/Feynman... · 2020. 10. 12. · Feynman Diagram Assignments in ASTR/PHYS 109 Learning to write

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Feynman Diagram Assignments in ASTR/PHYS 109

Learning to write down the diagrams that describe what occurs at various times during the evolution of the universe since the Big Bang until today

Since one of the simplest ways of describing interactions between particles is using the Feynman Diagram, introduced in Chapter 7, we will take some time to learn to get good at drawing them. For each of the 4 assignments you will draw a set of diagrams and submit it to an eCampus quiz. There will be one assignment per type of interaction that will be important and you will draw a set of diagrams for each (one diagram per type of interaction listed)

There are 4 short assignments for the course and they can be found in Quizzes > Feynman Diagrams > Feynman Diagram Assignment 1/2/3/4 . They are

1. Electromagnetic Force Interactions (Chapter 7) 2. Strong Force Interactions (Chapter 8) 3. Annihilation and Creation (Chapter 9) 4. Nuclear Decays (Chapter 12 and 14)

There are four sections in this document and an appendix. Section 1 follows the book and summarizes the pieces of the Feynman Diagrams you will need, and how to use them in the drawing. Section 2 is the list of Assignments. Section 3 is about to electronically submit, how you will be graded, and how to submit a Revision if you don’t get the grade you would like the first time. Section 4 shows some examples of excellent submissions. Appendix A has a copy of Figures 7.5 and 7.6 from the textbook for your convenience.

Note: There are three Warmup Quizzes which can be found in Quizzes >> Warmups >> Part 5: Understanding how to complete Feynman Diagram Assignments 5, that will help make sure you understand all the instructions in this document. You will need to pass all three before being able to submit your documents.

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1. Drawing Feynman Diagrams While the textbook shows simplified versions of the diagrams (see Appendix A), we will be more explicit in ours. For each diagram you will be indicating how each particle moves through space and time, and how it interacts.

1.1 Set up the Axes : The first thing we need is a set of axes (note that in this class we will always put time on the x-axis and space on the y-axis). In all your diagrams you should write them with the space direction being up and down, and time going from left to right. Make sure you label these on your diagrams explicitly.

1.2 How to indicate which way the particles move through space over time: Next we add the particles as they move through space (over time) in the figure below. The arrows for both matter and anti-matter particles always face the forward direction, as given in the table below, and mediators have no arrows . In this example we see two electrons moving through space towards each 1

other (they are attracted ). Like Figure 7.5, that’s why the lines are sloped; if they were horizontal it would mean they are not moving, like in Figure 7.6. In this example they never actually touch, but instead at some point in time they “interact”. The interaction is that they “exchange” a photon, and that is drawn with a wavy line. Since electrons are both negatively charged, we know they repel each other (that’s the information the photon is carrying), so AFTER the interaction you can see them moving away from each other (again, the sloped line).

1.3 How to indicate which particles are participating in the interaction : Since more than just electrons and photons interact, the table below lists all the particles we will be using in the class and how to draw each. Since we don’t want to write out the full particle name on every

1 We note that scientists often have arrows pointing in other directions but we do not do that here since we have labeled our space and time directions.

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diagram, just indicate each using the notation in the table. To draw it’s path through space we will use either a solid line with an arrow (for matter particles like electrons) or the indicated format if it is a mediator (photon or gluon).

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1.4 Interactions and Exchanges, Annihilations, Fusion and Decays There are four main types of diagrams we will need to be drawing: interactions and exchanges, annihilations, fusion and decays. In the first diagram we see an interaction between two electrons which are approaching each other. They exchange a photon and are repelled. Note that the photon is essentially vertical in this diagram, and that the matter particles are never vertical.

In the second diagram we see an electron and a positron annihilate and turn into a photon - which in turn then decays into an electron and a positron. Note that the photon is horizontal in this diagram.

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In the third diagram we see two protons fuse to form a helium-2 nucleus (2He), which then decays to form a deuterium nucleus (2H), as well as an electron and a neutrino.

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Particle Notation Matter or Mediator How to Draw electron e - Matter

positron e + Matter

photon Greek letter

ɣ (gamma) Mediator (Note: no arrow)

Proton (composite picture)

p Matter

proton (quark picture)

u u d

Matter

neutron (composite picture)

n Matter

neutron (quark picture)

u d d

Matter

up quark u Matter

down quark d Matter

gluon g Mediator (Note: no arrow)

neutrino Greek letter

𝜈 (nu) Matter

Deuterium (Hydrogen 2)

2H Matter

Helium 4 4He Matter

Helium 5 5He

Matter

Lithium 5 5Li Matter


Section 2: Assignments

Assignment 1: Electromagnetic Force Interactions The Electromagnetic force is described in Chapter 7. In Assignment 1 you will draw and submit 5 of the diagrams that will be important in how the parts of an atom interact, and how particles will interact in the early universe (later chapters). They are:

1. The repulsion of two electrons via a photon 2. The attraction of an electron and a positron via a photon 3. The repulsion of two positrons via a photon 4. The attraction of an electron and a proton via a photon 5. The repulsion of two protons via a photon

Assignment 2: Strong Force Interactions The strong force is described in Chapter 8, with example diagrams on the bottom of Figure 8.1 (also given in Appendix A). In that figure the attraction between a free up quark and a down quark happens via gluon exchange in the bottom left, and attraction between an up quark and a down quark in a neutron and proton respectively via gluon exchange in the bottom right . Note how we draw the other quarks in the interaction (both there and here we will simplify and ignore the extra interaction between them). In Assignment 2 you will draw and submit 5 diagrams that describe how quarks interact in protons, neutrons, and help keep them together in a nucleus. You will be using the quark picture style in the table above. Be sure to draw all the quarks, even the ones who are not interacting (if they are not interacting they can just follow the path of the interacting quark for simplicity like in Figure 8.1). They are:

1. Gluon exchange between two down quarks 2. Gluon exchange between two up quarks 3. Gluon exchange between an up and a down quark 4. Gluon exchange between two up quarks in a proton 5. Gluon exchange between two up quarks in a two separate neutrons

Assignment 3: Annihilation and Creation When a particle meets its antiparticle they can annihilate. While there are a number of things they can turn into, in chapter 9 we describe them as creating a photon which then turns into two more photons. This is shown without the Feynman diagram in Figure 9.6 so we will draw them here. In assignment 3 you will draw 2 of the diagrams that will be important in the early universe. They are:

1. An electron and a positron meet, then annihilate to create a photon which then “turns into” two photons (note that this is not actually a decay)

2. Two high energy photons meet, then annihilate to create a photon, which then turns into an electron and a positron

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Assignment 4: Nuclear Decays Many particles are unstable. We mentioned a number, for example we describe lithium-5 and helium-5 decay in Section 12.3 and 14.1, a muon decaying in Section 13.2, and a free neutron decaying in Figure 14.3. These are important in the early universe, as they determine why we don’t get many nuclei heavier than helium until the first stars turn on a half a billion years after the bang. In Assignment 4 you will draw and submit 2 diagrams showing this process. Note that you are not drawing the quarks explicitly in this case, just the nuclei, the protons and the neutrons since these aren’t true Feynman diagrams, but they’re good enough for us. They are:

1. A helium 4 nucleus and a proton interact, combine to create lithium 5, which then decays into a helium 4 nucleus and a proton

2. A helium 4 nucleus and a neutron interact, combine to create helium 5, which then decays into a helium 4 nucleus and a neutron

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3. How to Create/Submit Your Assignments, How You Will Be Graded, Helpful Tips, and Revision

3.1 Create/Submit Your Assignments While there is a specified way for the diagram to look, there are many ways to create your electronic “drawings”. You can simply draw each by hand and submit a photo of them (for example using OfficeLens on your phone), or you are more than welcome to use a fancy program of your choosing (for example PowerPoint) and save and submit that way to the quiz in eCampus.

Please submit all your diagrams in a single document (preferably a .pdf format) with all of them oriented right side up. Submitting multiple images lags the grading system.

3.2 How You Will Be Graded Feynman Diagram Assignments will be graded on a 0/5/10 scale, where 0 is given when assignments are not turned in, 5 is given for incomplete or incorrect assignments, and 10 is given for assignments that meet all the criteria.

Some things we expect explicitly (and we look for when assigning grades): ● Make sure you explicitly mark your space axis and time axis. 2

● Make sure every branch/particle of the Feynman diagram is properly labeled. This means one particle label per line.

● Make sure that you use solid, straight lines with arrows for matter particles (like electrons, positrons and quarks) and solid wavy lines for photons and solid curling lines for gluons. 3

● Make sure the arrows point in the proper direction, for example forward in time . 4

3.3 Helpful Tips One way to check your work is to use a straight-edge (your pencil works fine)

● Holding your straight edge vertically slide it from the left side to the right (simulating the passage of time)

● Where it touches your particle lines will show what particles exist at the given time. ● If your diagram is supposed to show an annihilation/creation, expect that your original particle(s)

disappear, and a new particle(s) is made

2 While we have asked you to always put time to the right, and space upwards, real scientists feel free to orient them how they need. 3 We note, in case you are interested, that you always use solid straight lines for all fermions (electrons, neutrinos, quark, anti-quark, etc.), and dashed lines for W + , W - , and Z bosons as well as for graviton (even though there is no evidence for them yet) 4 Note that anti-particles are actually particles moving backwards in time. Real scientists wouldn’t mark the charge on the particle, or if it’s an anti-particle, they would just denote all this with an arrow. For example, they would write “e” for an electron or a positron, but a forward arrow for an electron and a backward arrow for a positron. For this class however, we explicitly label each particle with its charge so ALL arrows in your assignment should point forward in time.

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● If it is just a particle exchange interaction (i.e. repulsion/attraction), there should be no jumps and

you should be able to follow the particles from beginning to end. Whether they move apart or together will dictate repulsion/attraction.

3.4 Revisions Since this assignment is done as a Quiz in eCampus, you are allowed to submit as many additional attempts as you like to get the grade you would like. Before submitting a Revision you should read the Feedback on your original to see what the problem is. To get your Feedback simply click on the assignment itself. Once you have finished using the feedback to make the submission excellent, to submit a Revision simply click on the Quiz again and use an additional attempt. Also, be aware that we are only allowing 2 attempts before you request more.

To request more, send the following information to [email protected] with the following information:

● Assignment number ● Diagram number ● Copy/paste of the Feedback ● Description of how you will fix it

4. Examples of Excellent Feynman Diagrams There are many ways to make and submit your Feynman diagrams. One way is to use a computer to generate them (Powerpoint, JaxoDraw, LaTex, etc.), but hand drawn Feynman diagrams are completely acceptable as well. Below are two examples of the same diagram (electron/positron annihilation), one hand written and one computer generated. Both are completely acceptable.

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mailto:[email protected]


Appendix A: Figures 7.5, 7.6 and 8.1 from the Textbook For your convenience we have copied Figure 7.5 and 7.6 from the textbook. Note that the Feynman Diagrams that are shown did NOT contain the arrows, but for this assignment you will need them

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Feynman Diagram Assignments in ASTR/PHYS 109people.physics.tamu.edu/toback/109/Diagrams/Feynman... · 2020. 10. 12. · Feynman Diagram Assignments in ASTR/PHYS 109 Learning to write