1. Computational Techniques for Scattering Amplitudes
Juliano Everett
Mentors: Dr. Giovanni Ossola, Ray D. Sameshima
Physics Department, Fall 2018
INSTRUCTIONS: Insert text in text boxes as indicated on the template. You can modify color, background, font, font size, etc. by using PowerPoint features noted in the tabs. You can add borders around text boxes and you can add lines or other graphics where desired. To add more text boxes, you can copy an existing one and move it to the desired location. You can add any graphic by dragging it onto the slide or by copying/pasting it. Be sure that your graphic has high dots per inch. Images/graphics must be cited if not original work. Use Sans Serif fonts for Titles, labels and section headers. Use Serif fonts for text in text boxes.
CONTENT:
*Introduction, Background, and/or Abstract (a place to quickly summarize your topic and trigger your audience’s interest). Usually in narrative, paragraph format.
*Materials and Methods or Process (a place to describe your process and what led to your results). Using bullet points can be a helpful way to present information.
*Results (the place where the results of your experiment are explained). Using bullet points can be a helpful way to present information.
*Conclusions or Discussion (the place where you explain why your results are conclusive and provide the reader with a short but solid justification of your hypothesis). Usually in narrative, paragraph format.
*References or Literature Cited (This is where you make a list of the literature you have cited regarding this project. List the names of authors, publications and publishing dates.) To save space, consider noting “selected references” – those references essential to the project. Citation style must follow rules designated by discipline, e.g., MLA, APA, etc.
*Acknowledgment s (this is where you acknowledge grants and research programs. Also, use this section to thank the people who helped with your project. Can sometimes include your Contact Information)
*Depending on your type of research and where you are in your project, you may have to use some variation of the above.
Feynman Diagrams with “FeynArts”
Abstract
Feynman Diagrams
First, create Feynman diagrams
Scattering amplitudes in quantum field theory can be described as the probability of a scattering process to happen within a high energy particle interaction, as well as a bridge between experimental measurements and the prediction of the theory.
In this research project, we explore the Standard Model of Particle Theory, it’s representation in terms of Feynman diagrams and the algebraic formulas associated with each combination.
Using the FeynArts program as a tool for generating Feynman diagrams, we evaluate the expressions of a set of physical processes, and explain why these techniques become necessary to achieve this goal.
Put simply, Feynman Diagrams are picture representations of the math that describes the interactions and behaviors of the particles found in the standard model.
Limit the diagrams to T3
Next, add fields and restrictions
What is the standard model?
The standard model describes fundamental particles, their interactions and the fundamental forces that govern them. According to CERN[1], the standard model is currently our best understanding of these fundamental particles, but it is also incomplete. The theory does not currently account for gravity and there are many other theoretical questions to be answered. For example, what is dark matter? Or What is the dark energy that makes up about 68% of our universe, and is counteracting gravity to expand our universe at an accelerating rate? [2]
The above are some examples of different types of Feynman diagrams.
Diagrams explained
Each of the diagrams shown above have what are called legs, and (a) vertex/vertices. These diagrams come in two types; Loop Diagrams and Tree diagrams.
Tree Diagrams contain no loops and are the simplest while loop diagrams have loops and correspond to higher orders of perturbation theory.[5]
Legs are the fundamental particles which are represented by the lines of the diagram, which can be squiggly or straight
The vertex is the point where particles meet and different interactions occur. This could be emission, deflection or absorption.
last, generate amplitudes
Perturbative expansion
In general perturbative theory is solving a simpler problem and working towards an approximation to a more complex problem. In terms of Feynman Diagrams a process is organized in a perturbative series and calculated towards some order of g:
The perturbative expansion becomes necessary because the leading order (LO) predictions aren’t enough.
Higher orders of expansion reduce theoretical errors, changes the shape of distributions and at the LHC they distinguish signals from the background[6]
(picture of a table of the standard model.)[3]
The above are commands and outputs from Feynarts[7,8] to generate some diagrams using specific particles, and then create amplitudes from that generation.
References
[1] “CERN Accelerating Science- The Standard Model”. CERN, home.cern/science/physics/standard-model.
[2] Tyson, Neil deGrasse, “Astrophysics for People in a Hurry”, W.W. Norton & Company, 2017.
[3] The Standard Model.”QuantumDiaries,
[4] CERN-Brochure Eng LHC guide book [5] Kresimir Kumericki, “Feynman Diagrams for Beginners”, arXiv: [physics.ed-ph]
[6] G.Ossola, Presentation “Feynman 100”, October 18, 2018, City Tech.
[7] V. Shtabovenko, R. Mertig and F. Orellana, ”New Developments in FeynCalc 9.0” Comput.Phys.Commun. 207 (2016) , arXiv: ;
[8] T. Hahn, Generating Feynman Diagrams and Amplitudes with FeynArts 3”, Comput.Phys.Commun. 140 (2001) , arXiv:hep-ph/
CERN’s Mathematical representation [4]