Physics 801

Supersymmetry

Supersymmetry

Lectures are TR 11-12:15, in Chamberlin 2135.

Gary Shiu, Chamberlin 5279. Office hours are by appointment. There is no teaching assistant or grader.

Supersymmetry is an enormous subject, ranging from its fundamental role in quantum field theory and string theory, to phenomenological model building, to calculations of cross sections and events, to experimental considerations. It has also become an indispensible tool in obtaining exact results of gauge theories, and even in mathematics. Obviously, it is impossible to cover all these topics in one semester, so we have to set a modest but realistic goal.

In anticipation of the LHC, and given the broad spectrum of students registering for the class (theoretcial and experimental, HEP, strings, phenomenology,
cosmology, astrophysics, nuclear, etc), the goal of this course is therefore
to introduce the basics of supersymmetry and to discuss topics that are of *common* interests to students from such diverse fields.
Hopefully, the materials covered in this course will provide you with a solid
background to pursue further topics of interests to your research area.
We will have achieved our modest goal if, by the end of the semester,
theory students can appreciate
the tremendous efforts behind the experimental searches of supersymmetry,
and experimenters
can acquire the theoretical knowledge
helpful for understanding and interpreting new signals.

Topics include: Supersymmetry algebra, superspace and superfields, supersymmetric gauge theories, breaking of supersymmetry, the minimal supersymmetric extension of the Standard Model (MSSM), elementary supergravity, gravity and gauge mediated supersymmetry breaking, phenomenology of the MSSM and some of its extensions, supersymmetry at colliders and in cosmology.

Due to time limitation, and the diverse interests and backgrounds of the class, I will leave the following interesting and important topics for a different occasion (perhaps a continuation of the course in the future?): extended supersymmetry, non-perturbative aspects and exact results of supersymmetric gauge theories, Seiberg duality, dynamical supersymmetry breaking, Seiberg-Witten theory, and other more recently proposed SUSY breaking and mediation scenarios. We are most welcomed, however, to choose these topics for your group presentation (see below).

The grade for the course is based on group presentation (see below), participation (your engagement in classroom discussions, and during your and other teams' presentations), and homework (your efforts and the differential progress you have made are important than the correctness of your results), with weights as follows:

Group presentation: 30 * (2-n/N)%, Participation: 20 * (2-n/N)%, Homework: 50 * n/N%

where N is the total number of homework assignments, and n is the number of homework you have turned in.Since there is no grader for the class, you will grade another student's assignment each week, based on a rotating schedule (see below). Solution sets will be posted below, with the assignments. You should turn in graded assignments to Gary.

- Homework 1, due February 15, Solutions 1
- Homework 2, due February 29, Solutions 2
- Homework 3, due March 28, Solutions 3

H. Baer and X. Tata, *Weak Scale Supersymmetry: From Superfields to Scattering Events*

**Other Useful resources:**

S. Martin, *A Supersymmetry Primer*,
hep-ph/9709356

M. Sohnius, *Introducing Supersymmetry*,
Phys. Reports 128

P. Fayet & S. Ferrara, *Supersymmetry*,
Phys. Reports 32

P. Argyres, *Lectures on Supersymmetry*,
1996 and 2001 versions

D.J.H. Chung, L.L. Everett, G.L. Kane, S.F. King, J.D. Lykken, L.T. Wang, *The soft supersymmetry-breaking Lagrangian: Theory and applications*,
hep-ph/0312378

D. Bailin and A. Love, *Supersymmetric Gauge Field Theory and String Theory*

P. Binetruy, *Supersymmetry: Theory, Experiment, and Cosmology*

M. Drees, R.M. Godbole, and P. Roy, *Theory and Phenomenology of Sparticles*

J. Terning, *Modern Supersymmetry: Dynamics and Duality*

S. Weinberg, *The Quantum Theory of Fields*, Vol. III

J. Wess & J. Bagger, *Supersymmetry and Supergravity*

The big issue in choosing conventions for a supersymmetry course is whether to use a two-component or a four-component notation for spinors. Each notation has its own merit: The 2-component Weyl notation is more convenient for discussing SUSY algebra and representations. The 4-component Dirac notaion is more commonly used among phenomenologists and experimentalists who deal heavily with Feynman diagram calculations. Many textbooks on SUSY have opted for the two-component Weyl notation. Two exceptions are our chosen text and Weinberg. I will try to follow our text and use the four-component Dirac notation except in the first stages of constructing the supersymmetry algebra and multiplets. Hopefully, this will make the materials presented in class more accessible to those who work on particle phenomenology and experiments

The following is a course schedule with reading assignments. The schedule will be filled out as the course progresses. The exact emphasis may depend on the expressed interests of the students.

Date |
Lecture Topic |
Reading |
---|---|---|

1/22 | Review of the Standard Model | Baer and Tata, Ch. 1 |

1/24 | Beyond the Standard Model | Baer and Tata, Ch. 2 |

1/29 | Motivation of SUSY | Baer and Tata, Ch. 2 |

1/31 | Coleman-Mandula Theorem and SUSY | Argyres's Lectures, Ch. 1 |

Addendum | ||

2/5 | Spinors | Bailin and Love, Ch. 1 |

2/7 | Overflow time | |

2/12 | Wess Zumino Model | Baer and Tata, Ch. 3 |

2/14 | Overflow time | |

2/19 | SUSY Algebra and Supermultiplets | Baer and Tata, Ch. 4 |

2/21 | Addendum | Baer and Tata, Ch. 4 |

2/26 | Superfield Formalism | Baer and Tata, Ch. 5 |

2/28 | Superfield Formalism (continued) | Baer and Tata, Ch. 5 |

3/4 | SUSY Gauge Theories | Baer and Tata, Ch. 6 |

3/6 | SUSY Gauge Theories (continued) | Baer and Tata, Ch. 6 |

3/11 | SUSY Gauge Theories (continued) | Baer and Tata, Ch. 6 |

3/13 | SUSY Breaking | Baer and Tata, Ch. 7 |

3/18 | Spring Break! | |

3/20 | Spring Break! | |

3/25 | SUSY Breaking (continued) | Baer and Tata, Ch. 7 |

3/27 | SUSY Breaking (continued) | Baer and Tata, Ch. 7 |

4/1 | MSSM | Baer and Tata, Ch. 8 |

4/3 | MSSM (continued) | Baer and Tata, Ch. 8 |

4/8 | MSSM (continued) | Baer and Tata, Ch. 8 |

4/10 | MSSM: Low energy constraints & RGE (digression) | Baer and Tata, Ch. 9 |

4/15 | MSSM (continued) | Baer and Tata, Ch. 8 |

4/17 | Implications of MSSM | Baer and Tata, Ch. 9 |

4/22 | SUGRA | Baer and Tata, Ch. 10 |

4/24 | SUGRA | Baer and Tata, Ch. 10 |

4/29 | Gauge Mediation of SUSY Breaking | Pheno Conference |

5/1 | Gravity Mediation | Baer and Tata, Ch. 11 |

5/6 | Gauge Mediation | Baer and Tata, Ch. 11 |

5/1 | Anomaly Mediation | Baer and Tata, Ch. 11 |

- Glatzmaier, Michael
- Gonderinger, Matthew
- Li, Ye
- Long, Andrew
- Mac Donald, Ray
- McFarlane, Michael
- McGuirk, Paul
- Passmore, Daniel
- Patel, Hiren
- Rao, Yongyan
- Stuart, Alexander
- Zhou, Peng

Of course, if someone skips an assignment, I will go to the next one in line, so the above formula is at best an estimate.

You can also go solo, or to write a term paper instead, if the above does not appeal to you.

- Gauge Mediation (Matthew Gonderinger, Andrew Long, Paul McGuirk, Daniel Passmore)
- Gravity Mediation (Youngyan Rao)
- Anomaly Mediation (Ye Li, Peng Zhou)
- SUSY Algebra (Alex Stuart)
- SUSY Dark Matter (Michael Glatzmaier, Michael McFarlane, Hiren Patel)