Theory of Elementary Particles

U. Tokyo graduate course, 2021 summer semester (code: 35603-0094)

Objectives

The course is virtually "Quantum Field Theory III," although we have applications to high-energy physics primarily in mind.
During the first half of this course, UV divergence, renormalization and renormalization group are discussed.
In the latter half, we start off with soft/collinear (IR) divergence, and will proceed to factorization theorem.

Various aspects of the Standard Model (such as electroweak symmetry breaking, quark/lepton masses and mixings) should be covered by other courses.
                Subatomic Physics     (s. semester, senior and graduate students),
                Elementary Particle Physics II     (a. semester, senior and grad students),
                Elementary Particle Physics III     (s. semester, grad students).

Prerequisite: We assume that students attending this course are familiar with tree-level computations using Feynman rules, already, or at least by late April. The instructor is happy to support the process of catching up.

Hours and Rooms: Mondays 10:25--11:55, on Zoom. Zoom login information is found on UTokyo ITC-LMS (learning management system).

Instructor: Taizan Watari,   Kavli IPMU, Kashiwa Campus

Language: Whenever an international student is in the classroom, English is used for explanation. Questions in Japanese are also welcome all the time during the class, however.

Announcement:
                (4) All the homework problems will be posted here ( = Classroom attendance is not required to get the course credit).
                (5) Homework submission final deadline: August 16(Monday) midnight.

Plan
0. Feynman rule (week 01)
1. UV divergence and regularization (week 02~03)
2. Renormalized perturbation theory (week 03~06)
3. Renormalization group (week 06~08)
4. Low-energy effective theory (week 09 08~09)
5. Soft and collinear divergence (week 10 09~10)
6. Cancellation of IR divergence (week 10~11)
7. Parton distribution and collinear factorization (week 12~14)

Lecture Notes and Homework Problems: (see general instruction on homework problems)

Apr. 05: note-01 ----- Feynman rules //
                                          [For references, see the week-4 entry of the QFT II course]
Apr. 19: note-02 ----- self-energy, UV divergence
                                          [7.1, 7.2, 6.3]
Apr. 26: note-03 hw-03 regularization // renormalized perturbation theory (on-shell)
                                          [7.1, 7.2, 10.2, 10.3]        
May 10: note-04 hw-04 renormalized perturbation theory (cont'd)
                                          [10.2, 10.3, 6.3]
May 17: note-05 ----- degree of divergence, renormalizability
                                          [10.1, 10.4, 7.4]
May 24: note-06 ----- renormalization in non-renormalizable models // choices of renormalization conditions
                                          [[W-I 12.3, W-II 19.5], 12.2, 12.3, 7.5]
May 31: note-07-v2 hw-07-v2 renormalization group, dim. regularization
                                          [7.5, 11.4, 12.1, 12.4]        
June 07: note-08 ----- Wilsonian interpretation // low-energy effective theory
                                            [12.1, 12.4, [W-I 12.3, 12.4], 18.2]

June 14: note-09 hw-09 operator product expansion // soft and collinear divergence
                                            [12.1, 12.4, 18.3--18.5, [W-II 20.1--20.3, 20.6], [St 2.1--2.3], 6.1, 6.4, 6.5]
June 21: note-10 ----- soft and collinear divergence (cont'd) // cacellation, Cutkosky rule
                                            [6.1, 6.4, 6.5, [St 2.1--3.3]]
June 28: note-11 ----- Cutkosky rule, total hadronic cross section, OPE //
                                            [[St 2.1--3.3], 17.2, 18.4]
July 05: note-12 ----- DIS, structure function, OPE
                                            [[pink 4.1], 17.3, 18.5]
July 12: note-13 ----- Mellin transformation, parton distribution function
                                            [[pink 4.3], 17.3, 17.5, 18.5, [W-II 20.6]]
July 19: note-14 ----- DGLAP equation, collinear factorization
                                            [17.5, 18.5, [W-II 20.6]]

[Advanced homework problems]

Materials not to be covered in this course include anomaly and topology.

numbers in [     ] are the relevant sections in textbooks and references. When the textbooks or references are not specified, that is [PS] below.

Textbooks and References:

This course is not based on a specific textbook. I often refer to the following textbooks, though, when I prepare for lectures:

[PS] M. Peskin and D. Schroeder, An Introduction to Quantum Field Theory,
[W-I, II] S. Weinberg, The Quantum Theory of Fields volume I and II.
[C] J. Collins, Foundations of Perturbative QCD.
[FR] J. Forshaw and D. Ross, Quantum Chromodynamics and the Pomeron.
[BP] V. Barone and E. Predazzi, High-Energy Particle Diffraction.

[St] G. Sterman TASI lecture "Parton, Factorization and Resummation",
[pink] R. Ellis, W. Stirling and B. Webber, QCD and Collider Physics.

Grading Scheme: Letter grading [ excellent, good, OK or fail ] based on reports.

All the homework problems will be posted here.
Each homework problem is in either one of categories A, B, C, D and E, and you will pass (excellent, good or OK) if

1 x #[A] + 1.5 x #[B] + 2 x #[C] + 4 x #[D] + 6 x #[E] is 6 or larger.
(if you have not got the credit of the QFT II course, it is OK to include the [B] or [C] problems in the QFT II course, 2020 up to 3 in the formula above.)

Submission: though U Tokyo ITC-LMS (learning management system).

Reports submitted are not returned, so please keep a copy if you need one.