Theory of Elementary Particles

U. Tokyo graduate course, 2025 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 (week 02--07).
In the latter half, we start off with soft/collinear (IR) divergence, and will proceed to factorization theorem (week 08--14).

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 13:00--14:45, room 285, Rigakubu 1 Goukan (Hongo Campus)

Instructor: Taizan Watari,   Kavli IPMU, Kashiwa Campus

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

Announcement:
                (a) Some of the materials for this course are posted here to provide access for the students even after the semester is over.
                (b) I have made a little more improvement on the lecture notes after the 2025 run before posting here.
                (c) I was assigned this same course (TEP 35603-0094) in 2012, 2017, 2021 and 2025. The course plan remained much the same for all the four times, although small adjustment had to be made to fit the academic calendar each time. Details below are for the 2025 run.

Pace of Progress
0. Feynman rule (week 01): this is for students who missed the QFT II course in the previous semester.

1. UV divergence and regularization (week 02~03)
2. Renormalized perturbation theory (week 03~05)
3. Renormalization group (week 06~07)
4. Low-energy effective theory (week 07 + 10)

5. Soft and collinear divergence (week 08~09)
6. Cancellation of IR divergence (week 09~10)
7. Parton distribution and collinear factorization (week 11~13)
8. Two-scale problems, TMD factorization (week 14)
            (only sketchy description in section 8 as an appetizer in the 2025 run)
            (in the 2017 run, 2.5 weeks (week 13--15) were spent for section 8)

Textbooks and References:

This course is not based on a specific textbook. Here is a list of textbooks and lecture notes that I referred to to prepare for the 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
[F] R. Field, Applications of Perturbative QCD.

Lecture Notes and References:
    The lecture notes posted below are prepared as a memo for what is to be written on blackboard during the class. They were made available to the students prior to the lectures, so the students do not have to be occupied by transcribing equations from the blackboard. Concepts and ideas are often more imporant than details in equations; they are explained in the class, but are not necessarily written in the lecture notes (I sometimes intentionally avoid writing them on distributed lecture notes so that students need to write them down by themselves in their own words; some were added before posting here).

    On average, 1 page = 15 minutes. What is written as "memo" in the lecture notes are often skipped to save time.

    The symbol [XX n.m] below means that related materials will be found at least in section n.m of the reference [XX] above.

Section 1 (ultraviolet divergence and regularization)
1.1 self energy     lecture notes week 2 (§1.1-1.2)     [PS 7.1, 7.2, 6.3]
1.2 evaluation of 1-loop self-energy
1.3 regularization     lecture notes week 3 (§1.3-2.1)     [PS7.1, 7.2, 10.2, 10.3]

Section 2 (renormalized perturbation theory)
2.1 the idea
2.2 QED in renormalized perturbation theory     lecture notes week 4 (§2.2)     [PS 10.2, 10.3, 6.3]
2.3 superficial degree of divergence     lecture notes week 5 (§2.3)     [PS 10.1, 10.4, 7.4]
2.4 renormalized perturbation theory of non-renormalizable theories     lecture notes week 6 (§3.4-3.2)     [W-I 12.3], [W-II 19.5], [PS 12.2, 12.3, 7.5]
Section 3 (renormalization group)
3.1 variations of renormalization conditions
3.2 renormalization at energy scale E and renormalization group     lecture notes week 7 (§3.2)     [PS 7.5, 11.4, 12.1, 12.4]
dimensional regularization [W-II 11.2, 18.6]
3.3 meaning of running coupling constants     lecture notes week 8 (§3.3--4.1)     [PS 12.1, 12.4, 18.2], [W-I 12.3, 12.4]
3.4 Wilson's interpretation of renormalization group

Section 4 (low-energy effective theory)
[PS 18.2--18.5], [W-II 20.1--20.3, 20.6]
4.1 matching
4.2 operator product expansion
Sections 5 (soft and collinear divergence) and 6 (their cancellation): lecture notes §5+6,
              (a supplementary note on unitarity and discontinuity ... in preparation??)

5.1 divergence in virtual corrections [PS], [W] [F 2], [St 2], [C 5]
5.2 divergence in real emissions (see refs. of section 5.1)
6.1 observable observables [PS] (cf Nucl. Phys. B157 (1979) 543,   hep-ph/0204244 section 3.1 for more)
6.2 Cutkosky rule [St app.B], [C 12.7], [PS], [BP 4.3], (hw E-5 for more)
6.3 OPE and non-perturbative corrections
              [PS 18.2--18.5??], [W-II 20.1--20.3, 20.6??] (cf section 2 of arXiv:1403.1277 for more)
Section 7 (parton distribution and collinear factorization): lecture notes §7
7.1 deep inelastic scattering
              Phys.Rev.Lett. 23 (1969) 930,     Phys.Rev.Lett. 23 (1969) 935,     Phys.Rev. D5 (1972) 528,     [BP 9.1]     (hw E-1 for more)
7.2 DIS structure functions
              [pink 4.1], [PS 18.5] [W-II 20.6]
7.3 evaluation of the Compton tensor by OPE at tree level
              [pink 4.2], [PS 18.5]

(Mellin transformation) [pink 4.3], [PS 18.5] [W-II 20.6]
7.4 parton distributiton functions
              [C 6], [PS 17.3, 18.5] [W-II 20.6], [BP 9.2], [FR 1.3], [BP 5.6]
7.5 initial state radiation [pink 4.3], [PS 17.5]
7.6 DGLAP equation and collinear factorization
              [PS 17.5, 18.5], [W-II 20.6], [pink 4.3], [F 4.4-4.9], [BP 9.3]
Section 8 (two scale problems, TMD factorization):     lecture notes §8
8.1 two scale problems
8.2 double log phase space in the 6D phi^3 theory
              [FR 2-4], [BP 8.3, 8.4]
8.3 Drell-Yan differential cross section and TMD factorization
              (cf [PS 17.4] for total cross section) [C 10, 13--14], [F 5]

Homework Problems
    after week 03     after week 04     after week 07     after week 09     problems in category D or E

Grading Scheme: Letter grading [ excellent, good, OK or fail ] based on reports.
(see general instruction on homework problems)

Each homework problem is in either one of categories A, B, C, D and E, and you will pass (excellent, good or acceptable) if

1 x #[A] + 1.5 x #[B] + 2 x #[C] + 4 x #[D] + 6 x #[E] is 6 or larger.

Submission: though UTOL (U Tokyo online learning management system).
Submission deadline: August 5 (Tue), 23:59.

my message after grading:
Never mind too much about which grade (A, B, C) you got. Such evaluations are never more valuable than what you have understood while working on the problems.
Most of the advanced homework problems asked you to submit such things as a reading note or at least a summary of what you have understood on reading materials. It is possible by 2025 to let an AI write a summary of a PDF document without digesting or scrutinizing the materials in those documents by yourself. I would not rule out such an approach entirely, if you still have learned something.