Modular Invariance Approach to the Lepton and Quark Flavour Problems: from Bottom-up to Top-down

13 May 2024, 09:00 → 17 May 2024, 17:00 Europe/Berlin

2413/2-430 - MITP Seminar Room (MITP - Mainz Institute for Theoretical Physics, Johannes Gutenberg University Mainz)

Understanding the origins of flavour in both quark and lepton sectors is one of the most challenging fundamental problems in contemporary particle physics. The Workshop will be devoted to the approach to the flavour puzzle based on modular invariance, proposed in 2017 and since then extensively studied both in a bottom-up and a top-down perspective. Modular invariance has been investigated in the context of field and superstring theories, being a key feature of several theoretical constructions such as theories with toroidal compactification of extra dimensions, superstring theories on tori or orbifolds, supergravity theories. In this context the modular group acts on the matter generation space and is broken by the vacuum expectation value of a single complex scalar field, offering an economic setup to understand the origin of flavour, including CP violation, in particle physics. Yukawa couplings are described by modular forms, extensively studied by mathematicians since the 19^th century, and more recently, in particular, for their major implications on number theory. Modular invariance can be investigated both in a bottom-up and in a top-down approach, thus representing a unique opportunity for phenomenologists and string theorists to confront their ideas. Open questions that will be discussed during the Workshop include:

• Connection between bottom-up and top-down constructions.
• The problem of moduli stabilisation and supersymmetry breaking.
• Extensions of the modular group, such as symplectic or metaplectic groups.
• CP violation in the quark and lepton sectors.
• Reduction of parameters needed to describe the quark sector.
• Relation between the flavour puzzle and critical phenomena.

We encourage participation from both the more mathematical and string theory related as well as phenomenology communities, to ensure a thorough discussion connecting bottom-up and top-down approaches to this formidable and extremely challenging endeavour.

The list of participants includes:

• Gui-Jun Ding (USTC, Hefei)
• Stephen King (University of Southampton)
• Xiang-Gan Liu (UC, Irvine)
• Myriam Mondragón (UNAM, Mexico)
• Hajime Otsuka (Kyushu University)
• João Penedo (INFN Roma Tre)
• Saul Ramos-Sanchez (UNAM, Mexico)
• Michael Ratz (UC, Irvine)
• Nicole Righi (King's College London)
• Morimitsu Tanimoto (Niigata University)

Monday 13 May

1 Registration

2 Flavour model building I

Speaker: Stephen King

King_Mainz_2024.pdf

11:00 Coffee break

3 Flavour model building II

Speaker: Myriam Mondragon

Mondragon_FlavourModelBuilding_Mainz2024.pdf

12:30 Lunch break

4 Flavour models with multiple modular symmetries

Speaker: Ye-Ling Zhou

Zhou_MITP2024.pdf

5 Quark-lepton mass relations in modular invariant models (blackboard talk)

Speaker: Omar Medina

15:30 Coffee break

6 Modular forms at level 2 for flavour (blackboard talk)

Speaker: Matteo Parriciatu

7 Modular invariant holomorphic observables (blackboard talk)

Speaker: Xueqi Li

Tuesday 14 May

8 Bottom-up modular invariance approach to flavour I

Speaker: Gui-Jun Ding

Ding_modular_symmetry_bottom-up_Mainz.pdf

10:30 Coffee break

9 Quark mass hierarchy and CP violation in modular symmetry

Speaker: Morimitsu Tanimoto

Tanimoto_Mainz2024May.pdf

10 Discussion session on the bottom-up approach I

12:00 Lunch break

11 What can modular flavour symmetries do for you? (joint with the local theory seminar)

In recent years, modular invariance has been applied to the SM flavour puzzle, yielding compelling results. In this string-inspired paradigm, one does not require a multitude of scalar fields (flavons) with aligned VEVs and complicated potentials. Taking a bottom-up approach, one may instead rely on a single complex field -- the modulus. Yukawa couplings and mass matrices are obtained from functions of its VEV, which can be the only source of flavour symmetry breaking and of CP violation. Such predictive modular setups may, among other things, shed light on the patterns of fermion mixing, the origin of fermion mass hierarchies and the strong CP problem.

Speaker: João Penedo

Penedo_Theorie_Palaver_final.pdf

12 Discussion session on the bottom-up approach II

15:30 Coffee break

13 Free discussion

Wednesday 15 May

14 Top-down modular invariance approach to flavour I

Speaker: Saul Ramos-Sanchez

Ramos-Sanchez_Mainz_2024.pdf

10:30 Coffee break

15 Top-down modular invariance approach to flavour II

Speaker: Hajime Otsuka

Otsuka.pdf

12:00 Lunch break

16 F-theory models: some ways of being discrete

Speaker: George Leontaris

LEONTARISmainz2024.pdf

17 Discussion session on the top-down approach

15:30 Coffee break

18 Free discussion

Thursday 16 May

19 Beyond SL(2,Z) in the top-down approach

Speaker: Kaito Nasu

Nasu_Mainz_2024.pdf

10:30 Coffee break

20 Beyond SL(2,Z) in the bottom-up approach

Speaker: Xiang-Gan Liu

Liu_FLAVOR2024.pdf

12:00 Lunch break

21 Metaplectic flavor symmetries from magnetized tori (blackboard talk)

Speaker: Victoria Knapp-Perez

22 Discussion session on beyond SL(2,Z)

15:30 Coffee break

23 Free discussion

Friday 17 May

24 Moduli stabilisation I

Speaker: Nicole Righi

Righi_Mainz_ModStab.pdf

10:30 Coffee break

25 Moduli stabilisation II

Speaker: Michael Ratz

Ratz_Mainz2024.pdf

12:00 Lunch break

26 Radiative stabilization and pseudo NG bosons from finite modular symmetry (blackboard talk)

Speaker: Junichiro Kawamura

27 Modulus stabilisation and hilltop inflation with modular symmetry (blackboard talk)

Speaker: Xin Wang

28 Discussion session on the moduli stabilisation

15:30 Coffee break

29 Free discussion