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 (CFTP, Lisbon)
• Saul Ramos-Sanchez (UNAM, Mexico)
• Michael Ratz (UC, Irvine)
• Nicole Righi (King's College London)
• Morimitsu Tanimoto (Niigata University)

Monday, 13 May

09:30 → 10:00 Registration

10:00 → 11:00 Flavour model building I

Speaker: Stephen King

11:00 → 11:30 Coffee break

11:30 → 12:30 Flavour model building II

Speaker: Myriam Mondragon

12:30 → 14:30 Lunch break

14:30 → 15:00 TBA

Speaker: Ye-Ling Zhou

15:00 → 15:30 TBA

Speaker: Omar Medina

15:30 → 16:00 Coffee break

16:00 → 16:30 Modular forms at level 2 for flavour

Speaker: Matteo Parriciatu

16:30 → 17:00 TBA

Speaker: Xueqi Li

Tuesday, 14 May

09:30 → 10:30 Bottom-up modular invariance approach to flavour I

Speaker: Gui-Jun Ding

10:30 → 11:00 Coffee break

11:00 → 12:00 Bottom-up modular invariance approach to flavour II

Speaker: João Penedo

12:00 → 14:00 Lunch break

14:00 → 14:30 Quark mass hierarchy and CP violation in modular symmetry

Speaker: Morimitsu Tanimoto

14:30 → 15:30 Discussion session on the bottom-up approach

15:30 → 16:00 Coffee break

16:00 → 17:00 Free discussion

Wednesday, 15 May

09:30 → 10:30 Top-down modular invariance approach to flavour I

Speaker: Saul Ramos-Sanchez

10:30 → 11:00 Coffee break

11:00 → 12:00 Top-down modular invariance approach to flavour II

Speaker: Hajime Otsuka

12:00 → 14:00 Lunch break

14:00 → 14:30 F-theory models: some ways of being discrete

Speaker: George Leontaris

14:30 → 15:30 Discussion session on the top-down approach

15:30 → 16:00 Coffee break

16:00 → 17:00 Free discussion

Thursday, 16 May

09:30 → 10:30 Beyond SL(2,Z) in the top-down approach

Speaker: Kaito Nasu

10:30 → 11:00 Coffee break

11:00 → 12:00 Beyond SL(2,Z) in the bottom-up approach

Speaker: Xiang-Gan Liu

12:00 → 14:00 Lunch break

14:00 → 14:30 Metaplectic flavor symmetries from magnetized tori

Speaker: Victoria Knapp-Perez

14:30 → 15:30 Discussion session on beyond SL(2,Z)

15:30 → 16:00 Coffee break

16:00 → 17:00 Free discussion

Friday, 17 May

09:30 → 10:30 Moduli stabilisation I

Speaker: Nicole Righi

10:30 → 11:00 Coffee break

11:00 → 12:00 Moduli stabilisation II

Speaker: Michael Ratz

12:00 → 14:00 Lunch break

14:00 → 14:30 Radiative stabilization and pseudo NG bosons from finite modular symmetry

Speaker: Junichiro Kawamura

14:30 → 15:00 Modulus stabilisation and hilltop inflation with modular symmetry

Speaker: Xin Wang

15:00 → 15:30 TBA

Speaker: Cai-Chang Li

15:30 → 16:00 Coffee break

16:00 → 17:00 Free discussion