Higher Flavor Symmetries in the Standard Model

TL;DR

This paper explores the complex higher-group structures of flavor symmetries in the Standard Model, revealing constraints on unification models and the role of Yukawa couplings as spurions within these symmetries.

Contribution

It introduces the concept of higher-group flavor symmetries in the Standard Model and analyzes their implications for unification and fermion multiplet structures.

Findings

Higher flavor symmetries form higher-groups intertwining zero- and one-form symmetries.

Constraints on unification models like Georgi-Glashow, SO(10), and Pati-Salam.

Yukawa couplings act as spurions breaking these higher symmetries in trinification.

Abstract

We initiate the study of the generalized global flavor symmetries of the Standard Model. The presence of nonzero triangle diagrams between the $U(3)^5$ flavor currents and the $U(1)_Y$ hypercharge current intertwines them in the form of a higher-group which mixes the zero-form flavor symmetries with the one-form magnetic hypercharge symmetry. This higher symmetry structure greatly restricts the possible flavor symmetries that may remain unbroken in any ultraviolet completion that includes magnetic monopoles. In the context of unification, this implies tight constraints on the combinations of fermion species which may be joined into multiplets. Three of four elementary possibilities are reflected in the classic unification models of Georgi-Glashow, $SO(10)$, and Pati-Salam. The final pattern is realized non-trivially in trinification, which exhibits the sense in which Standard Model Yukawa couplings which violate these flavor symmetries may be thought of as spurions of the higher-group. Such modifications of the ultraviolet flavor symmetries are possible only if new vector-like matter is introduced with masses suppressed from the unification scale by the Yukawa couplings.