Higher Flavor Symmetries in the Standard Model

TL;DR

The paper probes generalized flavor symmetries of the Standard Model by incorporating higher-group structures that couple zero-form flavor currents to the magnetic one-form hypercharge symmetry. It introduces the two-group emergence theorem, which, through a nonzero triangle coefficient $\kappa$, forces flavor symmetries to be broken at or below the hypercharge higgsing scale in UV completions that embed $U(1)_Y$ in a nonabelian group, with a mass-sector sum rule determining how massive states contribute. Using a toy model and the Standard Model content (with Yukawas turned off or on), the authors classify the maximal UV flavor patterns and show how these patterns map onto well-known GUTs (SO(10), Georgi–Glashow SU(5), Pati–Salam) and trinification, including the necessity of vector-like matter whose masses are Yukawa-suppressed to realize certain UV completions. They also discuss a scenario without monopoles (flipped SU(5)) where the two-group constraints can be bypassed, illustrating how UV Yukawas can break the higher-group structure down to the Standard Model in the infrared. Overall, the work provides a unifying framework that connects SM flavor symmetries, higher-form symmetries, and grand-unification patterns, offering new constraints and guiding principles for UV model-building in the presence of magnetic monopoles or their absence.

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.

Figures (2)

• Figure 1: A triangle diagram between the gauged hypercharge current and two global flavor currents leads to the Standard Model two-group structure we will focus on below.
• Figure 2: Symmetry-breaking scales in the Standard Model with approximate flavor symmetry $f$ broken by a Yukawa $y_f$. To the extent that the flavor symmetry is approximate, its higher-group structure may be modified by vector-like matter which lies parametrically below the unification scale.