Connecting Seesaw Effective Field Theory to Full Theory via Flavor Invariants

TL;DR

This paper establishes a novel connection between the full seesaw model and its low-energy effective theory using flavor invariants and Hilbert series, showing how low-energy measurements can probe high-energy physics and CP violation.

Contribution

It introduces a new approach using invariant theory and Hilbert series to relate the full seesaw model to its effective field theory, enabling insights into high-energy parameters from low-energy data.

Findings

Flavor invariants link low-energy SEFT to the full seesaw model.

Measurements of dimension-five and six operators can probe the full theory.

CP violation in the full model can be studied through low-energy observables.

Abstract

The canonical seesaw models are one of the simplest and most natural scenarios that can account simultaneously for neutrino masses and matter-antimatter asymmetry in our universe. Below the seesaw scale, one can integrate out the heavy degrees of freedom to construct the seesaw effective field theory (SEFT). In this talk, we investigate the connection between the full seesaw model and the low-energy SEFT from a brand-new perspective: the invariant theory. Using the powerful tool of Hilbert series, we demonstrate the intimate relation between the flavor space of the SEFT and that of its ultraviolet theory. Through the matching of flavor invariants, it is revealed that the precise measurements of dimension-five and dimension-six operators in the SEFT at low energies are powerful enough to probe the full seesaw model, including CP violation necessary for successful leptogenesis.