CP violation and flavor invariants in the seesaw effective field theory

Abstract

In this paper, we systematically study the algebraic structure of the ring of the flavor invariants and the sources of CP violation in the seesaw effective field theory (SEFT), which is obtained by integrating out heavy Majorana neutrinos in the type-I seesaw model at the tree level and thus includes the dimension-five Weinberg operator and one dimension-six operator. For the first time, we calculate the Hilbert series and explicitly construct all the primary flavor invariants in the SEFT. We show that all the physical parameters can be extracted using the primary invariants and any CP-violating observable can be expressed as the linear combination of CP-odd flavor invariants. The calculation of the Hilbert series shows that there is an equal number of primary flavor invariants in the SEFT and in the full seesaw model, which reveals the intimate connection between the flavor space of the SEFT and that of its ultraviolet theory. A proper matching procedure of the flavor invariants is accomplished between the SEFT and the full seesaw model, through which one can establish a direct link between the CP asymmetries in leptogenesis and those in low-energy neutrino oscillations.

44 pages, 4 tables, more discussions and references added, version accepted by JHEP

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• Hilbert Series, the Higgs Mechanism, and HEFT
• Adding Flavor to the SMEFT
• Opportunistic CP Violation
• 23, 381, 6242, 103268, 1743183, ...: Hilbert series for CP-violating operators in SMEFT
• The Geometric $\nu$SMEFT: Operators and Connections
• Spelling Out Leptonic CP Violation in the Language of Invariant Theory
• Constructing Operator Basis in Supersymmetry: A Hilbert Series Approach
• Discrete symmetries and Efficient Counting of Operators
• Counting Operators in $N=1$ Supersymmetric Gauge Theories
• Automated Ring-Diagram Framework for Classifying CP Invariants
• Leptonic CP violation from the seesaw
• Flavour Invariants of the N Higgs Doublet Model