Spelling Out Leptonic CP Violation in the Language of Invariant Theory

Abstract

In terms of flavor invariants, we establish the intimate connection between leptonic CP violation in the canonical seesaw model for neutrino masses and that in the seesaw effective field theory (SEFT). For the first time, we calculate the Hilbert series and explicitly construct the primary flavor invariants in the SEFT by considering both the dimension-five Weinberg operator ${\mathcal{O}}_5^{\alpha \beta }=\overline{{\ell }_{\alpha \mathrm{L}}^{}}\tilde{H}{\tilde{H}}^{\mathrm{T}}{\ell }_{\beta \mathrm{L}}^{\mathrm{C}}$ and the dimension-six operator ${\mathcal{O}}_6^{\alpha \beta }=\overline{{\ell }_{\alpha \mathrm{L}}^{}}\tilde{H}\mathrm{i}/\partial {\tilde{H}}^{†}{\ell }_{\beta \mathrm{L}}^{}$ at the tree-level matching. The inclusion of only the Wilson coefficients $C_5^{\alpha \beta }$ and $C_6^{\alpha \beta }$ already enables the SEFT to incorporate all physical information about the full seesaw model. Moreover, the minimal sufficient and necessary conditions for CP conservation both in the SEFT and in the full theory are clarified, and the matching between the flavor invariants in both theories is accomplished. Through the matching of flavor invariants, the CP asymmetries necessary for successful leptogenesis are directly linked to those in neutrino-neutrino and neutrino-antineutrino oscillations at low energies. Surprisingly, it is revealed that the precise measurements of $C_5^{\alpha \beta }$ and $C_6^{\alpha \beta }$ in low-energy experiments are powerful enough to probe the full seesaw model, including CP violation for cosmological matter-antimatter asymmetry.

7+5 pages, 2 tables, more discussions added, accepted for publication as a Letter in Phys. Rev. D

References in corpus (10)

• Physics Potential of a Long Baseline Neutrino Oscillation Experiment Using J-PARC Neutrino Beam and Hyper-Kamiokande
• Baryogenesis from the weak scale to the grand unification scale
• A new bridge between leptonic CP violation and leptogenesis
• Hilbert Series for Flavor Invariants of the Standard Model
• Properties of CP Violation in Neutrino-Antineutrino Oscillations
• Flavor Invariants and Renormalization-group Equations in the Leptonic Sector with Massive Majorana Neutrinos
• Beyond Jarlskog: 699 invariants for CP violation in SMEFT
• Non-unitary Leptonic Flavor Mixing and CP Violation in Neutrino-antineutrino Oscillations
• Sufficient and Necessary Conditions for CP Conservation in the Case of Degenerate Majorana Neutrino Masses
• CP violation and flavor invariants in the seesaw effective field theory

Cited by in corpus (8)

• 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
• Constructing Operator Basis in Supersymmetry: A Hilbert Series Approach
• Discrete symmetries and Efficient Counting of Operators
• CP violation in light neutrino oscillations and heavy neutrino decays: a general and explicit seesaw-bridged correlation