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Spelling out leptonic $C P$ violation in the language of invariant theory

Institute for High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China and School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

^*Corresponding author. zhoush@ihep.ac.cn
^†yubr@ihep.ac.cn

Phys. Rev. D 106, L051701 – Published 9 September, 2022

DOI: https://doi.org/10.1103/PhysRevD.106.L051701

Abstract

In terms of flavor invariants, we establish the intimate connection between leptonic $C P$ 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 $O_{5}^{α β} = \bar{ℓ_{α L}} \tilde{H} {\tilde{H}}^{T} ℓ_{β L}^{C}$ and the dimension-six operator $O_{6}^{α β} = (\bar{ℓ_{α L}} \tilde{H}) i \partial ({\tilde{H}}^{†} ℓ_{β L})$ at the tree-level matching. The inclusion of only the Wilson coefficients $C_{5}^{α β}$ and $C_{6}^{α β}$ already enables the SEFT to incorporate all physical information about the full seesaw model. Moreover, the minimal sufficient and necessary conditions for $C P$ 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 $C P$ 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 $C_{5}^{α β}$ and $C_{6}^{α β}$ in low-energy experiments are powerful enough to probe the full seesaw model, including $C P$ violation for cosmological matter-antimatter asymmetry.

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Phys. Rev. D 106, L051701– Published 9 September, 2022

Vol. 106, Iss. 5 — 1 September 2022

Received 8 March 2022
Accepted 24 August 2022

DOI: https://doi.org/10.1103/PhysRevD.106.L051701

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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Spelling out leptonic $C P$ violation in the language of invariant theory

Abstract

Physics Subject Headings (PhySH)

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Spelling out leptonic CP violation in the language of invariant theory

Abstract

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (51)

Spelling out leptonic $C P$ violation in the language of invariant theory