CERN Accelerating science

Article
Report number	arXiv:2406.00094 ; CERN-TH-2024-076 ; DESY-24-021 ; HU-EP-24/14
Title	The flavor invariants of the $\nu$SM
Related title	The flavor invariants of the νSM
Author(s)	Grojean, Christophe (DESY ; Humboldt U., Berlin ; CERN) ; Kley, Jonathan (DESY ; Humboldt U., Berlin) ; Leflot, Damien (Annecy, LAPTH) ; Yao, Chang-Yuan (DESY ; Nankai U.)
Publication	2024-12-10
Imprint	2024-05-31
Number of pages	60
In:	JHEP 2412 (2024) 069
DOI	10.1007/JHEP12(2024)069
Subject category	hep-ph ; Particle Physics - Phenomenology
Abstract	Sixty years after the experimental discovery of CP violation in the quark sector, the existence of a similar CP violation in the lepton sector is still to be established. Actually, the structure of such a violation depends crucially on the origin of the neutrino masses. In an attempt at categorizing the leptonic sources of CP violation, we studied the $\nu$SM, the Standard Model extended with three generations of sterile neutrinos, that can interpolate continuously between the Dirac and Majorana scenarios of neutrino masses. In particular, we perform a classification of the Jarlskog-like flavor invariants entering CP-violating observables and we study their suppression with the heavy Majorana mass in the seesaw limit of the model. To simplify the construction of the invariants, we introduce a graph-based method. With the guidance of the Hilbert series and plethystic logarithm of the theory, we construct the \emph{generating} and \emph{primary} sets of invariants for the $\nu$SM for the first time. Unlike in the Standard Model and some other theories, we find that the numbers of generating invariants and the syzygies among them cannot immediately be read off from the plethystic logarithm, but require a more careful examination. Our analysis reveals that the \emph{generating} set contains 459 invariants, out of which 208 are CP-even and 251 are CP-odd. In the seesaw limit of the $\nu$SM, we show that all parameters of the UV theory can be captured in the effective theory with a certain suppression with the heavy Majorana mass, while these parameters can only appear in a \emph{flavor-invariant} way with a \emph{higher} mass suppression. Furthermore, we discuss how the necessary and sufficient conditions for CP violation can be captured by utilizing these invariants. Along the way, we present useful algorithms to enumerate and build the flavor invariants.
Copyright/License	publication: © 2024 The Authors (License: CC-BY-4.0), sponsored by SCOAP³ preprint: (License: CC BY 4.0)

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