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@ARTICLE{Grojean:619881,
      author       = {Grojean, Christophe and Kley, Jonathan and Leflot, Damien
                      and Yao, Chang Yuan},
      title        = {{T}he flavor invariants of the ν{SM}},
      journal      = {Journal of high energy physics},
      volume       = {2024},
      number       = {12},
      issn         = {1029-8479},
      address      = {[Trieste]},
      publisher    = {SISSA},
      reportid     = {PUBDB-2024-07986, arXiv:2406.00094. CERN-TH-2024-076.
                      DESY-24-021. HU-EP-24/14},
      pages        = {69},
      year         = {2024},
      note         = {27 pages + appendices, 3 figures},
      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 νSM, 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 generating and primary sets of
                      invariants for the νSM 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 generating set contains 459
                      invariants, out of which 208 are CP-even and 251 are CP-odd.
                      In the seesaw limit of the νSM, 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 flavor-invariant
                      way with a 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.},
      keywords     = {CP Violation (autogen) / Flavour Symmetries (autogen) / New
                      Light Particles (autogen) / Sterile or Heavy Neutrinos
                      (autogen)},
      cin          = {T},
      ddc          = {530},
      cid          = {I:(DE-H253)T-20120731},
      pnm          = {611 - Fundamental Particles and Forces (POF4-611) / DFG
                      project G:(GEPRIS)390833306 - EXC 2121: Quantum Universe
                      (390833306) / ASYMMETRY - Essential Asymmetries of Nature
                      (101086085)},
      pid          = {G:(DE-HGF)POF4-611 / G:(GEPRIS)390833306 /
                      G:(EU-Grant)101086085},
      experiment   = {EXP:(DE-MLZ)NOSPEC-20140101},
      typ          = {PUB:(DE-HGF)16},
      eprint       = {2406.00094},
      howpublished = {arXiv:2406.00094},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:2406.00094;\%\%$},
      UT           = {WOS:001399239700002},
      doi          = {10.1007/JHEP12(2024)069},
      url          = {https://bib-pubdb1.desy.de/record/619881},
}