Abstract
CP-odd invariants are useful for studying the CP properties of Lagrangians in any basis. We explain how to build basis invariants for the scalar sector, and how to distinguish CP-odd invariants from CP-even invariants. Up to a certain order, we use these methods to systematically build all the CP-odd invariants. The CP-odd invariants signal either explicit or spontaneous violation of CP. Making use of the CP-odd invariants, we determine the CP properties of potentials with 3 and with 6 Higgs fields arranged as triplets of specific discrete symmetries in the Δ(3n2) or Δ(6n2) series (inlcuding A4, S4, Δ(27) and Δ(54) as well as the cases for n > 3).
Highlights
This contribution to the proceedings of DISCRETE 2016 is based on [1].CP violation (CPV) is present in the Standard Model (SM) in the Yukawa sector, due to the replication of fermion in 3 generations
Physics does not depend on choice of basis, and the amount of CPV in the SM can be calculated in a weak basis invariant which can be expressed in terms of the quark mass matrices [2, 3]
A CP-odd invariants (CPIs) can be built from a basis invariant that changes if all upper indices are exchanged with the lower indices, which, up to rearranging the tensors, corresponds to diagrams that are distinct when the arrows are reversed and to contraction matrices that not symmetric
Summary
This contribution to the proceedings of DISCRETE 2016 is based on [1]. CP violation (CPV) is present in the Standard Model (SM) in the Yukawa sector, due to the replication of fermion in 3 generations. CPV is enabled in the scalar sector of the 2 (or more) Higgs Doublet Model (HDM) [4]. We apply them to several potentials with 3 or 6 Higgs fields with a discrete symmetry from the ∆(3n2) and ∆(6n2) series These symmetries are considered frequently in the context of flavour and CP models [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38]. Our systematic study through the new CPIs revealed several novel results
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