publication . Other literature type . Article . 2016

CP-odd invariants for multi-Higgs models and applications with discrete symmetry

Ivo de Medeiros Varzielas; Stephen F King;
Open Access
  • Published: 20 Sep 2016
  • Publisher: American Physical Society (APS)
Abstract
CP-odd invariants provide a basis independent way of studying the CP properties of Lagrangians. We propose powerful methods for constructing basis invariants and determining whether they are CP odd or CP even, then systematically construct all of the simplest CP-odd invariants up to a given order, finding many new ones. The CP-odd invariants are valid for general potentials when expressed in a standard form. We then apply our results to scalar potentials involving three (or six) Higgs fields which form irreducible triplets under a discrete symmetry, including invariants for both explicit as well as spontaneous CP violation. The considered cases include one tripl...
Subjects
arXiv: High Energy Physics::Phenomenology
Funded by
RCUK| Exploring the Limits of the Standard Model and Beyond
Project
  • Funder: Research Council UK (RCUK)
  • Project Code: ST/J000396/1
  • Funding stream: STFC
,
EC| SIFT
Project
SIFT
Symmetry Investigations in Flavour Theories
  • Funder: European Commission (EC)
  • Project Code: 327195
  • Funding stream: FP7 | SP3 | PEOPLE
,
EC| INVISIBLES
Project
INVISIBLES
INVISIBLES
  • Funder: European Commission (EC)
  • Project Code: 289442
  • Funding stream: FP7 | SP3 | PEOPLE
,
EC| ELUSIVES
Project
ELUSIVES
The Elusives Enterprise: Asymmetries of the Invisible Universe
  • Funder: European Commission (EC)
  • Project Code: 674896
  • Funding stream: H2020 | MSCA-ITN-ETN
79 references, page 1 of 6

2 CP-odd invariants for scalar potentials 3 2.1 General formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 CP-odd invariants for explicit CP violation . . . . . . . . . . . . . . . . . 7 2.3 Diagrams for invariants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.4 CP-odd invariants only built from Z tensors . . . . . . . . . . . . . . . . . 11 2.5 CP-odd invariants built from Y and Z tensors . . . . . . . . . . . . . . . . 12

4 A4 = (12) invariant potentials 15 4.1 One avour triplet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 4.2 One avour triplet of Higgs doublets . . . . . . . . . . . . . . . . . . . . . 16 4.3 Two avour triplets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 4.4 Two avour triplets of Higgs doublets . . . . . . . . . . . . . . . . . . . . . 18 4.5 S4 invariant potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

5 (27) invariant potentials 21 5.1 One avour triplet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 5.2 One avour triplet of Higgs doublets . . . . . . . . . . . . . . . . . . . . . 23 5.3 Two avour triplets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 5.4 Two avour triplets of Higgs doublets . . . . . . . . . . . . . . . . . . . . . 24 5.5 (54) invariant potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

6 (3n2) invariant potentials with n > 3 26 6.1 One avour triplet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 6.2 One avour triplet of Higgs doublets . . . . . . . . . . . . . . . . . . . . . 26 6.3 Two avour triplets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 6.4 Two avour triplets of Higgs doublets . . . . . . . . . . . . . . . . . . . . . 28 6.5 (6n2) invariant potentials with n > 3 . . . . . . . . . . . . . . . . . . . . 29 8 CP-odd invariants for spontaneous CP violation 30 8.1 Minimisation condition in terms of diagrams . . . . . . . . . . . . . . . . . 32 8.2 Example applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 8.2.1 One triplet of A4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 8.2.2 One triplet of (27) . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Zaa51aa92 Za3a4 Za5a6 Za7a8 Za9a10 = a3a7 a6a8 a1a10 a2a4 2ds2 + d2s) (v2v3v12 + v1v3v22 + v1v2v32) 0 ~ 1; 0 k

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