Eur. Phys. J. C (2014) 74: 2953
https://doi.org/10.1140/epjc/s10052-014-2953-9

Regular Article - Theoretical Physics

Constraining multi-Higgs flavour models

¹ Instituto Superior de Engenharia de Lisboa-ISEL, Rua Conselheiro Emídio Navarro 1, 1959-007 , Lisbon, Portugal
² Centro de Física Teórica de Partículas (CFTP), Instituto Superior Técnico, Universidade de Lisboa, Avenida Rovisco Pais 1, 1049-001, Lisbon, Portugal
³ IFPA, Université de Liége, Allée du 6 Août 17, bâtiment B5a, 4000, Liége, Belgium
⁴ Sobolev Institute of Mathematics, Koptyug avenue 4, 630090, Novosibirsk, Russia
⁵ Department of Physics and Astronomy, Ghent University, Proeftuinstraat 86, 9000, Ghent, Belgium
⁶ Universidade Federal do ABC-UFABC, Santo André, SP, Brasil
⁷ Departament de Física Teòrica and IFIC, Universitat de València-CSIC, 46100, Burjassot, Spain

^* e-mail: gonzalez@cftp.ist.utl.pt
^** e-mail: ricardo.felipe@ist.utl.pt

Received: 26 April 2014
Accepted: 23 June 2014
Published online: 11 July 2014

Abstract

To study a flavour model with a non-minimal Higgs sector one must first define the symmetries of the fields; then identify what types of vacua exist and how they may break the symmetries; and finally determine whether the remnant symmetries are compatible with the experimental data. Here we address all these issues in the context of flavour models with any number of Higgs doublets. We stress the importance of analysing the Higgs vacuum expectation values that are pseudo-invariant under the generators of all subgroups. It is shown that the only way of obtaining a physical CKM mixing matrix and, simultaneously, non-degenerate and non-zero quark masses is requiring the vacuum expectation values of the Higgs fields to break completely the full flavour group, except possibly for some symmetry belonging to baryon number. The application of this technique to some illustrative examples, such as the flavour groups , and , is also presented.