Minimal Flavour Violation in a custodial Two Higgs Doublet Model

Refined measurements of the new scalar discovered during the first run of the LHC through more accumulated data have shown an impressive consistency with the Standard Model (SM) Higgs boson and its spontaneous symmetry breaking mechanism. However, there are numerous theoretical and experimental motivations to study alternative scenarios such as the Two Higgs Doublet Model (2HDM). The approach taken in this work falls in the context of the current success of the SM. While studying physics beyond the SM, one needs to ponder about the properties of the latter that make it so succesful and to think about the advantages or solutions the New Physics model might offer. On the one hand, while concentrating in the implications of a 2HDM in the flavour sector and in order to provide predictions that could be experimentally observed in the near future, we assume a Minimal Flavour Violation (MFV) hypothesis for the new flavour structures beyond the SM. In this way, additional fine-tuning, mass hierarchies or CP violating phases absent in the SM are avoided. On the other hand, the custodial symmetry that rises accidentally in the SM is hardly maintained in New Physics models with a broader scalar sector. Its experimental test is given by the electroweak precision tests. In this work, we consider a particular case in the 2HDM class where the custodial symmetry is preserved. The study of the phenomenology concerning flavour quantities coming from the neutral strange B mesons system, such as the mass diference or the two muons rare decay, or from CP violation in the neutral kaon system, provides then interesting constraints in the framework of this custodial invariant 2HDM with MFV.