## On discrete Minimal Flavour Violation

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Zwicky, Roman

Fischbacher, Thomas

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We investigate the consequences of replacing the global flavour symmetry of
Minimal Flavour Violation (MFV) SU(3)_QxSU(3)_UxSU(3)_Dx..., by a discrete
D_QxD_UxD_Dx.. symmetry. Goldstone bosons resulting from the breaking of the
flavour symmetry generically lead to bounds on new flavour structure many
orders of magnitude above the TeV-scale. The absence of Goldstone bosons for
discrete symmetries constitute the \emph{primary} motivation of our work. Less
symmetry implies further invariants and renders the mass flavour basis
transformation observable in principle and calls for a hierarchy in the Yukawa
matrix expansion. We show, through the dimension of the representations, that
the (discrete) symmetry in principle does allow for additional Delta F = 2
operators. If though the Delta F = 2 transitions are generated by two
subsequent Delta F = 1 processes, as for example in the Standard Model, then
the four crystal-like groups Sigma(168) ~ PSL(2,7), Sigma(72phi), Sigma(216phi)
and especially Sigma(360phi) do provide enough protection for a TeV-scale
discrete MFV scenario. Models where this is not the case have to be
investigated case by case. Interestingly Sigma(216phi) has a (non-faithful)
representation corresponding to an A4-symmetry. Moreover we argue that the,
apparently often omitted, (D)-groups are subgroups of an appropriate
Delta(6g^2). We would like to stress that we do not provide an actual model
that realizes the MFV scenario nor any other theory of flavour.

Comment: 25 pages (15 pages main text) added reference and edited appendix A.2.1. concerning (C) & (D) groups

Comment: 25 pages (15 pages main text) added reference and edited appendix A.2.1. concerning (C) & (D) groups

##### Keywords

High Energy Physics - Phenomenology