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Minimal flavour violation and beyond

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Abstract

We review the formulation of the Minimal Flavour Violation (MFV) hypothesis in the quark sector, as well as some “variations on a theme” based on smaller flavour symmetry groups and/or less minimal breaking terms. We also review how these hypotheses can be tested in B decays and by means of other flavour-physics observables. The phenomenological consequences of MFV are discussed both in general terms, employing a general effective theory approach, and in the specific context of the Minimal Supersymmetric extension of the SM.

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Notes

  1. The notion of MFV can also be extended to the lepton sector; however, in this case there is not a unique way to define the minimal sources of flavour symmetry breaking if one wants to accommodate non-vanishing neutrino masses. We postpone a discussion about this point to Sect. 3.3.

  2. As pointed out in [4], this statement is not fully correct since the a i could have non-vanishing flavour-blind phases proportional the Jarlskog invariant J CP=det[Y u(Y u)†,Y d(Y d)†]. However, the smallness of J CP implies that these phases play a negligible role in flavour-violating observables (unless enhanced by unnaturally large coefficients).

  3. The Unitarity Triangle shown on the left plot of Fig. 1 includes also the \(\varDelta M_{B_{s}}/\varDelta M_{B_{d}}\) constraint, assuming this ratio is not modified with respect to the SM. This condition holds only in the so-called constrained MFV scenario of Ref. [5] (see Sect. 2.2).

  4. The conclusion that K decays are the most sensitive probes of possible deviations from the strict MFV ansatz follows from the strong suppression of the s→d short-distance amplitude in the SM [\(V_{td}V_{ts}^{*} ={\mathcal{O}}(10^{-4})\)], and goes beyond the hypothesis of an underlying GUT. This is the reason why \(K \to\pi\nu\bar{\nu}\) decays, which are the best probes of s→d ΔF=1 short-distance amplitudes, play a key role in any extension of the SM containing non-minimal sources of flavour symmetry breaking.

  5. The combination of this flavour symmetry with the split-family hypothesis was dubbed “effective MFV” in Refs. [65, 66] but we stress that it goes beyond MFV in the sense of Sect. 2.

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Acknowledgements

We thank R. Barbieri, A.J. Buras, G. Giudice, G. Perez, and W. Altmannshofer for useful comments and discussions. G.I. acknowledges the support of the TU München—Institute for Advanced Study, funded by the German Excellence Initiative, and the EU ERC Advanced Grant FLAVOUR (267104). D.M.S. is supported by the EU ITN “Unification in the LHC Era”, contract PITN-GA-2009-237920 (UNILHC).

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Authors and Affiliations

  1. Laboratori Nazionali di Frascati, INFN, Via E. Fermi 40, 00044, Frascati, Italy

    Gino Isidori

  2. Theory Division, CERN, 1211, Geneva 23, Switzerland

    Gino Isidori

  3. Scuola Normale Superiore and INFN, Piazza dei Cavalieri 7, 56126, Pisa, Italy

    David M. Straub

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  1. Gino Isidori
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Isidori, G., Straub, D.M. Minimal flavour violation and beyond. Eur. Phys. J. C 72, 2103 (2012). https://doi.org/10.1140/epjc/s10052-012-2103-1

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