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the Yukawa eigenvalues. In this respect, the MFV criterion provides the maximal protection of FCNCs (or the minimal violation of flavor symmetry), since the full structure of Yukawa matrices is preserved. At the same time, this criterion is based on a renormalization-group-invariant symmetry argument, which can be implemented independently of any specific hypothesis about the dynamics of the new-physics framework. This model-independent structure does not hold in most of the alternative definitions of MFV models that can be found in the literature. For instance, the definition of Ref. [29] (denoted constrained MFV, or CMFV) contains the additional requirement that the effective FCNC operators playing a significant role within the SM are the only relevant ones also beyond the SM. This condition is realized only in weakly coupled theories at the TeV scale with only one light Higgs doublet, such as the MSSM with small tan β where no large logs, or sizable anomalous dimension are present [30] (see also [31]). It does not hold in several other frameworks, such as Higgsless models, 5D MFV models, or the MSSM with large tan β . 

In NP models where sizable anomalous dimensions are present, the expansion in powers of the Yukawa spurions cannot be truncated at the first non-trivial order. In this limit, denoted as General MFV (GMFV), higher-order terms in the third-generation Yukawa couplings need to be re-summed. As shown in Eq. (4.2), if only the top-quark Yukawa coupling is of order one, this resummation has negligible consequences for flavour-violating processes. (To measure the effect requires that the accuracy on rare K ( D ) decays would become strong enough to probe the contributions related to the charm (strange) quark Yukawa coupling [30]). However, significant differences from a linear expansion may arise if both top- and bottom-quark Yukawa couplings are order one as it happens, for instance, in the large tan β regime. 

