  In the framework of the Standard Model Effective Field Theory, we compare the
lower bounds on the scale of new physics possibly contributing to the
$f\bar{f}h$ effective couplings, obtained from the measurements of different
observables, under the assumption that the Wilson coefficients of the relevant
dim 6 operators respect certain flavour structure: either the Minimal Flavour
Violation (MFV) ansatz or a flavour symmetry, often invoked to explain the
observed pattern of fermion masses and mixings. We perform a global analysis of
the bounds following from the limits on the diagonal couplings measured in the
Higgs boson production and decays at the LHC experiments. Another set of bounds
is obtained from the limits on non-diagonal couplings constrained by the
variety of flavour changing neutral current (FCNC) and radiative decay
processes. With the present precision of the LHC data, the FCNC data give
stronger bounds on the scale of new physics than the collider data (obviously,
for the MFV ansatz only collider data are relevant): once the Wilson
coefficients respect some flavour structure, the obtained bounds are in the TeV
range. In the quark case, these limits are compatible with a few percent
deviations from the SM Yukawa couplings and only mildly more stringent than
those obtained from the available collider data. For leptons, instead, the FCNC
bounds are stronger and then a signal in the near future collider data would
mean the violation of the flavour symmetry or indicate the presence of
additional beyond the Standard Model contributions, affecting the flavour
observables, that leads to cancellations.
