  We investigate the information that can be gained by including flavour data
in fits of the Standard Model Effective Field Theory (SMEFT) with the
assumption of Minimal Flavour Violation (MFV), allowing - as initial conditions
at the high scale - leading terms in spurionic Yukawas only. Starting therefore
from a theory with no tree level flavour changing neutral currents at the scale
of new physics, we calculate effects in flavour changing processes at one loop,
and the resulting constraints on linear combinations of SMEFT coefficients,
consistently parameterising the electroweak parameters and the CKM within the
SMEFT. By doing a global fit including electroweak, Higgs and low energy
precision measurements among others, we show that flavour observables put
strong constraints on previously unconstrained operator directions. The
addition of flavour data produces four independent constraints at order TeV or
above on otherwise flat directions; reducing to three when complete U(3)^5
flavour symmetry is assumed. Our findings demonstrate that flavour remains a
stringent test for models of new physics, even in the most flavourless
scenario.
