  Short-distance new physics at (or slightly) above the TeV scale should not
excessively violate the approximate flavor symmetries of the SM in order to
comply with stringent constraints from flavor-changing neutral currents. In
this respect, flavor symmetries provide an effective organizing principle for
the vast parameter space of the SMEFT. In this work, we classify all possible
irreducible representations under $U(3)^5$ flavor symmetry of new heavy spin-0,
1/2, and 1 fields which integrate out to dimension-6 operators at the tree
level. For a general perturbative UV model, the resulting flavor-symmetric
interactions are very restrictive and, in most cases, predict a single
Hermitian operator with a definite sign. These leading directions in the SMEFT
space deserve particular attention. We derive an extensive set of present
experimental constraints by utilizing the existing global SMEFT fits, which
incorporate data from top quark, Higgs boson, and electroweak measurements,
along with constraints on dilepton and 4-lepton contact interactions. The
derived set of bounds comprehensively summarises the present knowledge from
indirect searches of flavor-blind new physics mediators.
