  A major task in phenomenology today is constraining the parameter space of
SMEFT and constructing models of fundamental physics that the SM derives from.
To this effect, we report an exhaustive list of sum rules for 4-fermion
operators of dimension 6, connecting low energy Wilson coefficients to
cross-sections in the UV. Unlike their dimension 8 counterparts which are
amenable to a positivity bound, the discussion here is more involved due to the
weaker convergence and indefinite signs of the dispersion integrals. We
illustrate this by providing examples with weakly coupled UV completions
leading to opposite signs of the Wilson coefficients for both convergent and
non-convergent dispersion integrals. We further decompose dispersion integrals
under weak isospin and color groups which lead to a tighter relation between IR
measurements and UV models. These sum rules can become an effective tool for
constructing consistent UV completions for SMEFT following the prospective
measurement of these Wilson coefficients.
