Four-fermion operators at dimension 6: Dispersion relations and UV completions

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