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

Understand

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.