  We derive bounds on couplings in the standard model effective field theory
(SMEFT) as a consequence of causality and the analytic structure of scattering
amplitudes. In the SMEFT, there are 64 independent operators at mass dimension
eight that are quartic in bosons (either Higgs or gauge fields) and that
contain four derivatives and/or field strengths, including both CP-conserving
and CP-violating operators. Using analytic dispersion relation arguments for
two-to-two bosonic scattering amplitudes, we derive 27 independent bounds on
the sign or magnitude of the couplings. We show that these bounds also follow
as a consequence of causality of signal propagation in nonvacuum SM
backgrounds. These bounds come in two qualitative forms: i) positivity of
(various linear combinations of) couplings of CP-even operators and ii) upper
bounds on the magnitude of CP-odd operators in terms of (products of) CP-even
couplings. We exhibit various classes of example completions, which all satisfy
our EFT bounds. These bounds have consequences for current and future particle
physics experiments, as part of the observable parameter space is inconsistent
with causality and analyticity. To demonstrate the impact of our bounds, we
consider applications both to SMEFT constraints derived at colliders and to
limits on the neutron electric dipole moment, highlighting the connection
between such searches suggested by infrared consistency.
