We compute the causality/positivity bounds on the Wilson coefficients of
scalar-tensor effective field theories. Two-sided bounds are obtained by
extracting IR information from UV physics via dispersion relations of
scattering amplitudes, making use of the full crossing symmetry. The graviton
t-channel pole is carefully treated in the numerical optimization, taking
into account the constraints with fixed impact parameters. It is shown that the
typical sizes of the Wilson coefficients can be estimated by simply inspecting
the dispersion relations. We carve out sharp bounds on the leading
coefficients, particularly, the scalar-Gauss-Bonnet couplings, and discuss how
some bounds vary with the leading (βΟ)4 coefficient and as well as
phenomenological implications of the causality bounds.Comment: 72 pages, 15 figure