Graviton loops and negativity

Abstract: We revisit dispersive bounds on Wilson coefficients of scalar effective field theories (EFT) coupled to gravity in various spacetime dimensions, by computing the contributions from graviton loops to the corresponding sum rules at low energies. Fixed-momentum-transfer dispersion relations are often ill-behaved due to forward singularities arising from loop-level graviton exchange, making naive positivity bounds derived from them unreliable. Instead, we perform a careful analysis using crossing-symmetric dispersion relations, and compute the one-loop corrections to the bounds on EFT coefficients. We find that including the graviton loops generically allows for negativity of Wilson coefficients by an amount suppressed by powers of Newton's constant, $G$. The exception are the few couplings that dominate over (or are degenerate with) the graviton loops at low energies. In $D=4$, we observe that assuming that the eikonal formula captures the correct forward behavior of the amplitude at all orders in $G$, and for energies of the order of the EFT cutoff, yields bounds free of logarithmic infrared divergences.