Princeton University High Energy Theory Seminar

Abstract: We consider dispersive bounds on Wilson coefficients of scalar effective field theories (EFT) coupled to gravity in various spacetime dimensions, including the contributions from graviton loops to the sum rules at low energies. Dispersion relations with fixed momentum-transfer are often ill-behaved in the forward limit due to singularities arising from loop-level graviton exchange, making naive 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 for the Wilson coefficients that obey positivity bounds at tree-level, including graviton loops generically allows for negativity by an amount suppressed by powers of Newton’s constant, G. 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.