Massless positivity in graviton exchange

We formulate positivity bounds for scattering amplitudes including exchange of massless particles. We generalize the standard construction through dispersion relations to include the presence of a branch cut along the real axis in the complex plane for the Maldestam variable s. In general, validity of these bounds requires the cancellation of divergences in the forward limit of the amplitude, proportional to t-1 and log(t). We show that this is possible in the case of gravitons if one assumes a Regge behavior of the amplitude at high energies below the Planck scale, as previously suggested in the literature, and that the concrete UV behavior of the amplitude is uniquely determined by the structure of IR divergences. We thus extend previous results by including a subleading logarithmic term, which we show to be universal. The bounds that we present here have the potential of constraining very general models of modified gravity and effective field theories of matter coupled to gravitation.

Automated summary

Positivity bounds for scattering amplitudes, incorporating massless particle exchange, have been formulated. The validity of these bounds is dependent on the cancellation of divergences, which can be achieved by assuming a Regge behavior of the amplitude at high energies below the Planck scale. These bounds have the potential to constrain a variety of models in the field of modified gravity and effective field theories of matter coupled to gravitation.