Massless positivity in graviton exchange
Mario Herrero-Valea (SISSA, Via Bonomea 265, 34136 Trieste, Italy and INFN Sezione di Trieste, 34127 Trieste, Italy, IFPU—Institute for Fundamental Physics of the Universe Via Beirut 2, 34014 Trieste, Italy); Raquel Santos-Garcia (Departamento de Física Teórica and Instituto de Física Teórica, IFT-UAM/CSIC, Universidad Autónoma de Madrid, Ciudad Universitaria de Cantoblanco, 28049 Madrid, Spain); Anna Tokareva (Department of Physics, University of Jyväskylä, P.O. Box 35 (YFL), FIN-40014 Jyväskylä, Finland, Institute for Nuclear Research of Russian Academy of Sciences, 117312 Moscow, Russia, Helsinki Institute of Physics (HIP), University of Helsinki, P.O. Box 64, 00014 Helsinki, Finland)
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 . In general, validity of these bounds requires the cancellation of divergences in the forward limit of the amplitude, proportional to and . 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.
