Massless Positivity in Graviton Exchange

Abstract

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 require 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. The bounds that we present here have the potential of constraining very general models of modified gravity and EFTs of matter coupled to gravitation.

Scalar Fields Near Compact Objects: Resummation versus UV Completion

“…at the level of the scattering amplitude there is no pole associated with this exchange). Since gravitational contributions can affect the positivity bounds [65,190] (see also [64,191,192]), it would be interesting in future to investigate whether this might open up new regions of parameter space in which screening can coexist with unitarity, causality and locality in a (gravitational) UV completion.…”

The IR-Side of Positivity Bounds

“…Generalization to arbitrary spinning particles [5,6] and to finite scattering angle [7][8][9][10], along with interesting applications in particle phenomenology [9,[11][12][13][14][15][16][17][18][19][20][21][22][23][24][25], and in gravitational physics [26][27][28][29][30][31][32][33][34][35][36], or in connection to the positivity of time delay [37][38][39], have recently lead to the uncovering of the architecture behind all positivity bounds, (called EFT-Hedron in [40]), where infinitely many Wilson coefficient are constrained, at tree-level, by double-sided bounds [40][41][42][43][44][45][46].…”

Gravitational Positivity Bounds on Scalar Potentials

“…In this letter, we explore quantum gravity constraints on scalar potentials in light of recently developed gravitational positivity bounds [14][15][16]. In non-gravitational theories, it is well-known that Wilson coefficients of lowenergy effective field theories (EFTs) have to satisfy an infinite set of inequalities called positivity bounds in order to have a standard UV completion [17].…”

“…In non-gravitational theories, it is well-known that Wilson coefficients of lowenergy effective field theories (EFTs) have to satisfy an infinite set of inequalities called positivity bounds in order to have a standard UV completion [17]. While its extension to gravitational theories has been non-trivial due to the graviton t-channel pole, the difficulty has been overcome recently by assuming Regge behavior of high-energy amplitudes [14][15][16] (see [18][19][20] for related discussions). Following this, we study a real scalar coupled to gravity,…”

“…2 Other sub-leading corrections in the square brackets are discussed in the appendix of [15]. If we go beyond the O(M −2 pl ) analysis, the O(ln −1 (s/M 2 s )) term plays an important role as discussed in [16].…”