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Register a new userThe Two-Loop Four-Graviton Scattering Amplitudes
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We present the analytic form of the two-loop four-graviton scattering amplitudes in Einstein gravity. To remove ultraviolet divergences we include counterterms quadratic and cubic in the Riemann curvature tensor. The two-loop numerical unitarity approach is used to deal with the challenging momentum dependence of the interactions. We exploit the algebraic properties of the integrand of the amplitude in order to map it to a minimal basis of Feynman integrals. Analytic expressions are obtained from numerical evaluations of the amplitude. Finally, we show that four-graviton scattering observables depend on fewer couplings than naively expected.
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We present first results of a systematic study of the structure of the low energy limit of the one-loop photon-graviton amplitudes induced by massive scalars and spinors. Our main objective is the search of KLT-type relations where effectively two photons merge into a graviton. We find such a relation at the graviton-photon-photon level. We also derive the diffeomorphism Ward identity for the 1PI one graviton - N photon amplitudes.
A method to unitarize the scattering amplitude produced by infinite-range forces is developed and applied to Born terms. In order to apply $S$-matrix techniques, based on unitarity and analyticity, we first derive an $S$-matrix free of infrared divergences. This is achieved by removing a divergent phase factor due to the interactions mediated by the massless particles in the crossed channels, a procedure that is related to previous formalisms to treat infrared divergences. We apply this method in detail by unitarizing the Born terms for graviton-graviton scattering in pure gravity and we find a scalar graviton-graviton resonance with vacuum quantum numbers ($J^{PC}=0^{++}$) that we call the textit{graviball}. Remarkably, this resonance is located below the Planck mass but deep in the complex $s$-plane (with $s$ the usual Mandelstam variable), so that its effects along the physical real $s$ axis peak for values significantly lower than this scale. We argue that the position and width of the graviball are reduced when including extra light fields in the theory. This could lead to phenomenological consequences in scenarios of quantum gravity with a large number of such fields or, in general, with a low-energy ultraviolet completion. We also apply this formalism to two non-relativistic potentials with exact known solutions for the scattering amplitudes: Coulomb scattering and an energy-dependent potential obtained from the Coulomb one with a zero at threshold. This latter case shares the same $J=0$ partial-wave projected Born term as the graviton-graviton case, except for a global factor. We find that the relevant resonance structure of these examples is reproduced by our methods, which represents a strong indication of their robustness.
We study graviton-graviton scattering in partial-wave amplitudes after unitarizing their Born terms. In order to apply S-matrix techniques, based on unitarity and analyticity, we introduce an S-matrix free of infrared divergences. This is achieved by removing a diverging phase factor related to the infinite-range character of the interactions mediated by graviton exchange in the crossed channels. A scalar graviton-graviton resonance with vacuum quantum numbers (J^{PC}=0^{++}) is obtained as a pole in the nonperturbative S-wave amplitude, which we call the {it graviball}. Its resonant effects along the physical real s axis may peak at values much lower than the UV cutoff of the theory. For some scenarios, this phenomenon could have phenomenological consequences at relatively low-energy scales.
We study the space of all kinematically allowed four photon and four graviton S-matrices, polynomial in scattering momenta. We demonstrate that this space is the permutation invariant sector of a module over the ring of polynomials of the Mandelstam invariants $s$, $t$ and $u$. We construct these modules for every value of the spacetime dimension $D$, and so explicitly count and parameterize the most general four photon and four graviton S-matrix at any given derivative order. We also explicitly list the local Lagrangians that give rise to these S-matrices. We then conjecture that the Regge growth of S-matrices in all physically acceptable classical theories is bounded by $s^2$ at fixed $t$. A four parameter subset of the polynomial photon S-matrices constructed above satisfies this Regge criterion. For gravitons, on the other hand, no polynomial addition to the Einstein S-matrix obeys this bound for $D leq 6$. For $D geq 7$ there is a single six derivative polynomial Lagrangian consistent with our conjectured Regge growth bound. Our conjecture thus implies that the Einstein four graviton S-matrix does not admit any physically acceptable polynomial modifications for $Dleq 6$. A preliminary analysis also suggests that every finite sum of pole exchange contributions to four graviton scattering also such violates our conjectured Regge growth bound, at least when $Dleq 6$, even when the exchanged particles have low spin.
The extended-BMS algebra of asymptotically flat spacetime contains an SO(3,1) subgroup that acts by conformal transformations on the celestial sphere. It is of interest to study the representations of this subgroup associated with gravitons. To reduce the equation of motion to a Schrodinger-like equation it is necessary to impose a non-covariant gauge condition. Using these solutions, leading-order gauge invariant Weyl scalars are then computed and decomposed into families of unitary principal series representations. An invertible holographic mapping is constructed between these unitary principal series operators and massless spin-2 perturbations of flat spacetime.
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