Amplitudes, Supersymmetric Black Hole Scattering at 𝒪(G^5), and Loop Integration
arxiv(2024)
摘要
We compute the potential-graviton contribution to the scattering amplitude,
the radial action, and the scattering angle of two extremal black holes in N =
8 supergravity at the fifth post-Minkowskian order to next-to-leading order in
a large mass expansion (first self-force order). Properties of classical
unitarity cuts allow us to focus on the integration-by-parts reduction of
planar integrals, while nonplanar integrals at this order are obtained from the
planar ones by straightforward manipulations. We present all master integrals
and solve their associated differential equations necessary to evaluate the
classical scattering amplitudes of massive scalar particles at this order in
all gravitational theories, in particular in N = 8 supergravity, and in general
relativity. Despite the appearance of higher-weight generalized polylogarithms
and elliptic functions in the solution to the differential equation for master
integrals, the final supergravity answer is remarkably simple and contains only
(harmonic) polylogarithmic functions up to weight 2. The systematic analysis of
elliptic integrals discussed here, as well as the particular organization of
boundary integrals in N = 8 observables are independent of supersymmetry and
may have wider applications, including to aspects of collider physics.
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