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arxiv 1901.08563 v2 pith:TAUAQYCW submitted 2019-01-24 hep-th

The two-loop five-point amplitude in mathcal N=8 supergravity

classification hep-th
keywords amplitudemathcaldimensionalfive-pointrationalsupergravitytwo-loopansatz
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We compute the symbol of the two-loop five-point amplitude in $\mathcal N=8$ supergravity. We write an ansatz for the amplitude whose rational prefactors are based on not only 4-dimensional leading singularities, but also $d$-dimensional ones, as the former are insufficient. Our novel $d$-dimensional unitarity-based approach to the systematic construction of an amplitude's rational structures is likely to have broader applications, for example to analogous QCD calculations. We fix parameters in the ansatz by performing numerical integration-by-parts reduction of the known integrand. We find that the two-loop five-point $\mathcal N=8$ supergravity amplitude is uniformly transcendental. We then verify the soft and collinear limits of the amplitude. There is considerable similarity with the corresponding amplitude for $\mathcal N=4$ super-Yang-Mills theory: all the rational prefactors are double copies of the Yang-Mills ones and the transcendental functions overlap to a large degree. As a byproduct, we find new relations between color-ordered loop amplitudes in $\mathcal N=4$ super-Yang-Mills theory.

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Cited by 2 Pith papers

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    Machine learning discovers a tube-seeding strategy for IBP reduction of Feynman integrals that scales linearly with numerator power, demonstrated on rank-20 2-loop 5-point integrals.

  2. A numerical evaluation of planar two-loop helicity amplitudes for a W-boson plus four partons

    hep-ph 2019-06 unverdicted novelty 7.0

    First numerical evaluation of planar two-loop helicity amplitudes for W-boson plus four partons using finite-field reduction and sector decomposition on a subset of master integrals.