Mao Zeng

Five-loop four-point integrand of N = 8 supergravity as a generalized double copy

We use the recently developed generalized double-copy procedure to construct an integrand for the fiveloop four-point amplitude of N = 8 supergravity. This construction starts from a naive double c ...

Dual conformal symmetry, integration-by-parts reduction, differential equations, and the nonplanar sector

We show that dual conformal symmetry, mainly studied in planar

Differential equations on unitarity cut surfaces

\mathcal N = 4

Two-Loop Four-Gluon Amplitudes from Numerical Unitarity

super-Yang-Mills theory, has interesting consequences for Feynman integrals in nonsupersymmetric theories such as QCD, including the nonplanar sector. A simple observation is that dual conformal transformations preserve unitarity cut conditions for any planar integrals, including those without dual conformal symmetry. Such transformations generate differential equations without raised propagator powers, often with the right hand side of the system proportional to the dimensional regularization parameter

Manifesting enhanced cancellations in supergravity: integrands versus integrals

\epsilon

Five-Point Two-Loop Amplitudes from Numerical Unitarity

. A nontrivial subgroup of dual conformal transformations, which leaves all external momenta invariant, generates integration-by-parts relations without raised propagator powers, reproducing, in a simpler form, previous results from computational algebraic geometry for several examples with up to two loops and five legs. By opening up the two-loop three- and four-point nonplanar diagrams into planar ones, we find a nonplanar analog of dual conformal symmetry. As for the planar case this is used to generate integration-by-parts relations and differential equations. This implies that the symmetry is tied to the analytic properties of the nonplanar sector of the two-loop four-point amplitude of

Two-loop

\mathcal N = 4

D

super-Yang-Mills theory.

-dimensional unitarity and dual conformal symmetry

A bstractWe reformulate differential equations (DEs) for Feynman integrals to avoid doubled propagators in intermediate steps. External momentum derivatives are dressed with loop momentum derivatives to form tangent vectors to unitarity cut surfaces, in a way inspired by unitarity-compatible IBP reduction. For the one-loop box, our method directly produces the final DEs without any integration-by-parts reduction. We further illustrate the method by deriving maximal-cut level differential equations for two-loop nonplanar five-point integrals, whose exact expressions are yet unknown. We speed up the computation using finite field techniques and rational function reconstruction.

Planar Two-Loop Five-Gluon Amplitudes from Numerical Unitarity

We present the first numerical computation of two-loop amplitudes based on the unitarity method. As a proof of principle, we compute the four-gluon process in the leading-color approximation. We discuss the new method, analyze its numerical properties, and apply it to reconstruct the analytic form of the amplitudes. The numerical method is universal, and can be automated to provide multiscale two-loop computations for phenomenologically relevant signatures at hadron colliders.