Integrand Reduction for Two-Loop Scattering Amplitudes through Multivariate Polynomial Division

Understand

We describe the application of a novel approach for the reduction of scattering amplitudes, based on multivariate polynomial division, which we have recently presented.

• This technique yields the complete integrand decomposition for arbitrary amplitudes, regardless of the number of loops.
• It allows for the determination of the residue at any multiparticle cut, whose knowledge is a mandatory prerequisite for applying the integrand-reduction procedure.
• By using the division modulo Groebner basis, we can derive a simple integrand recurrence relation that generates the multiparticle pole decomposition for integrands of arbitrary multiloop amplitudes.