Efficient integrand reduction for particles with spin

Abstract

Scattering amplitudes with spinning particles are shown to decompose into multiple copies of simple building blocks to all loop orders, which can be used to efficiently reduce these amplitudes to sums over scalar integrals. Absence of unphysical kinematic singularities cleanly exposed by the method uncover novel consistency relations among master integrals and their coefficients. Analytic results are obtained for the five gluon, two loop, and four gluon, three loop planar scattering amplitudes in pure Yang-Mills theory as well as for leading singularities to even higher orders.

Analytic Two-Loop Higgs Amplitudes in Effective Field Theory and the Maximal Transcendentality Principle

“…The computation of two-loop amplitudes in QCD, as is well known, is a challenging problem. While the analytical two-loop four-gluon amplitudes have been known for a long time [31][32][33], the computation of planar two-loop five-gluon amplitudes is still in progress [34][35][36][37][38][39][40][41][42][43]. The computation of Higgs amplitudes has extra complications.…”

Analytic Form of the Three-loop Four-gluon Scattering Amplitudes in Yang-Mills Theory

“…By this means, cut integrands are manifestly gauge invariant and consist of scalar products of polarization vectors of external gluons, internal and external momenta. The external polarizations in the cut integrands can be projected out by the gauge invariant bases method [19,20] making integrands containing only momenta. As shown in [20], the n-gluon scattering amplitudes can be expanded by a set of gauge invariant bases, which are constructed by the gauge invariant building blocks A i and C ij…”

“…The external polarizations in the cut integrands can be projected out by the gauge invariant bases method [19,20] making integrands containing only momenta. As shown in [20], the n-gluon scattering amplitudes can be expanded by a set of gauge invariant bases, which are constructed by the gauge invariant building blocks A i and C ij…”

“…where B α is the dual basis satisfying B α • B β = δ α β [20]. Polarization vectors are absorbed in B α , while the coefficients c α become regular Feynman integrals consisting of the scalar products of internal and external momenta.…”

“…We compute using d-dimensional unitarity method [17,18], gauge invariant bases method [19,20] and integration-by-parts (IBP) reduction [21]. A few progress on a single ladder type topology has been made [22], and master integrals for this task have been solved [23].…”