Planar two-loop five-parton amplitudes from numerical unitarity

Abstract

We compute a complete set of independent leading-color two-loop five-parton amplitudes in QCD. These constitute a fundamental ingredient for the next-to-next-toleading order QCD corrections to three-jet production at hadron colliders. We show how to consistently consider helicity amplitudes with external fermions in dimensional regularization, allowing the application of a numerical variant of the unitarity method. Amplitudes are computed by exploiting a decomposition of the integrand into master and surface terms that is independent of the parton type. Master integral coefficients are numerically computed in either finite-field or floating-point arithmetic and combined with known analytic master integrals. We recompute leading-color two-loop four-parton amplitudes as a check of our implementation. Results are presented for all independent four-and five-parton processes including contributions with massless closed fermion loops.

Polarised amplitudes and soft-virtual cross sections for b$$ \overline{b} $$→ Z H at NNLO in QCD

“…However, by the argument made above, a priori, a D-dimensional linearly-complete basis at the tree level is again not guaranteed to be linearly complete and faithful for M axi at loop orders. Such an issue is very similar to what was already observed in the D-dimensional form factor decomposition of four-quark scattering amplitude qq → QQ in [57,58], albeit of a different technical origin.…”

“…The following two subsections are thus devoted to a description of Lorentz structures included in the decomposition and the derivation of corresponding form factor projectors. Special attention is given to discussing a subtlety in the form factor decomposition of (3.1) with axial current vertices in D dimensions, which is similar to that known in the four-quark scattering amplitude qq → QQ discussed in [57,58].…”

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

“…The first steps towards helicity amplitudes for five-point amplitudes were taken through numerical evaluations of two-loop five point amplitudes in QCD using modular arithmetic [58][59][60][61]. These algorithms have been generalised to allow for a full reconstruction of the coefficients of the pentagon functions classified in [7] leading to an analytic form of the single-minus helicity amplitudes [9] and the complete leading colour five-parton helicity amplitudes within the numerical unitarity framework [10,11].…”

Prescriptive unitarity for non-planar six-particle amplitudes at two loops

“…Our six-particle results represent a natural step forward in complexity, following recent developments at two loops for five particles [60][61][62][63][64][67][68][69][70][71][72]. It furthermore opens up avenues for exploring a potential extension of dual conformal symmetry beyond the planar limit [44,55,56,[73][74][75] as well as an extension of the empirical second entry conditions for five-particle amplitudes [76].…”