Local integrands for two-loop all-plus Yang-Mills amplitudes

Abstract

Abstract:We express the planar five-and six-gluon two-loop Yang-Mills amplitudes with all positive helicities in compact analytic form using D-dimensional local integrands that are free of spurious singularities. The integrand is fixed from on-shell tree amplitudes in six dimensions using D-dimensional generalised unitarity cuts. The resulting expressions are shown to have manifest infrared behaviour at the integrand level. We also find simple representations of the rational terms obtained after integration in 4 − 2 dimensions.

Scattering amplitudes over finite fields and multivariate functional reconstruction

“…In this paper we however focus on multi-loop integrand reduction via generalized unitarity [23,24,[27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46], since the algorithm is suited for highmultiplicity processes and, as stated, writing scattering amplitudes as linear combinations of integrals (which may be further processed by IBPs at a later stage) is currently one of the main bottlenecks of high-multiplicity multi-loop calculations. These techniques have indeed been used in recent five-and six-point calculations of two-loop amplitudes in nonsupersymmetric Yang-Mills theory [37,47,48]. In order to provide the building blocks needed by generalized unitarity, we also discuss in some detail a finite-field implementation of the spinor-helicity formalism in four [49,50] and six dimensions [51][52][53], as well as the calculation of tree-level amplitudes over finite fields via Berends-Giele recursion [50].…”

“…We refer to these as momentum-twistor variables. Twistor variables can be interpreted as a rational parametrization of the phase space and, despite having been introduced in the context of conformal theories, they can be used in any relativistic quantum field theory and indeed they played an important role in multi-leg higher-loop calculations in non-supersymmetric gauge theories presented recent years [37,47,48]. Since they can give a complete description of the ratio A/A (phase) , a generic scattering amplitude can be rewritten in terms of them as…”

To $${d}$$ d , or not to $${d}$$ d : recent developments and comparisons of regularization schemes

“…The six-dimensional spinor-helicity formalism has been extensively developed in Ref. [65], and used in the context of multi-loop generalized unitarity for producing analytic results for five-and sixpoint two-loop all-plus amplitudes in (non-supersymmetric) Yang-Mills theory [64,66,67].…”

“…in Refs. [61][62][63]67]. The coefficients c T,α only depend on the external kinematics (they also have a polynomial dependence on d s ) and they can be determined by evaluating the integrand on values of the loop momenta such that the propagators of the corresponding loop sub-topology are put on-shell {D j = 0} j∈T .…”

“…This setup has been used for the calculation of planar five-and six-point two-loop amplitudes in Yang-Mills theory presented in Refs. [64,66,67], as well as for the first application of multivariate reconstruction techniques to generalized unitarity presented in Ref. [68].…”