Three-loop five-leg amplitude in planar N=4 sYM near mass shell is computed via 6D unitarity cuts and dimensional reduction, confirming IR exponentiation governed by octagon anomalous dimension with each of three kinematic structures having its own function of 't Hooft coupling.
Two-Loop g -> gg Splitting Amplitudes in QCD
3 Pith papers cite this work, alongside 229 external citations. Polarity classification is still indexing.
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abstract
Splitting amplitudes are universal functions governing the collinear behavior of scattering amplitudes for massless particles. We compute the two-loop g -> gg splitting amplitudes in QCD, N=1, and N=4 super-Yang-Mills theories, which describe the limits of two-loop n-point amplitudes where two gluon momenta become parallel. They also represent an ingredient in a direct x-space computation of DGLAP evolution kernels at next-to-next-to-leading order. To obtain the splitting amplitudes, we use the unitarity sewing method. In contrast to the usual light-cone gauge treatment, our calculation does not rely on the principal-value or Mandelstam-Leibbrandt prescriptions, even though the loop integrals contain some of the denominators typically encountered in light-cone gauge. We reduce the integrals to a set of 13 master integrals using integration-by-parts and Lorentz invariance identities. The master integrals are computed with the aid of differential equations in the splitting momentum fraction z. The epsilon-poles of the splitting amplitudes are consistent with a formula due to Catani for the infrared singularities of two-loop scattering amplitudes. This consistency essentially provides an inductive proof of Catani's formula, as well as an ansatz for previously-unknown 1/epsilon pole terms having non-trivial color structure. Finite terms in the splitting amplitudes determine the collinear behavior of finite remainders in this formula.
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In planar N=4 SYM the IR-finite hard amplitude satisfies an uncorrected tree-level soft theorem and represents the undeformed tree-level S-algebra of soft gluons.
Inconsistency in spanning cuts for IBP reductions arises because cuts can make hidden terms in IBP relations finite via pinch singularities that cancel vanishing parameters, linked to hidden linear relations between propagators, for which an algorithm is provided.
citing papers explorer
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Five legs @ three loops: N=4 sYM amplitude near mass-shell
Three-loop five-leg amplitude in planar N=4 sYM near mass shell is computed via 6D unitarity cuts and dimensional reduction, confirming IR exponentiation governed by octagon anomalous dimension with each of three kinematic structures having its own function of 't Hooft coupling.
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Soft Algebra for ${\cal N}=4$ SYM
In planar N=4 SYM the IR-finite hard amplitude satisfies an uncorrected tree-level soft theorem and represents the undeformed tree-level S-algebra of soft gluons.
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On the spanning cuts consistency problem in the IBP reductions of Feynman integrals
Inconsistency in spanning cuts for IBP reductions arises because cuts can make hidden terms in IBP relations finite via pinch singularities that cancel vanishing parameters, linked to hidden linear relations between propagators, for which an algorithm is provided.