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.
On hyperlogarithms and Feynman integrals with divergences and many scales
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abstract
It was observed that hyperlogarithms provide a tool to carry out Feynman integrals. So far, this method has been applied successfully to finite single-scale processes. However, it can be employed in more general situations. We give examples of integrations of three- and four-point integrals in Schwinger parameters with non-trivial kinematic dependence, involving setups with off-shell external momenta and differently massive internal propagators. The full set of Feynman graphs admissible to parametric integration is not yet understood and we discuss some counterexamples to the crucial property of linear reducibility. Furthermore we clarify how divergent integrals can be approached in dimensional regularization with this algorithm.
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UNVERDICTED 5representative citing papers
In a novel scaling limit on the Coulomb branch of planar N=4 SYM, the Sudakov form factor and four-point amplitude exhibit double-logarithmic behavior governed by a walking anomalous dimension that interpolates between cusp and octagon anomalous dimensions, with proposed all-loop expressions relying
First numerical evaluation of planar two-loop helicity amplitudes for W-boson plus four partons using finite-field reduction and sector decomposition on a subset of master integrals.
Three-loop five-point dual conformal master integrals on the Coulomb branch of N=4 SYM are computed via DCI-preserving regularization, cross-ratio factorization, and HyperInt for residual regions.
A new open FORM package implements parametric hyperlogarithm integration, demonstrated on zigzag Feynman integrals up to six loops.
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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Walking Sudakov: From Cusp to Octagon
In a novel scaling limit on the Coulomb branch of planar N=4 SYM, the Sudakov form factor and four-point amplitude exhibit double-logarithmic behavior governed by a walking anomalous dimension that interpolates between cusp and octagon anomalous dimensions, with proposed all-loop expressions relying
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A numerical evaluation of planar two-loop helicity amplitudes for a W-boson plus four partons
First numerical evaluation of planar two-loop helicity amplitudes for W-boson plus four partons using finite-field reduction and sector decomposition on a subset of master integrals.
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Five legs @ three loops: slightly off-shell dual conformal integrals
Three-loop five-point dual conformal master integrals on the Coulomb branch of N=4 SYM are computed via DCI-preserving regularization, cross-ratio factorization, and HyperInt for residual regions.
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HyperFORM -- a FORM package for parametric integration with hyperlogarithms
A new open FORM package implements parametric hyperlogarithm integration, demonstrated on zigzag Feynman integrals up to six loops.