16 Result(s)
within
Matt von Hippel
English
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Article
Open AccessAn infinite family of elliptic ladder integrals
We identify two families of ten-point Feynman diagrams that generalize the elliptic double box, and show that they can be expressed in terms of the same class of elliptic multiple polylogarithms to all loop or...
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Article
Open AccessCuts and isogenies
We consider the genus-one curves which arise in the cuts of the sunrise and in the elliptic double-box Feynman integrals. We compute and compare invariants of these curves in a number of ways, including Feynma...
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Chapter
Direct Integration for Multi-Leg Amplitudes: Tips, Tricks, and When They Fail
Direct hyperlogarithmic integration offers a strong alternative to differential equation methods for Feynman integration, particularly for multi-particle diagrams. We review a variety of results by the authors...
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Article
Open AccessA novel algorithm for nested summation and hypergeometric expansions
We consider a class of sums over products of Z-sums whose arguments differ by a symbolic integer. Such sums appear, for instance, in the expansion of Gauss hypergeometric functions around integer indices that dep...
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Article
Open AccessConformally-regulated direct integration of the two-loop heptagon remainder
We reproduce the two-loop seven-point remainder function in planar, maximally supersymmetric Yang-Mills theory by direct integration of conformally-regulated chiral integrands. The remainder function is obtain...
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Article
Open AccessRooting out letters: octagonal symbol alphabets and algebraic number theory
It is widely expected that NMHV amplitudes in planar, maximally supersymmetric Yang-Mills theory require symbol letters that are not rationally expressible in terms of momentum-twistor (or cluster) variables s...
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Article
Open AccessEmbedding Feynman integral (Calabi-Yau) geometries in weighted projective space
It has recently been demonstrated that Feynman integrals relevant to a wide range of perturbative quantum field theories involve periods of Calabi-Yau manifolds of arbitrarily large dimension. While the number...
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Article
Open AccessThe cosmic Galois group and extended Steinmann relations for planar \( \mathcal{N} \) = 4 SYM amplitudes
We describe the minimal space of polylogarithmic functions that is required to express the six-particle amplitude in planar ...
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Article
Open AccessSix-Gluon amplitudes in planar \( \mathcal{N} \) = 4 super-Yang-Mills theory at six and seven loops
We compute the six-particle maximally-helicity-violating (MHV) and next-to-MHV (NMHV) amplitudes in planar maximally supersymmetric Yang-Mills theory through seven loops and six loops, respectively, as an appl...
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Article
Open AccessRationalizing loop integration
We show that direct Feynman-parametric loop integration is possible for a large class of planar multi-loop integrals. Much of this follows from the existence of manifestly dual-conformal Feynman-parametric rep...
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Article
Open AccessThe double pentaladder integral to all orders
We compute dual-conformally invariant ladder integrals that are capped off by pentagons at each end of the ladder. Such integrals appear in six-point amplitudes in planar
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Article
Open AccessMulti-loop positivity of the planar \( \mathcal{N} \) = 4 SYM six-point amplitude
We study the six-point NMHV ratio function in planar N ...
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Article
Open AccessResumming the POPE at one loop
The Pentagon Operator Product Expansion represents polygonal Wilson loops in planar N ...
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Article
Open AccessThe four-loop six-gluon NMHV ratio function
We use the hexagon function bootstrap to compute the ratio function which characterizes the next-to-maximally-helicity-violating (NMHV) six-point amplitude in planar
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Article
Open AccessBootstrap** an NMHV amplitude through three loops
We extend the hexagon function bootstrap to the next-to-maximally-helicity-violating (NMHV) configuration for six-point scattering in planar ...
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Article
Open AccessHexagon functions and the three-loop remainder function
We present the three-loop remainder function, which describes the scattering of six gluons in the maximally-helicity-violating configuration in planar ...
