Sequential discontinuities of Feynman integrals and the monodromy group

Self Cite

106

We bootstrap the three-point form factor of the chiral part of the stresstensor supermultiplet in planar $$ \mathcal{N} $$ N = 4 super-Yang-Mills theory, obtaining new results at three, four, and five loops. Our construction employs known conditions on the first, second, and final entries of the symbol, combined with new multiple-final-entry conditions, “extended-Steinmann-like” conditions, and near-collinear data from the recently-developed form factor operator product expansion. Our results are expected to give the maximally transcendental parts of the gg → Hg and H → ggg amplitudes in the heavy-top limit of QCD. At two loops, the extended-Steinmann-like space of functions we describe contains all transcendental functions required for four-point amplitudes with one massive and three massless external legs, and all massless internal lines, including processes such as gg → Hg and γ* → $$ q\overline{q}g $$ q q ¯ g . We expect the extended-Steinmann-like space to contain these amplitudes at higher loops as well, although not to arbitrarily high loop order. We present evidence that the planar $$ \mathcal{N} $$ N = 4 three-point form factor can be placed in an even smaller space of functions, with no independent ζ values at weights two and three.

“…It would thus be interesting to elucidate the origin of these restrictions, perhaps using the types of methods employed in refs. [126][127][128][129][130][131].…”

Section: Discussionmentioning

confidence: 99%

A three-point form factor through five loops

Dixon

McLeod

Wilhelm

2021

Self Cite

106

“…Hence, from the latter there is the support that λ ± 12 and λ ± 14 cannot appear together in the causal representation of this loop topology. The Steinmann relations have been considered in recent works [77][78][79][80][81] and read as follows,…”

Section: Causal Representation Of Five-vertex Topologiesmentioning

confidence: 99%

Loop-tree duality from vertices and edges

Bobadilla

2021

The causal representation of multi-loop scattering amplitudes, obtained from the application of the loop-tree duality formalism, comprehensively elucidates, at integrand level, the behaviour of only physical singularities. This representation is found to manifest compact expressions for multi-loop topologies that have the same number of vertices. Interestingly, integrands considered in former studies, with up-to six vertices and L internal lines, display the same structure of up-to four-loop ones. The former is an insight that there should be a correspondence between vertices and the collection of internal lines, edges, that characterise a multi-loop topology. By virtue of this relation, in this paper, we embrace an approach to properly classify multi-loop topologies according to vertices and edges. Differently from former studies, we consider the most general topologies, by connecting vertices and edges in all possible ways. Likewise, we provide a procedure to generate causal representation of multi-loop topologies by considering the structure of causal propagators. Explicit causal representations of loop topologies with up-to nine vertices are provided.

“…In particular, the analytic structure of these types of functions can be systematically analyzed using the symbol and coaction [92][93][94][95][96], which makes it possible to expose all functional identities between such polylogarithms [97][98][99][100][101]. 1 This technology has proven to be increasingly useful as physical constraints on the analytic structure of amplitudes (and related quantities) have become better understood (see for instance [18,[103][104][105][106][107][108][109]). In the case of the two-loop remainder function, it has also led to the discovery of the various types of cluster-algebraic structure, which we will review in section 4.…”

Section: Jhep06(2021)142 3 Motivic Aspects Of Multiple Polylogarithmsmentioning

confidence: 99%

The two-loop remainder function for eight and nine particles

Golden

McLeod²

2021

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Two-loop MHV amplitudes in planar $$ \mathcal{N} $$ N = 4 supersymmetric Yang Mills theory are known to exhibit many intriguing forms of cluster-algebraic structure. We leverage this structure to upgrade the symbols of the eight- and nine-particle amplitudes to complete analytic functions. This is done by systematically projecting onto the components of these amplitudes that take different functional forms, and matching each component to an ansatz of multiple polylogarithms with negative cluster-coordinate arguments. The remaining additive constant can be determined analytically by comparing the collinear limit of each amplitude to known lower-multiplicity results. We also observe that the nonclassical part of each of these amplitudes admits a unique decomposition in terms of a specific A3 cluster polylogarithm, and explore the numerical behavior of the remainder function along lines in the positive region.