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Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes
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We show how the Hopf algebra structure of multiple polylogarithms can be used to simplify complicated expressions for multi-loop amplitudes in perturbative quantum field theory and we argue that, unlike the recently popularized symbol-based approach, the coproduct incorporates information about the zeta values. We illustrate our approach by rewriting the two-loop helicity amplitudes for a Higgs boson plus three gluons in a simplified and compact form involving only classical polylogarithms.
Forward citations
Cited by 8 Pith papers
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A Graphical Coaction for FRW Integrals from Partial/Relative Twisted (Co)homology
Constructs a graphical coaction for all-loop FRW integrals in conformally-coupled scalar theories via twisted (co)homology, with combinatorial description of kinematic flow and a public web app for computation.
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Bootstrapping the Four-Point NMHV Stress-Tensor Form Factor
Determines the unique two- and three-loop symbols for the four-point NMHV form factor from an 88-letter alphabet, providing first multi-loop non-MHV data and supporting alphabet universality.
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Integrand Analysis, Leading Singularities and Canonical Bases beyond Polylogarithms
Feynman integrals selected for unit leading singularities in complex geometries satisfy epsilon-factorized differential equations with new transcendental functions corresponding to periods and differential forms in th...
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Deriving motivic coactions and single-valued maps at genus zero from zeta generators
Proves conjectural reformulation of motivic coaction and single-valued maps via zeta generators for multiple polylogarithms at genus zero on the Riemann sphere.
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Eight loop form factors, amplitudes and patterns in planar $\mathcal{N}=4$ super-Yang-Mills theory
Eight-loop computation of the tr φ³ three-point form factor in planar N=4 SYM together with coefficient patterns in its symbol.
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Towards Motivic Coactions at Genus One from Zeta Generators
Proposes motivic coaction formulae for genus-one iterated integrals over holomorphic Eisenstein series using zeta generators, verifies expected coaction properties, and deduces f-alphabet decompositions of multiple mo...
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Leading singularities and chambers of Correlahedron
Four-loop four-point correlator integrand in planar N=4 SYM decomposes into chamber forms identical to three loops times local integrands, with leading singularities as linear combinations of those forms and a diagona...
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IterInt: Evaluating iterated integrals via differential equations
IterInt package evaluates iterated integrals by transforming them into solvable differential equation systems with built-in regularization.
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