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Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes. (English) Zbl 1397.16028

Summary: 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.

MSC:

16T05 Hopf algebras and their applications
33B30 Higher logarithm functions
81U99 Quantum scattering theory

Software:

HPL; CHAPLIN
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Full Text: DOI arXiv

References:

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