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Building Bases of Loop Integrands

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arxiv 2007.13905 v1 pith:E7KCIRYE submitted 2020-07-27 hep-th

Jacob L. Bourjaily , Enrico Herrmann , Cameron Langer , Jaroslav Trnka This is my paper · ORCID
classification hep-th
keywords arbitrarybasesintegrandssufficientdescribequantumtheoryamplitude
verification ladder T0 review T1 audit T2 compute T3 formal
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We describe a systematic approach to the construction of loop-integrand bases at arbitrary loop-order, sufficient for the representation of general quantum field theories. We provide a graph-theoretic definition of `power-counting' for multi-loop integrands beyond the planar limit, and show how this can be used to organize bases according to ultraviolet behavior. This allows amplitude integrands to be constructed iteratively. We illustrate these ideas with concrete applications. In particular, we describe complete integrand bases at two loops sufficient to represent arbitrary-multiplicity amplitudes in four (or fewer) dimensions in any massless quantum field theory with the ultraviolet behavior of the Standard Model or better. We also comment on possible extensions of our framework to arbitrary (including regulated) numbers of dimensions, and to theories with arbitrary mass spectra and charges. At three loops, we describe a basis sufficient to capture all `leading-(transcendental-)weight' contributions of any four-dimensional quantum theory; for maximally supersymmetric Yang-Mills theory, this basis should be sufficient to represent all scattering amplitude integrands in the theory---for generic helicities and arbitrary multiplicity.

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Cited by 2 Pith papers

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  1. Geometric Landau Analysis and Symbol Bootstrap

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    Boundary structure of negative geometries, combined with Landau analysis, determines physical singularities and yields symbol alphabets for six-point two-loop and five-point three-loop ladder integrals in planar N=4 s...

  2. Gravity loop integrands from the ultraviolet

    hep-th 2019-09 conditional novelty 7.0 of 10

    Four-dimensional N=8 supergravity loop integrands scale one power better at infinity than general-D power-counting predicts, and this homogeneous scaling combined with BCFW behavior uniquely fixes the integrand throug...

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