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- W3045701411 abstract "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." @default.
- W3045701411 created "2020-08-03" @default.
- W3045701411 creator A5010467826 @default.
- W3045701411 creator A5014587680 @default.
- W3045701411 creator A5020167813 @default.
- W3045701411 creator A5090966772 @default.
- W3045701411 date "2020-11-01" @default.
- W3045701411 modified "2023-09-26" @default.
- W3045701411 title "Building bases of loop integrands" @default.
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