Building bases of loop integrands
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Building bases of loop integrands. / Bourjaily, Jacob L.; Herrmann, Enrico; Langer, Cameron; Trnka, Jaroslav.
In: Journal of High Energy Physics, Vol. 2020, No. 11, 116, 23.11.2020.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Building bases of loop integrands
AU - Bourjaily, Jacob L.
AU - Herrmann, Enrico
AU - Langer, Cameron
AU - Trnka, Jaroslav
PY - 2020/11/23
Y1 - 2020/11/23
N2 - 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.
AB - 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.
KW - Scattering Amplitudes
KW - 1
KW - N Expansion
KW - Gauge Symmetry
KW - DIFFERENTIAL-EQUATIONS
KW - SCATTERING-AMPLITUDES
KW - FEYNMAN DIAGRAMS
KW - TREE AMPLITUDES
KW - REDUCTION
KW - UNITARITY
KW - RENORMALIZATION
KW - REGULARIZATION
U2 - 10.1007/JHEP11(2020)116
DO - 10.1007/JHEP11(2020)116
M3 - Journal article
VL - 2020
JO - Journal of High Energy Physics (Online)
JF - Journal of High Energy Physics (Online)
SN - 1126-6708
IS - 11
M1 - 116
ER -
ID: 253073317