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2018

1-loop Amplitudes from the Halohedron

Salvatori, Giulio

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We recently proposed the Halohedron to be the 1-loop Amplituhedron for planar $\phi^3$ theory.

Here we prove this claim by showing how it is possible to extract the integrand for the partial amplitude $m^1_n(1,\dots,n|1,\dots,n)$ from the canonical form of an Halohedron which lives in an abstract space.
This space is just a step away from ordinary kinematical space at 1-loop, because it is composed by abstract variables associated to propagators of 1-loop Feynman diagrams.
Such variables, however, are unbound from momentum conservation relations that would give problems such as double poles.

1-loop Amplitudes from the Halohedron · Around

Built on

S. L Devadoss, T. Heath and C. Vipismakul, Notices of the American Mathematical Society. 58. (2011)
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F. Cachazo, S. He and E. Y. Yuan, JHEP 1310
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N. Arkani-Hamed and J. Trnka, JHEP 1410
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F. Cachazo, S. He and E. Y. Yuan, Phys. Rev. D 90
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Earlier work this paper cites.

Similar

F. Cachazo, S. He and E. Y. Yuan, Phys. Rev. Lett. 113
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S. He and E. Y. Yuan, Phys. Rev. D 92
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Y. Geyer, L. Mason, R. Monteiro and P. Tourkine, JHEP 1603
2016
Cited alongside, same era.
G. Salvatori and S. L. Cacciatori, arXiv:1803.05809 [hep-th]
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N. Arkani-Hamed, Y. Bai, S. He and G. Yan, arXiv:1711.09102 [hep-th]
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S. Mizera, arXiv:1711.00469 [hep-th]
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S. He, G. Yan, C. Zhang and Y. Zhang, arXiv:1803.11302 [hep-th]
Original
Cited in the paper.

Then

N. Arkani-Hamed, Y. Bai and T. Lam, JHEP 1711
2017
Later among the works it cites.
S. Mizera, JHEP 1708
2017
Later among the works it cites.
F. Cachazo, S. Mizera and G. Zhang, JHEP 1703
2017
Later among the works it cites.

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