Multi-loop positivity of the planar $ \mathcal{N} $ = 4 SYM six-point amplitude

Dixon, Lance J.; von Hippel, Matt; McLeod, Andrew J.; Trnka, Jaroslav

doi:10.1007/JHEP02(2017)112

Title: Multi-loop positivity of the planar $$ \mathcal{N} $$ = 4 SYM six-point amplitude

Journal Article · Wed Feb 22 00:00:00 EST 2017 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP02(2017)112· OSTI ID:1334238

^[1]; von Hippel, Matt ^[2]; McLeod, Andrew J. ^[1]; Trnka, Jaroslav ^[3]

SLAC National Accelerator Lab., Menlo Park, CA (United States)
Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada)
Univ. of California, Davis, CA (United States). Center for Quantum Mathematics and Physics (QMAP)

We study the six-point NMHV ratio function in planar $$ \mathcal{N} $$ = 4 SYM theory in the context of positive geometry. The Amplituhedron construction of the integrand for the amplitudes provides a kinematical region in which the integrand was observed to be positive. It is natural to conjecture that this property survives integration, i.e. that the final result for the ratio function is also positive in this region. Establishing such a result would imply that preserving positivity is a surprising property of the Minkowski contour of integration and it might indicate some deeper underlying structure. We find that the ratio function is positive everywhere we have tested it, including analytic results for special kinematical regions at one and two loops, as well as robust numerical evidence through five loops. There is also evidence for not just positivity, but monotonicity in a “radial” direction. We also investigate positivity of the MHV six-gluon amplitude. While the remainder function ceases to be positive at four loops, the BDS-like normalized MHV amplitude appears to be positive through five loops.

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Research Organization:: SLAC National Accelerator Lab., Menlo Park, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP)

Grant/Contract Number:: AC02-76SF00515

OSTI ID:: 1334238

Report Number(s):: SLAC-PUB-16873; arXiv:1611.08325

Journal Information:: Journal of High Energy Physics (Online), Vol. 2017, Issue 2; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 25 works

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