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

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.
Authors:
ORCiD logo [1] ;  [2] ;  [1] ;  [3]
  1. SLAC National Accelerator Lab., Menlo Park, CA (United States)
  2. Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada)
  3. Univ. of California, Davis, CA (United States). Center for Quantum Mathematics and Physics (QMAP)
Publication Date:
Report Number(s):
SLAC-PUB-16873
Journal ID: ISSN 1029-8479; arXiv:1611.08325
Grant/Contract Number:
AC02-76SF00515
Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 2; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Research Org:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; HEPTH, MATH
OSTI Identifier:
1334238