Prescriptive unitarity for non-planar six-particle amplitudes at two loops
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Springer
Received: October 7, 2019 Accepted: November 18, 2019 Published: December 10, 2019
Jacob L. Bourjaily,a,b Enrico Herrmann,c Cameron Langer,d Andrew J. McLeoda and Jaroslav Trnkad a
Niels Bohr International Academy and Discovery Center, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100, Copenhagen Ø, Denmark b Center for the Fundamental Laws of Nature, Department of Physics Jefferson Physical Laboratory, Harvard University, Cambridge, MA 02138, U.S.A. c SLAC National Accelerator Laboratory, Stanford University, Stanford, CA 94039, U.S.A. d Center for Quantum Mathematics and Physics (QMAP), Department of Physics, University of California, Davis, CA 95616, U.S.A.
E-mail: [email protected], [email protected], [email protected], [email protected], [email protected] Abstract: We extend the applications of prescriptive unitarity beyond the planar limit to provide local, polylogarithmic, integrand-level representations of six-particle MHV scattering amplitudes in both maximally supersymmetric Yang-Mills theory and gravity. The integrand basis we construct is diagonalized on a spanning set of non-vanishing leading singularities that ensures the manifest matching of all soft-collinear singularities in both theories. As a consequence, this integrand basis naturally splits into infrared-finite and infrared-divergent parts, with hints toward an integrand-level exponentiation of infrared divergences. Importantly, we use the same basis of integrands for both theories, so that the presence or absence of residues at infinite loop momentum becomes a feature detectable by inspecting the cuts of the theory. Complete details of our results are provided as supplementary material. Keywords: Extended Supersymmetry, Scattering Amplitudes, Supergravity Models ArXiv ePrint: 1909.09131
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP12(2019)073
JHEP12(2019)073
Prescriptive unitarity for non-planar six-particle amplitudes at two loops
Contents 1 Introduction and overview
1 5 5 7 12
3 Six-point amplitude integrands of sYM and SUGRA 3.1 Prescriptive integrands for a spanning set of leading singularities 3.2 Putting everything together: MHV amplitudes in sYM and SUGRA
15 16 19
4 Conclusions and future directions
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A Explicit numerators for six-point integrands A.1 Representing (functions of) four-momenta A.2 Explicit expressions for the numerators of basis integrands
23 23 24
B Explicit leading singularities for sYM and SUGRA B.1 Color-dressed leading singularities of MHV amplitudes in sYM B.1.1 Color factors at two loops: diagrammatics & notation B.1.2 Kinematics: on-shell functions of ordered (MHV) amplitudes B.1.3 Closed formulae for all two-loop MHV leading singularities B.2 Two-loop leading singularities of MHV amplitudes in SUGRA
28 28 29 30 31 33
C Organization of the supplementary material
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1
Introduction and overview
Scattering amplitudes constitute fundamental objects in any weakly coupled quantum field theory, where they describe the basic
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