Graviton Scattering Amplitudes

These are the mathematica expressions of various graviton scattering amplitudes

They are accompanying the articles
''Augmented Recursion for One-Loop Gravity Amplitudes'' by David Dunbar, James Ettle and Warren Perkins, JHEP 1006 (2010) 027 [arXiv:1003.3398 [hep-th]]
''n-point Single Minus Gravity Amplitudes'' by Sam Alson, David Dunbar and Warren Perkins, Phys.Rev. D92 (2015) 065024 [arXiv:1507.08882[hep-th]]

M5( 1-, 2+, 3+, 4+, 5+) (compact form) (polynomial form )
M6( 1-, 2+, 3+, 4+, 5+, 6+, ) (compact form ) (polynomial form )
M7( 1-, 2+, 3+, 4+, 5+, 6+, 7+, ) ( polynomial form)
M8( 1-, 2+, 3+, 4+, 5+, 6+, 7+, 8+, ) (polynomial A ) (polynomial B ) (polynomial C ) (polynomial D )
"Complex Factorisation and Recursion for One-Loop Amplitudes" by Sam Alston, David Dunbar and Warren Perkins, Phys.Rev. D86 (2012) 085022 [arXiv:1208.0190.[hep-th]]
R5( 1-, 2-, 3+, 4+, 5+ ) ( math file ) The rational part of the scalar contribution
'' The N=4 Supergravity NMHV six-point one-loop amplitude'' by David Dunbar and Warren Perkins, [arXiv:1601.03918 [hep-th]] The complicated rational pieces of this are available
Information about the Mathematica files
It is intended to keep this web-site up to date with any corrections (hopefully none ). A list of the changes made will be kept here

Summary of Five Graviton Amplitude

The computation of the various helicity amplitudes is spread across five papers as follows.
Amplitude date
M[0] (+++++) 1998 [1]
M[0](-++++) 2010 [2]
MN=8(--+++) 1998 [1]
MN=6(--+++) 2011 [3]
MN=4(--+++) 2011 [3]
MN=1(--+++) 2011 [4]
M[0](--+++) 2012 [5]
  1. Z. Bern, Lance J. Dixon, M. Perelstein and J.S. Rozowsky "Multileg one loop gravity amplitudes from gauge theory" Nucl.Phys. B546 (1999) 423-479
  2. David C. Dunbar, James H. Ettle and Warren B. Perkins "Augmented Recursion For One-loop Gravity Amplitudes. JHEP 1006 (2010) 027
  3. David C. Dunbar, James H. Ettle and Warren B. Perkins "Perturbative expansion of N < 8 Supergravity" Phys.Rev. D83 (2011) 065015
  4. David C. Dunbar, James H. Ettle and Warren B. Perkins "Obtaining One-loop Gravity Amplitudes Using Spurious Singularities" Phys.Rev. D84 (2011) 125029
  5. Sam D. Alston, David C. Dunbar and Warren B. Perkins Complex Factorisation and Recursion for One-Loop Amplitudes
Last update 1st Aug 2012 . Any feedback/corections/suggestions is most welcome In no sense is any of this code claimed to be optimal !!!!

see also the six-gluon amplitude and the seven-gluon amplitude