The soft-collinear bootstrap: N = 4 Yang-Mills amplitudes at six- and seven-loops

J. L. Bourjaily, A. DiRe, A. Shaikh, M. Spradlin, A. Volovich

Research output: Contribution to journalArticle

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Abstract

Infrared divergences in scattering amplitudes arise when a loop momentum ℓ becomes collinear with a massless external momentum p. In gauge theories, it is known that the L-loop logarithm of a planar amplitude has much softer infrared singularities than the L-loop amplitude itself. We argue that planar amplitudes in N = 4 super-Yang-Mills theory enjoy softer than expected behavior as ℓ ∥ p already at the level of the integrand. Moreover, we conjecture that the four-point integrand can be uniquely determined, to any looporder, by imposing the correct soft-behavior of the logarithm together with dual conformal invariance and dihedral symmetry. We use these simple criteria to determine explicit formulae for the four-point integrand through seven-loops, finding perfect agreement with previously known results through five-loops. As an input to this calculation, we enumerate all four-point dual conformally invariant (DCI) integrands through seven-loops, an analysis which is aided by several graph-theoretic theorems we prove about general DCI integrands at arbitrary loop-order. The six- and seven-loop amplitudes receive non-zero contributions from 229 and 1873 individual DCI diagrams respectively. PDF and Mathematica files with all of our results are provided at http://goo.gl/qIKe8.

Original languageEnglish (US)
Article number032
JournalJournal of High Energy Physics
Volume2012
Issue number3
DOIs
StatePublished - 2012

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics

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