Polynomial reduction and evaluation of tree- and loop-level CHY amplitudes

Zlotnikov, Michael

doi:10.1007/JHEP08(2016)143

Title: Polynomial reduction and evaluation of tree- and loop-level CHY amplitudes

Journal Article · Wed Aug 24 00:00:00 EDT 2016 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP08(2016)143· OSTI ID:1395574

Zlotnikov, Michael ^[1]

Brown Univ., Providence, RI (United States)

We develop a polynomial reduction procedure that transforms any gauge fixed CHY amplitude integrand for n scattering particles into a σ-moduli multivariate polynomial of what we call the standard form. We show that a standard form polynomial must have a specific ladder type monomial structure, which has finite size at any n, with highest multivariate degree given by (n – 3)(n – 4)/2. This set of monomials spans a complete basis for polynomials with rational coefficients in kinematic data on the support of scattering equations. Subsequently, at tree and one-loop level, we employ the global residue theorem to derive a prescription that evaluates any CHY amplitude by means of collecting simple residues at infinity only. Furthermore, the prescription is then applied explicitly to some tree and one-loop amplitude examples.

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Research Organization:: Brown Univ., Providence, RI (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: FG02-11ER41742; SC0006887

OSTI ID:: 1395574

Journal Information:: Journal of High Energy Physics (Online), Vol. 2016, Issue 8; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 20 works

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