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

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.
Authors:
 [1]
  1. Brown Univ., Providence, RI (United States)
Publication Date:
Grant/Contract Number:
FG02-11ER41742; SC0006887
Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 8; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Research Org:
Brown Univ., Providence, RI (United States)
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Scattering Amplitudes; Differential and Algebraic Geometry; Field Theories in Higher Dimensions
OSTI Identifier:
1395574

Zlotnikov, Michael. Polynomial reduction and evaluation of tree- and loop-level CHY amplitudes. United States: N. p., Web. doi:10.1007/JHEP08(2016)143.
Zlotnikov, Michael. Polynomial reduction and evaluation of tree- and loop-level CHY amplitudes. United States. doi:10.1007/JHEP08(2016)143.
Zlotnikov, Michael. 2016. "Polynomial reduction and evaluation of tree- and loop-level CHY amplitudes". United States. doi:10.1007/JHEP08(2016)143. https://www.osti.gov/servlets/purl/1395574.
@article{osti_1395574,
title = {Polynomial reduction and evaluation of tree- and loop-level CHY amplitudes},
author = {Zlotnikov, Michael},
abstractNote = {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.},
doi = {10.1007/JHEP08(2016)143},
journal = {Journal of High Energy Physics (Online)},
number = 8,
volume = 2016,
place = {United States},
year = {2016},
month = {8}
}