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.
- 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}
}