One-loop corrections from higher dimensional tree amplitudes
Abstract
We show how one-loop corrections to scattering amplitudes of scalars and gauge bosons can be obtained from tree amplitudes in one higher dimension. Starting with a complete tree-level scattering amplitude of n + 2 particles in five dimensions, one assumes that two of them cannot be “detected” and therefore an integration over their LIPS is carried out. The resulting object, function of the remaining n particles, is taken to be four-dimensional by restricting the corresponding momenta. We perform this procedure in the context of the tree-level CHY formulation of amplitudes. The scattering equations obtained in the procedure coincide with those derived by Geyer et al. from ambitwistor constructions and recently studied by two of the authors for bi-adjoint scalars. They have two sectors of solutions: regular and singular. We prove that the contribution from regular solutions generically gives rise to unphysical poles. However, using a BCFW argument we prove that the unphysical contributions are always homogeneous functions of the loop momentum and can be discarded. We also show that the contribution from singular solutions turns out to be homogeneous as well.
- Authors:
-
- Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada)
- Chinese Academy of Sciences (CAS), Beijing (China)
- Princeton Univ., NJ (United States)
- Publication Date:
- Research Org.:
- Princeton Univ., NJ (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1434626
- Grant/Contract Number:
- SC0009988
- Resource Type:
- Journal Article: Accepted Manuscript
- Journal Name:
- Journal of High Energy Physics (Online)
- Additional Journal Information:
- Journal Volume: 2016; Journal Issue: 8; Journal ID: ISSN 1029-8479
- Publisher:
- Springer Berlin
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Scattering Amplitudes; Field Theories in Higher Dimensions
Citation Formats
Cachazo, Freddy, He, Song, and Yuan, Ellis Ye. One-loop corrections from higher dimensional tree amplitudes. United States: N. p., 2016.
Web. doi:10.1007/JHEP08(2016)008.
Cachazo, Freddy, He, Song, & Yuan, Ellis Ye. One-loop corrections from higher dimensional tree amplitudes. United States. https://doi.org/10.1007/JHEP08(2016)008
Cachazo, Freddy, He, Song, and Yuan, Ellis Ye. 2016.
"One-loop corrections from higher dimensional tree amplitudes". United States. https://doi.org/10.1007/JHEP08(2016)008. https://www.osti.gov/servlets/purl/1434626.
@article{osti_1434626,
title = {One-loop corrections from higher dimensional tree amplitudes},
author = {Cachazo, Freddy and He, Song and Yuan, Ellis Ye},
abstractNote = {We show how one-loop corrections to scattering amplitudes of scalars and gauge bosons can be obtained from tree amplitudes in one higher dimension. Starting with a complete tree-level scattering amplitude of n + 2 particles in five dimensions, one assumes that two of them cannot be “detected” and therefore an integration over their LIPS is carried out. The resulting object, function of the remaining n particles, is taken to be four-dimensional by restricting the corresponding momenta. We perform this procedure in the context of the tree-level CHY formulation of amplitudes. The scattering equations obtained in the procedure coincide with those derived by Geyer et al. from ambitwistor constructions and recently studied by two of the authors for bi-adjoint scalars. They have two sectors of solutions: regular and singular. We prove that the contribution from regular solutions generically gives rise to unphysical poles. However, using a BCFW argument we prove that the unphysical contributions are always homogeneous functions of the loop momentum and can be discarded. We also show that the contribution from singular solutions turns out to be homogeneous as well.},
doi = {10.1007/JHEP08(2016)008},
url = {https://www.osti.gov/biblio/1434626},
journal = {Journal of High Energy Physics (Online)},
issn = {1029-8479},
number = 8,
volume = 2016,
place = {United States},
year = {Mon Aug 01 00:00:00 EDT 2016},
month = {Mon Aug 01 00:00:00 EDT 2016}
}
Web of Science
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