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Title: 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:
 [1];  [2];  [3]
  1. Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada)
  2. Chinese Academy of Sciences (CAS), Beijing (China)
  3. 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}
}

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Works referenced in this record:

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journal, January 2011


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journal, March 2016


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text, January 2014


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report, April 2008


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text, January 2013


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text, January 2014


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text, January 2015


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text, January 2015


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Works referencing / citing this record:

Bootstrapping solutions of scattering equations
journal, February 2019


CHY loop integrands from holomorphic forms
journal, March 2017


Gluons and gravitons at one loop from ambitwistor strings
journal, March 2018


Expanding Einstein-Yang-Mills by Yang-Mills in CHY frame
journal, May 2017


Polynomial reduction and evaluation of tree- and loop-level CHY amplitudes
journal, August 2016


A Monte Carlo approach to the 4D scattering equations
journal, August 2018


Double soft theorem for perturbative gravity
journal, September 2016


New Relations for Gauge-Theory and Gravity Amplitudes at Loop Level
journal, April 2017


String Amplitudes from Field-Theory Amplitudes and Vice Versa
journal, May 2019


Non-planar one-loop Parke-Taylor factors in the CHY approach for quadratic propagators
text, January 2018