One-loop corrections from higher dimensional tree amplitudes

Cachazo, Freddy; He, Song; Yuan, Ellis Ye

doi:10.1007/JHEP08(2016)008

Title: One-loop corrections from higher dimensional tree amplitudes

Journal Article · Mon Aug 01 00:00:00 EDT 2016 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP08(2016)008· OSTI ID:1434626

Cachazo, Freddy ^[1]; He, Song ^[2]; Yuan, Ellis Ye ^[3]

Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada)
Chinese Academy of Sciences (CAS), Beijing (China)
Princeton Univ., NJ (United States)

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.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Princeton Univ., NJ (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0009988

OSTI ID:: 1434626

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

Citation Metrics:

Cited by: 68 works

Citation information provided by
Web of Science

References (30)

Scattering in three dimensions from rational maps Cachazo, Freddy; He, Song; Yuan, Ellis Ye Journal of High Energy Physics, Vol. 2013, Issue 10 https://doi.org/10.1007/JHEP10(2013)141	journal	October 2013
On BCFW shifts of integrands and integrals Boels, Rutger Journal of High Energy Physics, Vol. 2010, Issue 11 https://doi.org/10.1007/JHEP11(2010)113	journal	November 2010
Scattering equations and BCJ relations for gauge and gravitational amplitudes with massive scalar particles Naculich, Stephen G. Journal of High Energy Physics, Vol. 2014, Issue 9 https://doi.org/10.1007/JHEP09(2014)029	journal	September 2014
Loop Integrands for Scattering Amplitudes from the Riemann Sphere Geyer, Yvonne; Mason, Lionel; Monteiro, Ricardo Physical Review Letters, Vol. 115, Issue 12 https://doi.org/10.1103/PhysRevLett.115.121603	journal	September 2015
The polynomial form of the scattering equations Dolan, Louise; Goddard, Peter Journal of High Energy Physics, Vol. 2014, Issue 7 https://doi.org/10.1007/JHEP07(2014)029	journal	July 2014
From loops to trees by-passing Feynman's theorem Catani, Stefano; Gleisberg, Tanju; Krauss, Frank Journal of High Energy Physics, Vol. 2008, Issue 09 https://doi.org/10.1088/1126-6708/2008/09/065	journal	September 2008
New Representations of the Perturbative $S$ Matrix Baadsgaard, Christian; Bjerrum-Bohr, N. E. J.; Bourjaily, Jacob L. Physical Review Letters, Vol. 116, Issue 6 https://doi.org/10.1103/PhysRevLett.116.061601	journal	February 2016
Proof of the formula of Cachazo, He and Yuan for Yang-Mills tree amplitudes in arbitrary dimension Dolan, Louise; Goddard, Peter Journal of High Energy Physics, Vol. 2014, Issue 5 https://doi.org/10.1007/JHEP05(2014)010	journal	May 2014
Scattering of Massless Particles in Arbitrary Dimensions Cachazo, Freddy; He, Song; Yuan, Ellis Ye Physical Review Letters, Vol. 113, Issue 17 https://doi.org/10.1103/PhysRevLett.113.171601	journal	October 2014
New recursion relations for tree amplitudes of gluons Britto, Ruth; Cachazo, Freddy; Feng, Bo Nuclear Physics B, Vol. 715, Issue 1-2 https://doi.org/10.1016/j.nuclphysb.2005.02.030	journal	May 2005
The Amplituhedron Arkani-Hamed, Nima; Trnka, Jaroslav Journal of High Energy Physics, Vol. 2014, Issue 10 https://doi.org/10.1007/JHEP10(2014)030	journal	October 2014
Scattering equations and matrices: from Einstein to Yang-Mills, DBI and NLSM Cachazo, Freddy; He, Song; Yuan, Ellis Ye Journal of High Energy Physics, Vol. 2015, Issue 7 https://doi.org/10.1007/JHEP07(2015)149	journal	July 2015
Progress in One-Loop qcd Computations Bern, Zvi; Dixon, Lance; Kosower, David A. Annual Review of Nuclear and Particle Science, Vol. 46, Issue 1 https://doi.org/10.1146/annurev.nucl.46.1.109	journal	December 1996
Integration rules for loop scattering equations Baadsgaard, Christian; Bjerrum-Bohr, N. E. J.; Bourjaily, Jacob L. Journal of High Energy Physics, Vol. 2015, Issue 11 https://doi.org/10.1007/JHEP11(2015)080	journal	November 2015
Loops and trees Caron-Huot, S. Journal of High Energy Physics, Vol. 2011, Issue 5 https://doi.org/10.1007/JHEP05(2011)080	journal	May 2011
Direct Proof of the Tree-Level Scattering Amplitude Recursion Relation in Yang-Mills Theory Britto, Ruth; Cachazo, Freddy; Feng, Bo Physical Review Letters, Vol. 94, Issue 18 https://doi.org/10.1103/PhysRevLett.94.181602	journal	May 2005
The all-loop integrand for scattering amplitudes in planar $ \mathcal{N} = 4 $ SYM Arkani-Hamed, N.; Bourjaily, J.; Cachazo, F. Journal of High Energy Physics, Vol. 2011, Issue 1 https://doi.org/10.1007/JHEP01(2011)041	journal	January 2011
Scattering of massless particles: scalars, gluons and gravitons Cachazo, Freddy; He, Song; Yuan, Ellis Ye Journal of High Energy Physics, Vol. 2014, Issue 7 https://doi.org/10.1007/JHEP07(2014)033	journal	July 2014
The Q $$ \mathcal{Q} $$ -cut representation of one-loop integrands and unitarity cut method Huang, Rijun; Jin, Qingjun; Rao, Junjie Journal of High Energy Physics, Vol. 2016, Issue 3 https://doi.org/10.1007/JHEP03(2016)057	journal	March 2016
Proof of the formula of Cachazo, He and Yuan for Yang-Mills tree amplitudes in arbitrary dimension Louise, Dolan,; Peter, Goddard, The University of North Carolina at Chapel Hill University Libraries https://doi.org/10.17615/80f9-x885	text	January 2014
The polynomial form of the scattering equations Peter, Goddard,; Louise, Dolan, The University of North Carolina at Chapel Hill University Libraries https://doi.org/10.17615/e4mn-dg81	text	January 2014
From Loops to Trees By-passing Feynman's Theorem Catani, Stefano; Gleisberg, Tanju; Krauss, Frank https://doi.org/10.2172/927533	report	April 2008
Ambitwistor strings and the scattering equations Mason, Lionel; Skinner, David arXiv https://doi.org/10.48550/arxiv.1311.2564	text	January 2013
The Polynomial Form of the Scattering Equations Dolan, Louise; Goddard, Peter arXiv https://doi.org/10.48550/arxiv.1402.7374	text	January 2014
Scattering equations and BCJ relations for gauge and gravitational amplitudes with massive scalar particles Naculich, Stephen G. arXiv https://doi.org/10.48550/arxiv.1407.7836	text	January 2014
Loop Integrands for Scattering Amplitudes from the Riemann Sphere Geyer, Yvonne; Mason, Lionel; Monteiro, Ricardo arXiv https://doi.org/10.48550/arxiv.1507.00321	text	January 2015
Integration Rules for Loop Scattering Equations Baadsgaard, Christian; Bjerrum-Bohr, N. E. J.; Bourjaily, Jacob L. arXiv https://doi.org/10.48550/arxiv.1508.03627	text	January 2015
One-loop amplitudes on the Riemann sphere Geyer, Yvonne; Mason, Lionel; Monteiro, Ricardo arXiv https://doi.org/10.48550/arxiv.1511.06315	text	January 2015
Progress in One-Loop QCD Computations Bern, Z.; Dixon, L.; Kosower, D. A. arXiv https://doi.org/10.48550/arxiv.hep-ph/9602280	text	January 1996
New Recursion Relations for Tree Amplitudes of Gluons Britto, Ruth; Cachazo, Freddy; Feng, Bo arXiv https://doi.org/10.48550/arxiv.hep-th/0412308	text	January 2004

Cited By (19)

Bootstrapping solutions of scattering equations Liu, Zhengwen; Zhao, Xiaoran Journal of High Energy Physics, Vol. 2019, Issue 2 https://doi.org/10.1007/jhep02(2019)071	journal	February 2019
CHY loop integrands from holomorphic forms Gomez, Humberto; Mizera, Sebastian; Zhang, Guojun Journal of High Energy Physics, Vol. 2017, Issue 3 https://doi.org/10.1007/jhep03(2017)092	journal	March 2017
Gluons and gravitons at one loop from ambitwistor strings Geyer, Yvonne; Monteiro, Ricardo Journal of High Energy Physics, Vol. 2018, Issue 3 https://doi.org/10.1007/jhep03(2018)068	journal	March 2018
Expanding Einstein-Yang-Mills by Yang-Mills in CHY frame Teng, Fei; Feng, Bo Journal of High Energy Physics, Vol. 2017, Issue 5 https://doi.org/10.1007/jhep05(2017)075	journal	May 2017
Polynomial reduction and evaluation of tree- and loop-level CHY amplitudes Zlotnikov, Michael Journal of High Energy Physics, Vol. 2016, Issue 8 https://doi.org/10.1007/jhep08(2016)143	journal	August 2016
A Monte Carlo approach to the 4D scattering equations Farrow, Joseph A. Journal of High Energy Physics, Vol. 2018, Issue 8 https://doi.org/10.1007/jhep08(2018)085	journal	August 2018
Double soft theorem for perturbative gravity Saha, Arnab Priya Journal of High Energy Physics, Vol. 2016, Issue 9 https://doi.org/10.1007/jhep09(2016)165	journal	September 2016
New Relations for Gauge-Theory and Gravity Amplitudes at Loop Level He, Song; Schlotterer, Oliver Physical Review Letters, Vol. 118, Issue 16 https://doi.org/10.1103/physrevlett.118.161601	journal	April 2017
String Amplitudes from Field-Theory Amplitudes and Vice Versa He, Song; Teng, Fei; Zhang, Yong Physical Review Letters, Vol. 122, Issue 21 https://doi.org/10.1103/physrevlett.122.211603	journal	May 2019
Polynomial reduction and evaluation of tree- and loop-level CHY amplitudes Zlotnikov, Michael arXiv https://doi.org/10.48550/arxiv.1605.08758	text	January 2016
Double Soft Theorem for Perturbative Gravity Saha, Arnab Priya arXiv https://doi.org/10.48550/arxiv.1607.02700	text	January 2016
A note on connected formula for form factors He, Song; Liu, Zhengwen arXiv https://doi.org/10.48550/arxiv.1608.04306	text	January 2016
Expanding Einstein-Yang-Mills by Yang-Mills in CHY frame Teng, Fei; Feng, Bo arXiv https://doi.org/10.48550/arxiv.1703.01269	text	January 2017
Four dimensional ambitwistor strings and form factors of local and Wilson line operators Bork, L. V.; Onishchenko, A. I. arXiv https://doi.org/10.48550/arxiv.1704.04758	text	January 2017
One-loop Parke-Taylor factors for quadratic propagators from massless scattering equations Gomez, Humberto; Lopez-Arcos, Cristhiam; Talavera, Pedro arXiv https://doi.org/10.48550/arxiv.1707.08584	text	January 2017
Non-planar one-loop Parke-Taylor factors in the CHY approach for quadratic propagators Ahmadiniaz, Naser; Gomez, Humberto; Lopez-Arcos, Cristhiam arXiv https://doi.org/10.48550/arxiv.1802.00015	text	January 2018
Two-Loop Scattering Amplitudes from Ambitwistor Strings: from Genus Two to the Nodal Riemann Sphere Geyer, Yvonne; Monteiro, Ricardo arXiv https://doi.org/10.48550/arxiv.1805.05344	text	January 2018
A Monte Carlo Approach to the 4D Scattering Equations Farrow, Joseph A. arXiv https://doi.org/10.48550/arxiv.1806.02732	text	January 2018
String Correlators: Recursive Expansion, Integration-by-Parts and Scattering Equations He, Song; Teng, Fei; Zhang, Yong arXiv https://doi.org/10.48550/arxiv.1907.06041	text	January 2019

Similar Records

Scattering equations in AdS: scalar correlators in arbitrary dimensions

Journal Article · Fri Nov 27 00:00:00 EST 2020 · Journal of High Energy Physics (Online) · OSTI ID:1434626

Eberhardt, Lorenz; Komatsu, Shota; Mizera, Sebastian

Scattering forms and the positive geometry of kinematics, color and the worldsheet

Journal Article · Tue May 15 00:00:00 EDT 2018 · Journal of High Energy Physics (Online) · OSTI ID:1434626

Arkani-Hamed, Nima; Bai, Yuntao; He, Song; +1 more

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) · OSTI ID:1434626

Zlotnikov, Michael

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Scattering Amplitudes
Field Theories in Higher Dimensions

Title: One-loop corrections from higher dimensional tree amplitudes

Citation Formats

References (30)

Cited By (19)

Similar Records

Related Subjects