Abstract
In the CHY-frame for the tree-level amplitudes, the bi-adjoint scalar theory has played a fundamental role because it gives the on-shell Feynman diagrams for all other theories. Recently, an interesting generalization of the bi-adjoint scalar theory has been given in [1] by the “Labelled tree graphs”, which carries a lot of similarity comparing to the bi-adjoint scalar theory. In this note, we have investigated the Labelled tree graphs from two different angels. In the first part of the note, we have shown that we can organize all cubic Feynman diagrams produces by the Labelled tree graphs to the “effective Feynman diagrams”. In the new picture, the pole structure of the whole theory is more manifest. In the second part, we have generalized the action of “picking pole” in the bi-adjoint scalar theory to general CHY-integrands which produce only simple poles.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
X. Gao, S. He and Y. Zhang, Labelled tree graphs, Feynman diagrams and disk integrals, JHEP 11 (2017) 144 [arXiv:1708.08701] [INSPIRE].
F. Cachazo, S. He and E.Y. Yuan, Scattering of Massless Particles in Arbitrary Dimensions, Phys. Rev. Lett. 113 (2014) 171601 [arXiv:1307.2199] [INSPIRE].
F. Cachazo, S. He and E.Y. Yuan, Scattering of Massless Particles: Scalars, Gluons and Gravitons, JHEP 07 (2014) 033 [arXiv:1309.0885] [INSPIRE].
F. Cachazo, S. He and E.Y. Yuan, Scattering equations and Kawai-Lewellen-Tye orthogonality, Phys. Rev. D 90 (2014) 065001 [arXiv:1306.6575] [INSPIRE].
F. Cachazo, S. He and E.Y. Yuan, Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM, JHEP 07 (2015) 149 [arXiv:1412.3479] [INSPIRE].
F. Cachazo, S. He and E.Y. Yuan, Einstein-Yang-Mills Scattering Amplitudes From Scattering Equations, JHEP 01 (2015) 121 [arXiv:1409.8256] [INSPIRE].
L. Dolan and P. Goddard, The Polynomial Form of the Scattering Equations, JHEP 07 (2014) 029 [arXiv:1402.7374] [INSPIRE].
C. Kalousios, Scattering equations, generating functions and all massless five point tree amplitudes, JHEP 05 (2015) 054 [arXiv:1502.07711] [INSPIRE].
R. Huang, J. Rao, B. Feng and Y.-H. He, An Algebraic Approach to the Scattering Equations, JHEP 12 (2015) 056 [arXiv:1509.04483] [INSPIRE].
M. Søgaard and Y. Zhang, Scattering Equations and Global Duality of Residues, Phys. Rev. D 93 (2016) 105009 [arXiv:1509.08897] [INSPIRE].
L. Dolan and P. Goddard, General Solution of the Scattering Equations, JHEP 10 (2016) 149 [arXiv:1511.09441] [INSPIRE].
C. Cardona and C. Kalousios, Comments on the evaluation of massless scattering, JHEP 01 (2016) 178 [arXiv:1509.08908] [INSPIRE].
C. Cardona and C. Kalousios, Elimination and recursions in the scattering equations, Phys. Lett. B 756 (2016) 180 [arXiv:1511.05915] [INSPIRE].
C. Baadsgaard, N.E.J. Bjerrum-Bohr, J.L. Bourjaily and P.H. Damgaard, Integration Rules for Scattering Equations, JHEP 09 (2015) 129 [arXiv:1506.06137] [INSPIRE].
C. Baadsgaard, N.E.J. Bjerrum-Bohr, J.L. Bourjaily and P.H. Damgaard, Scattering Equations and Feynman Diagrams, JHEP 09 (2015) 136 [arXiv:1507.00997] [INSPIRE].
C. Baadsgaard, N.E.J. Bjerrum-Bohr, J.L. Bourjaily, P.H. Damgaard and B. Feng, Integration Rules for Loop Scattering Equations, JHEP 11 (2015) 080 [arXiv:1508.03627] [INSPIRE].
C. Cardona, B. Feng, H. Gomez and R. Huang, Cross-ratio Identities and Higher-order Poles of CHY-integrand, JHEP 09 (2016) 133 [arXiv:1606.00670] [INSPIRE].
R. Huang, F. Teng and B. Feng, Permutation in the CHY-Formulation, Nucl. Phys. B 932 (2018) 323 [arXiv:1801.08965] [INSPIRE].
B. Feng, CHY-construction of Planar Loop Integrands of Cubic Scalar Theory, JHEP 05 (2016) 061 [arXiv:1601.05864] [INSPIRE].
B. Feng and C. Hu, One-loop CHY-Integrand of Bi-adjoint Scalar Theory, JHEP 02 (2020) 187 [arXiv:1912.12960] [INSPIRE].
R. Huang, B. Feng, M.-x. Luo and C.-J. Zhu, Feynman Rules of Higher-order Poles in CHY Construction, JHEP 06 (2016) 013 [arXiv:1604.07314] [INSPIRE].
S. Mizera, Scattering Amplitudes from Intersection Theory, Phys. Rev. Lett. 120 (2018) 141602 [arXiv:1711.00469] [INSPIRE].
H. Frost, Biadjoint scalar tree amplitudes and intersecting dual associahedra, JHEP 06 (2018) 153 [arXiv:1802.03384] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2009.02394
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Feng, B., Zhang, Y. Note on the Labelled tree graphs. J. High Energ. Phys. 2020, 96 (2020). https://doi.org/10.1007/JHEP12(2020)096
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2020)096