Note on the Labelled tree graphs
arXiv:2009.02394 · doi:10.1007/JHEP12(2020)096
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 arXiv:1708.08701 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.
arXiv comment52 pages, 41 figures
References in corpus (22)
- Scattering of Massless Particles in Arbitrary Dimension
- Scattering of Massless Particles: Scalars, Gluons and Gravitons
- Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM
- Scattering Equations and KLT Orthogonality
- Einstein-Yang-Mills Scattering Amplitudes From Scattering Equations
- Scattering Amplitudes from Intersection Theory
- The Polynomial Form of the Scattering Equations
- Integration Rules for Loop Scattering Equations
- Scattering Equations and Feynman Diagrams
- Integration Rules for Scattering Equations
- Cross-ratio Identities and Higher-order Poles of CHY-integrand
- An Algebraic Approach to the Scattering Equations
- Scattering Equations and Global Duality of Residues
- Elimination and recursions in the scattering equations
- Labelled tree graphs, Feynman diagrams and disk integrals
- General Solution of the Scattering Equations
- Comments on the evaluation of massless scattering
- Scattering equations, generating functions and all massless five point tree amplitudes
- Biadjoint scalar tree amplitudes and intersecting dual associahedra
- Feynman Rules of Higher-order Poles in CHY Construction
- One-loop CHY-Integrand of Bi-adjoint Scalar Theory
- Permutation in the CHY-Formulation