Tree and $1$-loop fundamental BCJ relations from soft theorems

Abstract

We provide a new derivation of the fundamental BCJ relation among double color ordered tree amplitudes of bi-adjoint scalar theory, based on the leading soft theorem for external scalars. Then, we generalize the fundamental BCJ relation to $1$-loop Feynman integrands. We also use the fundamental BCJ relation to understand the Adler's zero for tree amplitudes of non-linear Sigma model and Born-Infeld theories.

24 pages, 4 figures

References in corpus (14)

• New Relations for Gauge-Theory Amplitudes
• Asymptotic symmetries and subleading soft graviton theorem
• Effective Field Theories from Soft Limits
• Einstein-Yang-Mills Scattering Amplitudes From Scattering Equations
• Soft sub-leading divergences in Yang-Mills amplitudes
• Subleading soft theorem in arbitrary dimension from scattering equations
• Scattering amplitudes in N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity
• Sub-subleading soft gravitons and large diffeomorphisms
• Expansion of All Multitrace Tree Level EYM Amplitudes
• Subleading Soft Theorem for Multiple Soft Gravitons
• Soft pion theorem, asymptotic symmetry and new memory effect
• The B-field soft theorem and its unification with the graviton and dilaton
• Tree level amplitudes from soft theorems
• On the Symmetry Foundation of Double Soft Theorems