On differential operators and unifying relations for $1$-loop Feynman integrands

Abstract

We generalize the unifying relations for tree amplitudes to the $1$-loop Feynman integrands. By employing the $1$-loop CHY formula, we construct differential operators which transmute the $1$-loop gravitational Feynman integrand to Feynman integrands for a wide range of theories, include Einstein-Yang-Mills theory, Einstein-Maxwell theory, pure Yang-Mills theory, Yang-Mills-scalar theory, Born-Infeld theory, Dirac-Born-Infeld theory, bi-adjoint scalar theory, non-linear sigma model, as well as special Galileon theory. The unified web at $1$-loop level is established. Under the well known unitarity cut, the $1$-loop level operators will factorize into two tree level operators. Such factorization is also discussed.

arXiv comment42 pages, 3 figures, 4 tables

References in corpus (26)

• New Relations for Gauge-Theory Amplitudes
• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• Scattering of Massless Particles in Arbitrary Dimension
• Scattering of Massless Particles: Scalars, Gluons and Gravitons
• Gravity as the Square of Gauge Theory
• Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM
• Scattering Equations and KLT Orthogonality
• Ambitwistor strings and the scattering equations
• Einstein-Yang-Mills Scattering Amplitudes From Scattering Equations
• Ambitwistor strings and the scattering equations at one loop
• Loop Integrands for Scattering Amplitudes from the Riemann Sphere
• One-loop amplitudes on the Riemann sphere
• Unifying Relations for Scattering Amplitudes
• One-Loop Corrections from Higher Dimensional Tree Amplitudes
• One-loop Scattering Equations and Amplitudes from Forward Limit
• New Representations of the Perturbative S-Matrix
• Gluons and gravitons at one loop from ambitwistor strings
• Evaluation of the CHY Gauge Amplitude
• Note on differential operators, CHY integrands, and unifying relations for amplitudes
• Transmuting CHY formulae
• Worldsheet factorization for twistor-strings
• The Q-cut Representation of One-loop Integrands and Unitarity Cut Method
• A Gluing Operator for the Ambitwistor String
• One-loop CHY-Integrand of Bi-adjoint Scalar Theory
• Transmuting off-shell CHY integrals in the double-cover framework
• Factorizations for tree amplitudes in the double-cover framework: from gravity to other theories

Cited by in corpus (4)

• A Type of Unifying Relation in (A)dS Spacetime
• Differential Operators and Unifying Relations for 1-loop Feynman Integrands from Berends-Giele Currents
• Transmutation operators and expansions for $1$-loop Feynman integrands
• The off-shell expansion relation of the Yang-Mills scalar theory