Quadratic Feynman Loop Integrands From Massless Scattering Equations

Abstract

Recently the Cachazo-He-Yuan (CHY) approach has been extended to loop level, but the resulting loop integrand has propagators that are linear in the loop momentum unlike Feynman's. In this note we present a new technique that directly produces quadratic propagators identical to Feynman's from the CHY approach. This paper focuses on ${\Phi }^3$ theory but extensions to others theories are briefly discussed. In addition, our proposal has an interesting geometric meaning, we can interpret this new formula as a unitary cut on a higher genus Riemann surface.

26 pages, typos fixed and references added

References in corpus (17)

• New Relations for Gauge-Theory Amplitudes
• Einstein-Yang-Mills Scattering Amplitudes From Scattering Equations
• Subleading soft theorem in arbitrary dimension from scattering equations
• Scattering equations and BCJ relations for gauge and gravitational amplitudes with massive scalar particles
• Gravity from Rational Curves
• Two-Loop Scattering Amplitudes from the Riemann Sphere
• New Relations for Einstein-Yang-Mills Amplitudes
• Next to subleading soft-graviton theorem in arbitrary dimensions
• New Relations for Gauge-Theory and Gravity Amplitudes at Loop Level
• Manifesting Color-Kinematics Duality in the Scattering Equation Formalism
• Scattering equations, generating functions and all massless five point tree amplitudes
• CHY Loop Integrands from Holomorphic Forms
• CHY-Graphs on a Torus
• Permutation Symmetry of the Scattering Equations
• A Combinatoric Shortcut to Evaluate CHY-forms
• Note on recursion relations for the $\mathcal{Q}$-cut representation
• Scattering equations, supergravity integrands, and pure spinors

Cited by in corpus (19)

• New BCJ representations for one-loop amplitudes in gauge theories and gravity
• Gluons and gravitons at one loop from ambitwistor strings
• Cosmological Scattering Equations
• One-loop Correlators and BCJ Numerators from Forward Limits
• Cosmological Scattering Equations at Tree-level and One-loop
• Two-Loop Scattering Amplitudes: Double-Forward Limit and Colour-Kinematics Duality
• Propagators, BCFW Recursion and New Scattering Equations at One Loop
• One-loop Parke-Taylor factors for quadratic propagators from massless scattering equations
• Perfecting one-loop BCJ numerators in SYM and supergravity
• Non-planar one-loop Parke-Taylor factors in the CHY approach for quadratic propagators
• One-loop amplitudes in Einstein-Yang-Mills from forward limits
• One-Loop Yang-Mills Integrands from Scattering Equations
• One-loop diagrams with quadratic propagators from the worldsheet
• One-loop Bern-Carrasco-Johansson Numerators on Quadratic Propagators from the Worldsheet
• D3-Brane Loop Amplitudes from M5-Brane Tree Amplitudes
• BCJ Numerators from Differential Operator of Multidimensional Residue
• Note on solutions of scattering equations
• CHY Theory for Several Fields
• One-loop matrix elements of effective superstring interactions: ${\alpha }^{\prime }$-expanding loop integrands