Analytical amplitudes from numerical solutions of the scattering equations

Abstract

The CHY formalism for massless scattering provides a cohesive framework for the computation of scattering amplitudes in a variety of theories. It is especially compelling because it elucidates existing relations among theories which are seemingly unrelated in a standard Lagrangian formulation. However, it entails operations that are highly non-trivial to perform analytically, most notably solving the scattering equations. We present a new Python package ( https://github.com/GDeLaurentis/seampy ) to solve the scattering equations and to compute scattering amplitudes. Both operations are done numerically with high-precision floating-point algebra. Elimination theory is used to obtain solutions to the scattering equations for arbitrary kinematics. These solutions are then applied to a variety of CHY integrands to obtain tree amplitudes for the following theories: Yang-Mills, Einstein gravity, biadjoint scalar, Born-Infeld, non-linear sigma model, Galileon, conformal gravity and $(\text{DF}{)}^2$. Finally, we exploit this high-precision numerical implementation to explore the singularity structure of the amplitudes and to reconstruct analytical expressions which make manifest their pole structure. Some of the expressions for conformal gravity and the $(\text{DF}{)}^2$ gauge theory are new to the best of our knowledge.

arXiv comment27 pages, more details in discussion

References in corpus (29)

• 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
• Ambitwistor strings and the scattering equations
• Conformal Supergravity in Twistor-String Theory
• Einstein Gravity from Conformal Gravity
• Ambitwistor strings and the scattering equations at one loop
• Loop Integrands for Scattering Amplitudes from the Riemann Sphere
• Ambitwistor strings in 4-dimensions
• Scattering in Three Dimensions from Rational Maps
• S@M, a Mathematica Implementation of the Spinor-Helicity Formalism
• Proof of the Formula of Cachazo, He and Yuan for Yang-Mills Tree Amplitudes in Arbitrary Dimension
• The Polynomial Form of the Scattering Equations
• From conformal to Einstein Gravity
• A Coding of Real Null Four-Momenta into World-Sheet Co-ordinates
• From Twistor String Theory To Recursion Relations
• Unraveling conformal gravity amplitudes
• An Algebraic Approach to the Scattering Equations
• Ambitwistor formulations of $R^2$ gravity and $(DF{)}^2$ gauge theories
• Scattering Equations and Global Duality of Residues
• Elimination and recursions in the scattering equations
• On the solutions of the scattering equations
• General Solution of the Scattering Equations
• Conformal Gravity from Gauge Theory
• Extracting analytical one-loop amplitudes from numerical evaluations
• One-Loop Calculations with BlackHat
• A Monte Carlo Approach to the 4D Scattering Equations
• New Worldsheet Formulae for Conformal Supergravity Amplitudes

Cited by in corpus (5)

• Interpolation of Dense and Sparse Rational Functions and other Improvements in $\text{FireFly}$
• Cosmological Scattering Equations at Tree-level and One-loop
• Ansätze for Scattering Amplitudes from $p$-adic Numbers and Algebraic Geometry
• Pushforwards via Scattering Equations with Applications to Positive Geometries
• Note on solutions of scattering equations