One-loop amplitudes in Einstein-Yang-Mills from forward limits

Abstract

We present a method to compute the integrands of one-loop Einstein-Yang-Mills amplitudes for any number of external gauge and gravity multiplets. Our construction relies on the double-copy structure of Einstein-Yang-Mills as (super-)Yang-Mills with the so-called YM+${\varphi }^3$ theory -- pure Yang-Mills coupled to bi-adjoint scalars -- which we implement via one-loop Cachazo-He-Yuan formulae. The YM+${\varphi }^3$ building blocks are obtained from forward limits of tree-level input in external gluons and scalars, and we give the composition rules for any number of traces and orders in the couplings $g$ and $\kappa$. On the one hand, we spell out supersymmetry- and dimension-agnostic relations that reduce loop integrands of Einstein-Yang-Mills to those of pure gauge theories. On the other hand, we present four-point results for maximal and half-maximal supersymmetry where all supersymmetry cancellations are exposed. In the half-maximal case, we determine six-dimensional anomalies due to chiral hypermultiplets in the loop.

51 + 8 pages, 18 figures, submission includes an ancillary data file; v2: typos fixed, matches version to be published in JHEP

References in corpus (15)

• New Relations for Gauge-Theory Amplitudes
• The Momentum Kernel of Gauge and Gravity Theories
• Einstein-Yang-Mills Scattering Amplitudes From Scattering Equations
• Scattering amplitudes in N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity
• From loops to trees by-passing Feynman's theorem
• Two-Loop Scattering Amplitudes from the Riemann Sphere
• New Relations for Einstein-Yang-Mills Amplitudes
• Einstein-Yang-Mills from pure Yang-Mills amplitudes
• Amplitude relations in heterotic string theory and Einstein-Yang-Mills
• Relations for Einstein-Yang-Mills amplitudes from the CHY representation
• One-loop Correlators and BCJ Numerators from Forward Limits
• Positive helicity Einstein-Yang-Mills amplitudes from the Double Copy
• One-loop Parke-Taylor factors for quadratic propagators from massless scattering equations
• Chiral Splitting and $\mathcal{N}=4$ Einstein--Yang--Mills Tree Amplitudes in 4d
• Einstein Yang-Mills Amplitudes from Intersections of Twisted Forms

Cited by in corpus (3)

• One-loop diagrams with quadratic propagators from the worldsheet
• One-loop Bern-Carrasco-Johansson Numerators on Quadratic Propagators from the Worldsheet
• Algebraic Consistency and Explicit Construction of One-Loop BCJ Numerators of Yang-Mills and Related Theories