Recursion relations for scattering amplitudes with massive particles

Abstract

We use the recently developed massive spinor-helicity formalism [1] of Arkani- Hamed et al. to propose a new class of recursion relations for tree-level amplitudes in gauge theories. These relations are based on a combined complex deformation of massless as well as massive external momenta. We use these relations to study tree-level amplitudes in scalar QCD as well as amplitudes involving massive vector bosons in the Higgsed phase of Yang-Mills theory. We prove the validity of our proposal by showing that in the limit of infinite momenta of two of the external particles, the amplitude once again is controlled by an enhanced Spin-Lorentz symmetry paralleling the proof of BCFW shift for massless gauge theories. Simple examples illustrate that the proposed shift may lead to an efficient computation of tree-level amplitudes.

arXiv comment31 pages, v3: change in title, matched with published version

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• Graviton particle statistics and coherent states from classical scattering amplitudes
• Scattering of Gravitons and Spinning Massive States from Compact Numerators
• Color-kinematics duality, double copy and the unitarity method for higher-derivative QCD and quadratic gravity
• All-multiplicity amplitudes with four massive quarks and identical-helicity gluons
• Massive On-shell Recursion Relations for n-point Amplitudes
• Recursion relations for scattering amplitudes with massive particles II: massive vector bosons
• Scattering Amplitudes and BCFW in $\mathcal{N}=2^{\ast }$ Theory
• An SZ-Like Effect on Cosmological Gravitational Wave Backgrounds
• Loop Amplitudes in the Coulomb Branch of $\mathcal{N}=4$ Super-Yang-Mills Theory
• Massive Gauge Theories from Consistency Conditions of Amplitudes