Amplitudes for massive vector and scalar bosons in spontaneously-broken gauge theory from the CHY representation

Abstract

In the formulation of Cachazo, He, and Yuan, tree-level amplitudes for massless particles in gauge theory and gravity can be expressed as rational functions of the Lorentz invariants $k_a\cdot k_b$, ${\epsilon }_a\cdot k_b$, and ${\epsilon }_a\cdot {\epsilon }_b$, valid in any number of spacetime dimensions. We use dimensional reduction of higher-dimensional amplitudes of particles with internal momentum $\kappa$ to obtain amplitudes for massive particles in lower dimensions. In the case of gauge theory, we argue that these massive amplitudes belong to a theory in which the gauge symmetry is spontaneously broken by an adjoint Higgs field. Consequently, we show that tree-level $n$-point amplitudes containing massive vector and scalar bosons in this theory can be obtained by simply replacing $k_a\cdot k_b$ with $k_a\cdot k_b-{\kappa }_a{\kappa }_b$ in the corresponding massless amplitudes, where the masses of the particles are given by $|{\kappa }_a|$.

7 pages, no figures; v2: added paragraph, published version

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• Direct Evaluation of $n$-point single-trace MHV amplitudes in 4d Einstein-Yang-Mills theory using the CHY Formalism
• CHY formula and MHV amplitudes
• All-multiplicity amplitudes with four massive quarks and identical-helicity gluons
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• BCJ Amplitude Relations for Anti-de Sitter Boundary Correlators in Embedding Space
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