Massive On-shell Recursion Relations for n-point Amplitudes

Abstract

We construct two and three-line shifts for tree-level amplitude with massless and/or massive particles, and provide a method to construct general multi-line shifts for all masses. We choose the massless-massive BCFW shift from these shifts and examine its validity in renormalizable theories. Using such a shift, we find that amplitudes with at least one massless vector boson are constructible. This reveals the importance of gauge theory in the construction of amplitudes with massive particles. We also find that this kind of amplitudes have a cancellation related to group structure among different channels, which is essential for constructibility. Furthermore, we show that in the limit of large shift parameter $z$, the amplitude with four massive vector bosons, which can include transverse massive vector particles, have structures proportional to the amplitude with shifted vector particles replaced by Goldstone bosons in the leading order. This is responsible for the failure of massive-massive BCFW recursion relations in the amplitudes with four massive vector bosons.

37 pages, 6 figures, 3 tables, major revision, submitted to JHEP

References in corpus (7)

• A note on dual superconformal symmetry of the N=4 super Yang-Mills S-matrix
• Tree Level Recursion Relations In General Relativity
• On-shell constructibility of tree amplitudes in general field theories
• SUSY Ward identities for multi-gluon helicity amplitudes with massive quarks
• Graviton particle statistics and coherent states from classical scattering amplitudes
• On-shell constructibility of Born amplitudes in spontaneously broken gauge theories
• Recursion relations for scattering amplitudes with massive particles II: massive vector bosons

Cited by in corpus (4)

• Scattering Amplitudes and BCFW in $\mathcal{N}=2^{\ast }$ Theory
• Exploring $HVV$ amplitudes with $CP$ violation by decomposition and on-shell scattering amplitude methods
• Loop Amplitudes in the Coulomb Branch of $\mathcal{N}=4$ Super-Yang-Mills Theory
• Massive Gauge Theories from Consistency Conditions of Amplitudes