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Momentum shift and on-shell constructible massive amplitudes
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We construct tree-level amplitude for massive particles using on-shell recursion relations based on two classes of momentum shifts: an all-line transverse shift that deforms momentum by its transverse polarization vector, and a massive BCFW-type shift. We illustrate that these shifts allow us to correctly calculate four-point and five-point amplitudes in massive QED, without an ambiguity associated with the contact terms that may arise from a simple ''gluing'' of lower-point on-shell amplitudes. We discuss various aspects and applicability of the two shifts, including the large-z behavior and complexity scaling. We show that there exists a ''good'' all-line transverse shift for all possible little group configurations of the external particles, which can be extended to a broader class of theories with massive particles such as massive QCD and theories with massive spin-1 particles. The massive BCFW-type shift enjoys more simplicity, but a ''good'' shift does not exist for all the spin states due to the specific choice of spin axis.
Forward citations
Cited by 7 Pith papers
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Supersymmetry, Supergravity and the Consistency of On-Shell Massive Superamplitudes
Consistent scattering amplitudes force a massless spin-3/2 particle to be the gravitino of a supergravity theory, and constrain massive BPS vector couplings to form a Lie algebra.
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Supergravity from the Bottom Up
Massive spin-3/2 fermion interactions are consistent up to the Planck scale only in broken supergravity, with gravity required by unitarity and the Ward identity.
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Massive Helicity-Chirality Spinor Formalism from Massless Amplitudes with On-shell Mass Insertion
A new helicity-chirality spinor basis with a 'transversality' charge claims a one-to-one UV-IR correspondence between massive amplitudes and massless amplitudes with Higgs insertions, and reproduces pion decay, top de...
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Massive Gauge Theories from Consistency Conditions of Amplitudes
Massive vector-boson and scalar amplitudes through four points are uniquely fixed by two on-shell consistency conditions, forcing spontaneously-broken gauge theories — or Stueckelberg theory when scalar masses are equ...
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Relativistic Particle on Light-Front
A front-form construction with a reference null vector makes the massive-to-massless Wigner classification continuous and derives the massless spin-1 polarization shift coefficient from the angle between reference vectors.
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On-shell recursion relations for higher-spin Compton amplitudes
The all-line transverse shift makes four-point electromagnetic and gravitational Compton amplitudes on-shell constructible for massive spin s≤3/2 and s≤5/2, respectively, starting from minimal three-point amplitudes.
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Extended Poincare Symmetry Dictates Massive Scattering Amplitudes
A new U(1) 'transversality' symmetry, embedded in SO(5,1), fixes the structure of massive three-point amplitudes and resolves the e+e- to mu+mu- discrepancy in the spinor-helicity formalism.
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