Massive Helicity-Chirality Spinor Formalism from Massless Amplitudes with On-shell Mass Insertion

Abstract

We introduce a helicity-chirality spinor formalism to describe scattering amplitudes for particles of any masses and spins. The massive spin-spinors introduced by Arkani-hamed-Huang-Huang have been extended to the spin/helicity-transversality spinors, in which a new quantum number transversality, closely related to chirality, is introduced by extending the Poincare symmetry. The massive helicity-chirality amplitudes can be written by the large and small components of massless spinors $\lambda$ and $\eta$ following the $\lambda \sim \sqrt{E}, \eta \sim \mathbf{m}/\sqrt{E}$ expansion order by order, which formulate the power counting rules of a large energy effective theory. Diagrammatically the mass expansion in amplitudes originates from the on-shell mass insertion: the helicity flip and chirality flip, which completely determines the three-point massive amplitudes. From the chirality-helicity unification at the UV, any massive helicity-chirality amplitude can be one-to-one corresponded to massless helicity amplitudes with (without) additional Higgs insertion. This UV-IR correspondence explains the mass enhancement in the weak decay processes $\pi^+ \to \mu^+ \nu$ and $t \to W^+ b$, and isolates the correct UV of the three-point massive QED $F\bar{F}\gamma$ amplitudes in Arkani-hamed-Huang-Huang formalism. From massless-massive correspondence, the massless on-shell techniques can be utilized to construct higher-point massive amplitudes.