Extended Poincare Symmetry Dictates Massive Scattering Amplitudes

TL;DR

This paper reveals an extended Poincare symmetry in massive scattering amplitudes, enabling the use of massless on-shell techniques to construct complex massive amplitudes by relating spin and transversality.

Contribution

It introduces an extended symmetry framework for massive amplitudes, connecting massless and massive states through new spinor structures and symmetry relations.

Findings

Extended Poincare symmetry $ISO(2) imes ISO(3,1)$ identified.

Massive three-point amplitudes fully determined by $T^ ext{±}$ and $m$ generators.

Massless techniques applicable to higher-point massive amplitude calculations.

Abstract

We identify an extended Poincare symmetry $ISO(2) \times ISO(3,1)$ for on-shell massive scattering amplitudes, transforming under the $U(2)$ Little group symmetry. Thus the one-particle state involves in both spin and transversality $t$ (related to chirality), and the spin-spinors are extended to the spin-transverality spinors. The massive spin-$s$ spinors with different transversality can be related by the $SO(5,1)$ symmetry, although the $U(2)$ Little group breaks the symmetry explicitly. The three-point massive amplitudes can be fully determined from the $T^\pm$ and $m$ generators, diagrammatically denoted as the mass insertion and chirality flip, which provide correspondence between massless ultraviolet and massive chiral-eigenstate amplitudes. Thus the massless on-shell technique can be utilized to construct higher-point tree- and loop-level massive amplitudes.