Extended Poincare Symmetry Dictates Massive Scattering Amplitudes

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.