Algebraic Classification of Regge Poles

Abstract

Starting from the Lorentz invariance and usual on-mass-shell analyticity properties of scattering amplitudes, we prove that: (a) massless "particles," transforming according to infinite-spin representations of the two-dimensional Euclidean group, are necessarily "elementary," corresponding to Kronecker-$\delta$ singularities in the $j$ plane; (b) the classification algebra of Regge poles, at vanishing invariant mass, is necessarily the Lie algebra of the homogeneous Lorentz group $\mathrm{SL}(2,C)\mathrm{}$. We calculate the contributions of Regge poles to scattering amplitudes of particles with arbitary finite mass and spin at vanishing momentum transfer, taking into account the "conspiracy" of Regge poles arising from their classification according to $\mathrm{SL}(2,C)\mathrm{}$. The Regge contributions are indeed found to have the required analyticity properties and, therefore, a uniform asymptotic behavior for large energies.