Reggeization, Massless Particles, and Vanishing Renormalization Constants

Abstract

This paper has three purposes: to generalize earlier work on Reggeization in field theories to allow treatment of massless particles; to show that Reggeization occurs in other processes than just vector-spinor scattering; and to recover the one-to-one correspondence between certain poles in the partial-wave amplitudes and dynamical states which was called into question by recent work. In problems involving massless spin-1 and spin-2 mesons, we make use of a modified amplitude defined by Eriksson which contains no infrared divergences and directly yields physical cross sections. We show that if the proper experimental procedure is defined, infrared-divergent diagrams do not alter the positions of Regge poles in this amplitude and these diagrams change the residues only to higher orders in the coupling constant. The dilemma about factorization of amplitudes when some of the helicity amplitudes are missing is resolved. These results are then applied to the scattering of photons by spin-\textonehalf{} and spin-0 electrons; in each case, it is found that a dynamical trajectory is formed but that the electron is not Reggeized (does not lie on the trajectory). Then we calculate the Compton scattering of gravitons (massless spin-2 particles) by spinor or scalar electrons. In each case, it is shown that no trajectory is generated near the highest nonsense value available, and that near the electron there is generated only one trajectory. In each case the electron is Reggeized. A theory involving massive spin-2 particles is formulated but not used for calculations. Finally, the dynamical criterion furnished by vanishing renormalization constants is applied to Reggeized particles. This test is found to correctly identify a Reggeized particle as elementary; thus the contribution of a Reggeized particle to the scattering amplitude is essentially different from the contribution of a true dynamical state. This allows us once again to associate certain moving poles directly with dynamical particles, without regard for amplitudes in other channels.