Angular distributions and a selection rule in charge-pole reactions

In the scattering of electrically and magnetically charged particles, it is found that, besides the orbital and spin angular momentum of each particle, there is a residual angular momentum in the electromagnetic field of the in or out scattering states given by M=i>ij×pipj[(pipj)2-pi2pj2]-12, where ij=(4)-1(eigj-giej) and pi, ei, gi are the 4-momentum and electric and magnetic charges of the ith particle. Because of the addition of this M to the generator of Lorentz transformations, the scattering states do not transform like free-particle states, but the modification has a simple group-theoretical description. For each pair of particles i and j, M generates a one-dimensional representation of the little group of the pair of 4-vectors pi, pj. This is the subgroup of the Lorentz group which leaves both 4-vectors invariant and is isomorphic to the one-parameter group of rotations about the z axis. The problem of constructing scattering amplitudes satisfying the new kinematics is solved. For two-body decay processes 12+3, there results the selection rule s1+s2+s3|23|=(4)-1|e2g3-g2e3| relating the spins si of the particles to their electric and magnetic charges. Parity- and time-reversal-violating angular distributions are found. For example, in the decay 12+3, if particle 1 has spin one and polarization vector and particles 2 and 3 are spinless with 23=1, the center-of-mass angular distribution is *-q*q×*q, where q is the direction of particle 2. It is found that a consistent Lorentz transformation law requires ij to take on integral or half-integral values, but the usual connection between spin and statistics further limits ij to integral values only.