Angular distributions and a selection rule in charge-pole reactions

Daniel Zwanziger

    Research output: Contribution to journalArticle

    Abstract

    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.

    Original languageEnglish (US)
    Pages (from-to)458-470
    Number of pages13
    JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
    Volume6
    Issue number2
    DOIs
    StatePublished - 1972

    Fingerprint

    poles
    angular distribution
    Lorentz transformations
    electric charge
    angular momentum
    scattering
    decay
    subgroups
    scattering amplitude
    leaves
    center of mass
    charged particles
    parity
    electromagnetic fields
    kinematics
    generators
    statistics
    momentum
    orbitals
    polarization

    ASJC Scopus subject areas

    • Physics and Astronomy (miscellaneous)

    Cite this

    Angular distributions and a selection rule in charge-pole reactions. / Zwanziger, Daniel.

    In: Physical Review D - Particles, Fields, Gravitation and Cosmology, Vol. 6, No. 2, 1972, p. 458-470.

    Research output: Contribution to journalArticle

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