Abstract
Theories with both electric and magnetic charges (“mutually non-local” theories) have several major obstacles to calculating scattering amplitudes. Even when the interaction arises through the kinetic mixing of two, otherwise independent, U(1)’s, so that all low-energy interactions are perturbative, difficulties remain: using a self-dual, local formalism leads to spurious poles at any finite order in perturbation theory. Correct calculations must show how the spurious poles cancel in observable scattering amplitudes. Consistency requires that one type of charge is confined as a result of one of the U(1)’s being broken. Here we show how the constraints of confinement and parity conservation on observable processes manages to cancel the spurious poles in scattering and pair production amplitudes, paving the way for systematic studies of the experimental signatures of “dark” electric-magnetic processes. Along the way we demonstrate some novel effects in electric-magnetic interactions, including that the amplitude for single photon production of magnetic particles by electric particles vanishes.
Highlights
Even when the interaction arises through the kinetic mixing of two, otherwise independent, U(1)’s, so that all low-energy interactions are perturbative, difficulties remain: using a self-dual, local formalism leads to spurious poles at any finite order in perturbation theory
Along the way we demonstrate some novel effects in electric-magnetic interactions, including that the amplitude for single photon production of magnetic particles by electric particles vanishes
We have shown that the spurious poles are cancelled when the total magnetic charge in a given process is zero, as required by magnetic charge confinement
Summary
This section briefly reviews Zwanziger’s self-dual formalism [3], focusing on the case of perturbative electric and magnetic charges. The spacelike vector nμ plays the role of the direction of the Dirac string [31] This self-dual Lagrangian leads to photon propagators that describe interactions between two electric charges (details of the derivation are given in appendix A ). Where again the first (second) line is the result from the amplitude corresponding to the left (right) diagram of figure 1 Note that in this case the propagation is through a massless boson and that the effective coupling of the photon to the dark monopole is −eεgD/eD as expected from eq (2.10). The decoupling limit, we are left with only the visible photon interaction, but as before the bound nature of the monopoles conspires to eliminate the photon’s coupling to the point-like bound state
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