Classical radiation zeros in gauge-theory amplitudes

Abstract

The electromagnetic radiation from classical convection currents in relativistic $n$-particle collisions is shown to vanish in certain kinematical zones, due to complete destructive interference of the classical radiation patterns of the incoming and outgoing charged lines. We prove that quantum tree photon amplitudes vanish in the same zones, at arbitrary photon momenta including spin, seagull, and internal-line currents, provided only that the electromagnetic couplings and any other derivative couplings are as prescribed by renormalizable local gauge theory (spins ≤1). In particular, the existence of this new class of amplitude zeros requires the familiar gyromagnetic-ratio value $g=2\mathrm{}$ for all particles. The location of the zeros is spin independent, depending only on the charges and momenta of the external particles. Such null zones are the relativistic generalization of the well-known absence of electric and magnetic dipole radiation for nonrelativistic collisions involving particles with the same charge-to-mass ratio and $g$ factor. The origin of zeros in reactions such as $u\overline{d}\to W^{+}\gamma$ is thus explained and examples with more particles are discussed. Conditions for the null zones to lie in physical regions are established. A new radiation representation, with the zeros manifest and of practical utility independently of whether the null zones are in physical regions is derived for the complete single-photon amplitude in tree approximation, using a gauge-invariant vertex expansion stemming from new internal-radiation decomposition identities. The question of whether amplitudes with closed loops can vanish in null zones is addressed. A low-energy theorem for general quantum amplitudes (including closed loops) is found. Important relations between the photon couplings and Poincaré transformations are discovered. The null zone and these relations are discussed in terms of the Bargmann-Michel-Telegdi equation. The extension from photons to general massless gauge bosons is carried out.