Classical radiation zeros in gauge-theory amplitudes

Radiation tree amplitudes: Zeroing in on more photons and gluons

“…So the neutral particle must be massless (which is fine for photons!) and travel parallel to the photon (which are just the conditions derived [5,15] from the zero-charge limit, Q r → 0, of the null zone equations, forcing p r · q → 0). Furthermore J r can vanish when p r ∝ q for a massless vector neutral particle r if it is coupled to a conserved current (which is also fine for photons!)…”

“…A radiation representation has been found in [5] where the formulas are organized according to the original vertices in the RsourceS graphs to which the photons would be attached. The radiation amplitude can be written as a sum of vertex attachments with coefficients related to the rest of the original source graph.…”

“…We refer the reader to Sec. III and a related discussion in [5]. Equation (2.6) is therefore sufficient.…”

“…3. Drawing again on our previous experience [5], we can collapse the results into the following form…”

“…We are reminded that there are zeros associated with any gauge group when the corresponding massless gauge bosons are emitted [5,14]. In this reaction, we can think of two ways its tree amplitude can vanish:…”