In Peskin, a derivation about the radiated energy at low frequencies is given, as well as a derivation about the (mean) number of radiated photons. Both are found to depend on the differential intensity $\mathcal{I}(\textbf{v},\textbf{v}')$, which is given by (6.15) $$\mathcal{I}(\textbf{v},\textbf{v}')=\int\frac{d\Omega_k}{4\pi}\bigg(\frac{2(1-\textbf{v}\cdot\textbf{v}')}{(1-\hat{k}\cdot\textbf{v})(1-\hat{k}\cdot\textbf{v}')}-\frac{m^2/E^2}{(1-\hat{k}\cdot\textbf{v})^2}-\frac{m^2/E^2}{(1-\hat{k}\cdot\textbf{v}')^2}\bigg)$$ where $\textbf{v}$ and $\textbf{v}'$ are the initial and final velocities of the emitting fermion.
If one tries to take the massless limit, i.e. the limit in which a massless fermion emits a photon, then the peaks in eq. (6.15) become infinitely large. The divergence is associated with the direction of the motion of the emitted photon being parallel to the direction of the initial/final fermion's momentum.
Does that mean that a photon being emitted by a massless fermion can not have direction of motion parallel to the emitting particle? Or does it have to do with the fact that it is not possible for a detector to detect two particles moving at the same direction (if something like this is true)?
