Lorentz Boost of a photon? I'm a bit confused about a remark given to me by one of my professors, I appreciate any help you may provide even though my question may be unclear.
When discussing a decay channel 
$\rm e^+e^- \to \eta_c \gamma \pi^+ \pi^-$,
 I was told that I need to make sure that the photon ($\gamma$) I have contributing to the decay channel is MONOCHROMATIC.
I can do that by boosting the photon into the mother's particle frame.
I don't understand why the photon should be monochromatic? why boosting it could do the trick?
Please let me know if I should provide you with any more details.
 A: The most famous example of a problem like this is electromagnetic annihilation
of para-positronium into photons:
$$ \rm e^+e^- \to \gamma\gamma$$
In that decay, there always exists a reference frame where the total momentum of the electron-positron pair is zero.  In that reference frame, the photons must carry equal and opposite momentum, and so annihilation photons are "monochromatic" with an energy of 511 keV.
Contrast that with ortho-positronium, which must decay to three photons to conserve angular momentum.  In that case, the extra degree of freedom of an angle between the photons means there are many sets of photon energies which can conserve energy and momentum.  In general, two-body decays are monochromatic, while many-body decays have energies that fill some phase space.
You see the same division between alpha decays, which have two-body final states and produce alpha particles with definite energy; beta decays, with three-body final states and an energy spectrum for all particles; and electron-capture decays, with a two-body final state again and a definite neutrino energy.
I'm not familiar with the process you're discussing in your question, but if the photon is monochromatic that suggests it's emitted from some intermediate state which is a two-body decay.  If that were the case, your treatment of the intermediate state would conserve momentum in its rest frame --- but that probably wouldn't be the rest frame of the initial electron-positron pair.
