For two massive particles producing a single photon,
<BR>conservation of total 4-momentum would read
$$\tilde m_1 + \tilde m_2 = \tilde k,$$
where $\tilde k$ is lightlike ($\tilde k \cdot \tilde k=0$).

However, the sum of two future-directed timelike vectors is future-directed
timelike.<BR> 
So, $(\tilde m_1 + \tilde m_2)$ is not lightlike.


[If two future-directed timelike vectors could be lightlike, then
one could send a sequence of timelike signals instead of a single light-signal. But that doesn't happen in special relativity... 
<BR><BR>
(You can't reach an event-Z on the light cone of event-A with a sequence of future-timelike-displacements starting at A.)
]