Is there an example of two elementary particles colliding to result in a single elementary particle? Apologies for the novice question, but I don't know enough particle physics to immediately answer my own questions. 
I have the following questions.


*

*Is there an example of an inelastic collision where two elementary particles "combine" to spawn a new elementary particle? ("Combine" is the wrong choice of words, because I'm interested in fundamental/elementary particles only.) 

*If not, is there a reason why? 


The reason for these questions is that I am curious if there is an example of a particle collision where mass is not conserved and the extra/missing mass cannot possibly be blamed on any internal energy modes.
An obvious example would be electron-positron annihilation $e^{+} + e^{-}\rightarrow \gamma + \gamma$, but that involves four particles in the entire process. Is there a less obvious example (preferably involving only three particles in total)?
 A: 
Is there an example of an inelastic collision where two elementary particles "combine" to spawn a new elementary particle? ("Combine" is the wrong choice of words, because I'm interested in fundamental/elementary particles only.) 

If you look at the elementary particles table the Z is an elementary particle.
It is produced in e+e- scattering as seen here: (it is now fig51.2), world data on the total crossection ...

So in the strict mathematical sense and within the standard model of particle physics the answer to the title is YES. It is a resonance, its lifetime very short, but it is a basic elementary particle in the standard model.
The four vectors of the summed e+e- have the invariant mass of the Z, which decays in multiple ways.
The peaks with smaller mass are not considered elementary particle of the standard model, just resonances. The Z due to its large mass goes mostly to a large number of particles/hadrons , although Z to gamma gamma or mu+mu- exists ( the lower plot utilizes the mu+mu- crossection for the ratio with the hadronic crossection, if you read the link)

an example of a particle collision where mass is not conserved

Mass is not a conserved quantity in elementary particle physics, because it obeys laws of special relativity. What is conserved is energy and momentum, considered a single four vector. . The before and after interaction conservation of energy and momentum  ensures that the length of the summed four vectors have the same invariant  mass, before and after.
