Can Protons and Antiprotons Annihilate into W Bosons?

[mateomy]

$$p + \bar{p} \rightarrow W^+ + W^-$$

I'm just going through various "Is this particle annihilation/decay possible" questions and came across this one...then started thinking...then started over-thinking. Is this possible? It seems because the W bosons are so much more massive than the protons it shouldn't be. But looking through various books and hyperphysics I'm not sure. I'm thinking it's due to conservation of mass/energy but not positive. Where is my thinking going astray?Thanks.

 

[vela]

Hint: Why do physicists build big particle accelerators?