I'm Looking for a part name and info on what could have caused the problem.

So I have an 03 peugoet 206 1.4 HDI and I lost a cylinder after going though them by disconnecting each injector and can see the 3rd from the left is not working. So I have striped the rocker cover off and can see that there is a little thing that goes to the top of the valves (in between the camshaft and valves) has snapped in half what is this part called?

If the camshaft has manged to snap this part what could have caused it? could the valve have seized to cause this? I have had a new cam belt quite recently could the be caused by it skipping a tooth?