Hi Puffballs,
Whether he knew you were together or not, another guy hitting on your girl affirms that you have good taste and can pull quality women. I take my hat off to you.
As for your question, beating him up will do the most to set the guy straight. Hey, why not kill him while you're at it?
If your priority is to keep your girl interested in you, that's just going to look desperate. In fact, it comes off as very shrill; it just shouts "I know if guys start hitting on you, you're going to find someone better and leave, so I have to do my utmost to scare off the competition". That's not the aura you want to emit.
Running a guy down to a girl does no good, either; when a chick is entertaining the notion that you're jealous, it's very easy to convince her that she's right--and defensive actions will help her reach that conclusion very quickly.
If you're trying to keep your woman, the best you can do is let the guy know in no uncertain terms that she's off the market. If he doesn't like it, he should learn to live with it, because there's not a single thing he can do about it. If you think you can pull it off properly, you might just mention casually to your girlfriend that you take it as a confirmation of your good taste when other guys hit on her, but you're sure that she knows any mucking around on her part will see her out the door with no hesitation. Don't say it if you don't mean it, though; there are only some lies that women can sense a mile off, but that's one of them.
I am
The Main Event.