Don't leave him right away, MORE
I think that leaving him right away would hurt you and him, and I do not think it is the answer. not at all.
I know this because I suffered great jealosey when I first met my wife, I dodn't like her talking about other guy friends and such, I admit that I was terrible.
Now, it took me a little while, I saw a therapist only about 3 times, who helped me look inside myself and at myself with variouse techniques, and you know, this thing went away quite rapidly. I do not mind at all now if my wife has guy friends ect, I am not over everything, such as x lovers from the past, but I am over guy friends and x husbands (who I never had a problem with anyway).
If we had broken up it would have been awful, I can't immagine life without my wife, and thats why I say don;t throw it all away right now, its not as easy as some people think it is to throw away lots of love and a person and just deal with it.
Ask him about couselling, He might not want to go with you and thats ok, but try and get him to see someone, maybe even tell him that its disturbing you and even tell him that you do not like that this makes you slap him sometimes.
Give it a couple or few tries, its not good juts to throw someone away, and then get someone else who could have all the same problems all over again, there is no onw who is absolutely perfect and we all deserve a second chance.
I hope this helps
Husky