Warmonger penalty

Anyone know is there decay on it? If there is how long? I can not find any relevant posts.

Yes, but at the rate it does the carbon-14 dating on the archaeological sites probably decays faster.

It is the score that decays 5 points every turn. The corresponding hate(the diplo modifier) is on average 20 times smaller than the score. So in effect it takes 20 times longer for the same warmonger hate to decay than normal hate(denouncing for example). The score for a single DOW is 250 which equates to an average of 2.5 worth of hate. Some civs really hate warmongers so even a single DOW can show up which will take 50 turns to decay.