Ok the analyses. I have posted about this concept in the past and I believe it to be very important to help you maximize your gains in this situation.
I had AA and when the guy three bets me he pretty much tells me he has AK at the minimum, KK or QQ more likely. I guess he could have something as little as JJ or 1010 but most of the time a three bet preflop from a non maniac spells out VERY big pocket pair or AKs usually at the minimum. So the important part, DO NOT CAP THE POT IF IT IS HEADS UP. Why blow your cover now for just another one small bet when you by disguising your hand can gain a bigger advantage postflop. Very likely if I cap here I lead out on the flop and may just get called down for 2.5 Big bets + the other 0.5 that I got for capping the flop for a total of 3 BB. Maximum I think I could get 4.5 Big Bets if I cap the flop. The way I played it I got -0.5 BB for not capping flop + 6 Big Bets for a total of 5.5 Big Bets which is much better than the 3 to 4.5 that I would have got by capping preflop.
The play was perfect. A nice flop of Jack high go ahead and lead out representing the Jack knowing you are going to get raised and then just call so he keeps the initiative for the turn where you can do the popping and in this case the repopping
The flop lead out is much better than the flop check call because you nearly guarantee yourself another small bet and also provide misinformation to the raiser (I have a Jack) so he can continue to further compound his problems. Now if he had just called my flop bet then I might have been a little worried about JJ but the raise assured me he didn't hold this hand. The rest of the hand plays itself. He had QQ.
Limit holdem is a game were the winners and losers are separated by a razor thin line for the most part. You have to constantly be thinking how can I play my hand for the greatest benefit and sometimes that means NOT capping with AA preflop if given the opportunity. Hope this example helps you out some.