Easy answer, they could just behead him U_U.Now how would they execute him? The Sokyoku was destroyed wasn't it? The only way to kill him was for Yamamoto to use Zanka No Tachi, which would almost probably destroy Seiretei. Aizen's still alive simply because of plot.
He still has the hogyouku, it's part of him and as we have seen even if you remove it it will just go back to him, so he's still immortal. There hasn't been anything shown or said that says otherwise.