aw come on you brought it up take a shot. someone else surely will
I'll try.
I'd imagine some combination of:
The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and no Warrants shall issue, but upon probable cause, supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized.
and:
Every person who, under color of any statute, ordinance, regulation, custom, or usage, of any State or Territory or the District of Columbia, subjects, or causes to be subjected, any citizen of the United States or other person within the jurisdiction thereof to the deprivation of any rights, privileges, or immunities secured by the Constitution and laws, shall be liable to the party injured in an action at law, suit in equity, or other proper proceeding for redress
Combined with a lot of time and money could do it.
Unfortunatly, I'd bet, and the cops are betting, that the wronged person in this case has neither the time nor the money for a civil suit. It's a shame because I'd like to see the LEO that led this raid lose his career and house over this. If you fail basic reading comprehension, you shouldn't be a cop.