There is no technical term. If they did not have a warrant, or other justifiable reason such as imminent danger, they are not allowed to enter your home. YOur remedy depends if anyone was charged with a crime or not.
I believe you've posted a related question before. If so, you really need to hire a lawyer as the questions in this forum are not going to help you resolve your situation.
They are not allowed to enter without a warrant unless an authorized person allows them in.
Please be advised my answers to questions does not constitute legal advise and you should not rely on it, due to the fact that we have never met, I have not been aprised of the facts in you case nor have I reviewed any documents.
I believe this is the first part of a DWI question you posted last week. The police have a community caretaking exception to the warrant requirement they can assert. Otherwise they need a warrant. The radio transmissions would help greatly here.