Fourth Amendment
Absent exigent circumstance, a warrantless arrest made across the threshold - where the police are outside and arrestee inside after being summoned to the door by the police - violates the Fourth Amendment.
Compelled by earlier circuit precedent.
http://www.ca2.uscourts.gov/decisions/isysquery/d4b80e2f-29b7-4b35-941f-313aacb7b3f6/1/doc/13-3333_complete_opn.pdf#xml=http://www.ca2.uscourts.gov/decisions/isysquery/d4b80e2f-29b7-4b35-941f-313aacb7b3f6/1/hilite/
Since 2011. An occasional commonplacing of the U.S. Circuit Courts of Appeal.
Neither an authoritative statement of the law nor legal advice. Quick work.