State and local police are investigating the beating of a woman in her home Tuesday afternoon. The woman was airlifted in critical condition to a Boston hospital from the scene on Lowell Street. Carrie Kimball Monahan, a spokeswoman for the Essex district attorney, said the victim remained in the hospital Wednesday. Monahan said a search warrant had been executed at the woman's home. Monahan would not say if there were any suspects in the attack. The victim’s live-in boyfriend, James McMackin, 30, was arrested on an outstanding warrant for unpaid court fees regarding a prior incident, Monahan said. State Police detectives assigned to the district attorney’s office are investigating, along with the State Police crime scene unit and local police.