LAS VEGAS — Federal and airport authorities say they are investigating why an air traffic controller became incapacitated and went silent while working a night shift alone in the tower at busy McCarran International Airport in Las Vegas. The Federal Aviation Administration and the airport issued statements Friday declaring that no “safety events” occurred during the incident late Wednesday. Air traffic recordings available on the internet had the female controller slurring words and then apparently losing consciousness while pilots radioed approaches to land, sought clearance to take off and asked directions for taxiing. Officials said a male controller on break was summoned to take over tower operations shortly before midnight and paramedics responded. The woman is on administrative leave, and the agency has ordered two controllers to be in the tower during busy hours.