Story highlights FAA releases audio recording of air controllers and Southwest crew after landing

Flight 4013 landed at small municipal airport in January, not its intended destination

The matter is under investigation and pilots remain on paid leave for now

Audio recordings released on Monday reveal confusion between air traffic controllers and the veteran crew of a Southwest Airlines jet after they landed at the wrong airport in Missouri in January.

"I assume I'm not at your airport," one of the pilots radioed to controllers at Branson Airport, the Boeing 737's intended destination.

"4013, um, have you landed?" comes the response, according to the recordings released by the Federal Aviation Administration.

"Yea," says the pilot, after a brief pause.

Then the controller calls to another air traffic facility for the area to inquire about the plane, and there is this exchange:

"Did you watch Southwest land?"

"Yea, why?"

"Did you see it come here? They're saying it landed at the wrong airport."

"Are you kidding?"

"Yea, no, I'm not."

The plane from Chicago actually landed several miles away at a municipal airport in Taney County, which doesn't have a control tower.

And that wasn't all.

The Taney County airport's runway is 3,738 feet, about half the length of the Branson runway, which is 7,140 feet. That forced pilots to act fast and brake hard when the aircraft with 129 passengers and crew touched down.

No one was injured and the jet took off the next day.

The National Transportation Safety Board is investigating.

The pilots remain on paid leave pending the outcome of the investigation, Southwest said in a statement.