I think I may have a water leak underneath my foundation. The tile feels warm. Are there any new methods out there for detection and repair without tearing up the slab?

They can find a underslab leak with ultrasonic leak detectors, but if you feel it warm in one concentraded area then I would save the money that you would spend hiring someone
To find your leak for you. The only way to repair your leak is to break out the slab and weld it up if its copper or the option of repiping your house through the attic. Good luck, Mike

"if you feel it warm in one concentraded area then i would save the money that you would spend hiring someone
to find your leak for you."
I totally disagree! The leak could be feet away from the hot spot. Water, likie electricity, will take the path of least resistance. Use Sleuth or another leak locater to pinpoint the leak. There's no way I know of to repair a pressure leak under the slab without taking up the cement. Good luck, Tom

Had this happen to me and yes I hired a "professional" at the request of my insurance company to "pinpoint" the leak, he was two feet off the leak, and charged me $500 to find the leak, I broke out the slab and found the leak right where the hot spot was. I realize you may have a great deal of experience in the plumbing field but you can be sure if its hot in one area, the leak is going to be close by and the ground will absorb the heat before it gets very far away, so this is why I said I would not waste my money.

You can sometimes re-route above. It was hot water. We should have done both.

There is a process now that can be done to repair a leak in a water line without breaking up the concrete floor or tunneling under. Look in the phone book for someone that advertises no breaking up of the floor.
If you have a loop system where all of the joints are about the floor it is possible to find out which line is leaking and then disconnect each end and push a 3/8 inch pex line through the copper pipe, or what ever your lines are, then reconnect to where it was disconnected with pex fittings.