What are the correct utility functions?
It would be really tough to find papers (other than structural models) that empirically determine a particular utility function. Because of their subjective nature, it is incredibly tough to obtain observable data to estimate them. So researchers study the primitive preference relations that utility functions represent. Arguably, the preference relation is what you want to study when talking about rationality and choice. Utility functions are useful insofar as it opens up a tool-box of real analysis tools which a binary relation doesnt typically allow.
So you should rather look for papers that test rationality from observable choice data. I have elaborated a bit on this in an answer to a related question: Click Here