Yes JoJo, I used to live in Murfreesboro, and the photos I have of a queen European Hornet that made a nest in my swarm trap is from there. Nope, there are no established colonies of Giant Asian Hornets in the Western Hemisphere.
Asian Hornets (Which are not the same as Giant Asian Hornets) are established in Western Europe, and creating havoc over there, and the German Yellowjacket has invaded the Northeastern USA, and will hunt honeybee larvae. The native Yellowjackets do not hunt honeybees.