LAM FACIAL PLASTICS

I have an extremely short philtrum. My lips don't touch at rest, akin to what a rabbit's mouth look's like. I've heard there is a procedure to "snip" the muslce that connects the gum and the upper lip to improve this situation. What is the name of that muscle and what is the name of that procedure? Also, are there any avenues worth exploring for my condition. Thank you for reading this.

in short, i have no idea how to do that. i am sure someone does obviously but that person is not I. sorry.
best,
s.