I want to introduce a new type of math accent that is basically an overbar, but also has small (scriptscriptsize?) text set to the right of the bar. Basically something like
but I'd like the text to be set higher---preferably centered vertically on the bar. And I'd like to not have to tweak the height because I'll be making arbitrarily many of these. Is this feasible?
The context is: I'm working on some math that requires an unusually large number of operations similar to complex conjugation. There is no consensus in the literature on which symbols to use for which operations (Hermitian dagger, overbar, overtilde, overset smiley, etc.), which is endlessly confusing. I want to introduce a new notation. My goal is to use an overbar for everything, but also have a short string describing which type of conjugate this is. The string will always be just two or three characters;
co in the example above.