Great question Larry!
As far as I know there is no word for this in English. German has the noun, 'ein Ohrwurm' (literally an earworm), which can either be a hook, ear candy or simply a catchy tune. But one can also have an 'Ohrwurm', i.e. be stuck with a certain song or musical phrase on one's mind. I believe French has a similar meaning word too (BelM please confirm).
Wait for others to chime in [sic], but otherwise I think you can start coming up with your own neologism.

BTW, we all bid you welcome.