This discipline is known by many names. Try searching film music, cinema music, motion picture music, and movie music.
Make sure you have the correct composer if you're looking at a film that has several versions. For example: four films called Romeo and Juliet have been made since 1950. Only one version had a score from the legendary Nino Rota (1968 Franco Zeffirelli, director).
If you're looking at an international film, you'll want to know the name of the film in English and it's original language.
Prominent scholars: James Buhler, David Neumeyer, Caryl Flinn, Kathryn Kalinak, Nathan Platte, James Wierzbicki.
Print books / ebooks
Film and television scores, 1950-1979: a critical survey by genre by Kristopher Spencer [Ebook]
