What defines pop music is that it is music that is marketed for mass audiences and therefore will have an industrial influence. That means input from theatre professionals where large performances can be assembled and performed. Therefore, the history with musical theatre will have a large impact on pop of all kinds, including independent pop.
With that in mind, we need to characterise pop music by the various niches it fills. Not all pop songs will be about love. If you go through the pop charts, you will see that other topics are discussed. However, love songs are particularly popular and they will very often climb to the top spots. The influence of musical theatre comes here. Pop artists cover a variety of songs that together can build a narrative. Here are some song types that can be employed in a performance set:
torch song: a sad song of love unrequited
sentimental ballad: a sweet song of love requited
broadside: topical song of event that has happened
jeremiad: topical song addressed to the audience, of anger usually
philippic: topical song addressed to a person in power, of anger usually
anthem: topical song drawing the audience to observe
novelty song: humorous, light song
chorus: song calling to dance
dance number: a more instrumental number with identifiable and performable dances associated with it.
fantasia: a narrative song telling of the surreal
As you might note, this does require interpretation of poetry and therefore some literary analysis is involved. Music theory here will be necessary to not create a mis-match between the lyrics and the music.
Two common terms that get bandied about in pop music that are frequently cited to be important is the hook and the groove. These words are not theoretically well defined, and perhaps why to this day do not have any non-English word for them that we can use to obscure the phenomenon.
My best attempt at defining hook is the key memorable phrase of a song that the audience can recall and anticipate and when repeated by the performer, satisfies the audience's expectations. It is the performer telling the audience that they know what the audience is hearing.
The groove is similar. But instead of concerning the performer-audience relationship, it concerns the relationship between the band-members. If the band-members can anticipate the changes that come next, to the point that they can let the lead (often times the lead-singer) take control of the performer-audience relationship.
These to me seem to be the central feature of pop music.