London Calling." A later scene continues the music. In it, the father administers what he hopes will be a cure for his daughter, kisses her good-bye, then pays the price for that cure.
Michael Giacchino, should be proud.
The unified version for piano and orchestra that is found on the CD is nice, but a Youtube user called ThePandaTooth adapted it for piano alone. He plays it faster than it is played in the movie but is, again, worth listening to.
Sheet music of his arrangement is on-line. You can find a couple of other sheet music transcriptions if you poke around the Internet. I don't know enough about written music to tell you which is best.
Update: Well, aren't I the cultural illiterate! I didn't realize that the title of this piece, "London Calling," was a reference to an album by The Clash. It makes sense, though: Another piece from Star Trek into Darkness is "The Kronos Wartet," an obvious reference to the Klingon Home World Kronos (or Qo'noS), the Klingons' favourite activity (war), and the Kronos Quartet.
If you're not familiar with the Kronos Quartet, their rendition of "Purple Haze" by Jimi Hendrix may come as a pleasant surprise.