Not a teacher.
In my opinion the right answer is absence. I`ll support my words. Absence means that something is not present and it is the state for a while at least. The object`s present location cease to be known before the moment of speaking. Disappearance however denotes the act of becoming absent i.e. at or around the moment of speaking. In the sentence it is clearly marked that the location of the earrings is unknown long before the moment of speaking. This leads us to absence, i.e. the state of being gone, rather than disappearance, i.e. the act of becoming gone.
Student or Learner