A big part of being an experimentalist is looking for things that shouldn’t be there. If every test you do comes out exactly as you planned, you haven’t learned anything. Currently we have a rather robust theory that covers particle physics. It is so robust in fact, that it is dubbed The Standard Model. But there are some problems with it. Mainly that it doesn’t include gravity. There is also hope that the strong nuclear force (QCD) and the electroweak force can be framed in a way that unifies them as the electroweak force is a unification of electromagnetism and the weak nuclear force. But we don’t know how to do that yet.
One way for researchers to find new ways is to find new things that happen in the universe that are unexplained by our current theories. One such unexplained happening is the anomalous magnetic moment of the muon.