The experiment, based at the Fermi National Accelerator Laboratory (Fermilab) in Batavia, Illinois, searches for signs of new phenomena in physics by studying the behavior of sub-atomic particles called muons.
There are building blocks of our world that are even smaller than the atom. Some of these sub-atomic particles are made up of even smaller constituents, while others can't be broken down into anything else (fundamental particles).
The muon is one of these fundamental particles; it's similar to the electron, but more than 200 times heavier.
The Muon g-2 experiment involves sending the particles around a 14-meter ring and then applying a magnetic field. Under the current laws of physics, encoded in the Standard Model, this should make the muons wobble at a certain rate.
Instead, the scientists found that muons wobbled at a faster rate than expected.
Theoretical physicists believe that it might also be associated with an as-yet-undiscovered sub-atomic particle. There is more than one concept for what this hypothetical particle might be. One is called a leptoquark, another is the Z' boson (Z-prime boson).
Last month, physicists working at the LHCb experiment at the Large Hadron Collider described results that could point to a new particle and force.
Dr Mitesh Patel, from Imperial College London, who was involved with that project, said: "The race is really on now to try and get one of these experiments to really get the proof that this really is something new. That will take more data and more measurements and hopefully show evidence that these effects are real."
Prof Allanach has given the possible fifth force various names in his theoretical models. Among them are the "flavor force", the "third family hyper force" and - most prosaic of all - "B minus L2".
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