New theoretical calculation solves the ‘muon g-2’ puzzle

As a scientist, the most exciting moments in your professional life arise when you work hard to get a result, and — no matter how hard you try to understand it — it simply doesn’t match up with your expectations. For theorists, that moment comes when you derive a result that conflicts with what’s experimentally and observationally known to be true. For experimentalists, that moment arrives when you make a measurement that defies a theorist’s predictions. But those moments can go one of two ways: either they can be harbingers of a scientific revolution, exposing a crack in the foundations of science, or they can simply be the result of a previously undiscovered error, on either the theoretical or experimental ends.

Perhaps the greatest quest in particle physics, for perhaps half a century now, has been to find a discrepancy between theory and experiment when it comes to the Standard Model. One fascinating place to look is at the magnetic moment of the muon: a heavy, unstable relative of the electron. A Fermilab experiment known as “muon g-2″ has revealed a discrepancy between theory and experiment at greater than the 4-sigma level: approaching the gold standard for discovery. But is this evidence for new physics?

According to a new theoretical calculation, the answer is no: it’s a flaw in the technique used by the majority of the theoretical community. Using new lattice QCD techniques, theory and experiment align, suggesting that the puzzle has finally been solved. Here’s how.

What is g, the magnetic moment of the muon?

Imagine you had a tiny, point-like particle, and that particle has an intrinsic electric charge to it. Despite the fact that there’s only an electric charge — and not a fundamental magnetic one — that particle is going to have magnetic properties, too. Whenever an electrically charged particle moves, it generates a magnetic field. If that particle either moves around another charged particle or spins on its axis, like an electron orbiting a proton or the Earth rotating as it orbits the Sun, it will develop what we call a magnetic moment: where it behaves like a magnetic dipole. This is a behavior that’s been familiar to physicists since the 19th century: back from the days of classical electromagnetism.

Now, we don’t have a classical universe when it comes to fundamental particles; we have a quantum one. In quantum mechanics, point particles don’t actually spin on their axis, but rather behave like they have an intrinsic angular momentum to them: what we call quantum mechanical spin. The first motivation for this came in 1925, where atomic spectra showed two different, very closely-spaced energy states corresponding to opposite spins of the electron. This hyperfine splitting was explained 3 years later, when Dirac successfully wrote down the relativistic quantum mechanical equation describing the electron.

If you only used classical physics, you would’ve expected that the spin magnetic moment of a point particle would just equal one-half multiplied by the ratio of its electric charge to its mass multiplied by its spin angular momentum. But, because of purely quantum effects, it all gets multiplied by a prefactor, which we call “g.” If the Universe were purely quantum mechanical in nature, g would equal 2, exactly, as predicted by Dirac.

If g is supposed to be 2, then why are we performing a “g-2″ experiment?

As you might have guessed, g doesn’t equal 2 exactly, and that means the Universe isn’t purely describable by old-school quantum mechanics. In quantum mechanics, particles are quantum, but fields are classical. The advance of quantum field theory overruled and superseded that picture: not only are the particles that exist in the Universe quantum in nature, but the fields that permeate the Universe — the ones associated with each of the fundamental forces and interactions — are quantum in nature, too. An electron…

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