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Look, there is a crack in the Standard Model! April 7, 2021

Posted by apetrov in Uncategorized.
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This post is about the result of the Muon g-2 experiment announced today at Fermilab. It has an admittedly bad title: the Standard Model has not cracked in any way, it is still a correct theory that decently describes interactions of known elementary particles at the energies we checked. Yet, maybe we finally found an observable that is not completely described by the Standard Model. Its theoretically computed value needs an additional component to agree with the newly reported experimental value and this component might well be New Physics! What is this observable?

This observable is the value of the anomalous magnetic moment of the muon. The muon, an elementary particle (a lepton), is a close cousin of an electron. It has very similar properties to the electron, but is about 200 times heavier and is unstable — it only lives for about two microseconds. We don’t yet know why Nature chose to create two similar copies of an electron: muon and tau-lepton. But we can study their properties to find out.

Just like an electron, the muon has spin, which makes it susceptible to the effects of the magnetic field, which is characterized by its magnetic moment. The magnetic moment tells us how the muon reacts to its presence: think of the compass needle as a classical analogy. Over a century ago, brilliant physicist Paul Dirac predicted the value of an electron’s magnetic moment, which is directly applicable to muon as well. This prediction involved a parameter, which he called g, from the gyromagnetic ratio or a g-factor. Dirac’s prediction was that, for an electron (and a muon), it is supposed to be exactly g=2. This was one of the predictions that allowed experimentalists to test the validity of Dirac’s theory which eventually led to its triumph.

With further development of quantum field theories, it was realized that g is not exactly two. The effects of virtual particles lead to the effect that the photon of the magnetic field probing the muon could instead hit those virtual particles instead, potentially changing the value of the g-factor. Now, dealing with virtual particles could be tricky in theoretical computations, as their effects lead to unphysical infinities that need to be absorbed in the definitions of muon’s mass, charge, and the wave-function. But the leading effect of such particles — assuming only the Standard Model particles — turns out to be finite! Julian Schwinger showed that in his 1948 paper. This result was so influential at the time that is literally engraved on his tombstone! This paved the way to compute the quantum radiative corrections to muon’s magnetic moment. Since the effect of such radiative corrections is to change the magnetic moment, they lead to the deviation to the Dirac’s theory prediction and lead to the non-zero value of a = (g-2)/2, which is conventionally referred to as the anomalous magnetic moment. This is precisely what Muon g-2 collaboration measured very precisely.

Why is it interesting? The thing is that among the known virtual particles there could also be new, unknown particles. If those particles interact with the photons, they could also affect the numerical value of the anomalous magnetic moment. So the idea is simple: compute it with as much precision as possible and then compare it to the measurement that is done with the best precision possible. This is precisely what was done.

Easily said but not so easily done. Precise predictions of the anomalous magnetic moment involved computations of thousands of Feynman diagrams and evaluation of contributions that can not be computed by expanding in some small quantity (aka non-perturbative effects). There are many theoretical methods used to compute those, including numerical computations in lattice QCD. But there is now an agreement among the theorists on the anomalous magnetic moment of the muon: a = 0.00116591810(43) (see here for a paper). This number is known with astonishing precision, which is indicated by the bracketed numbers.

The experimental analysis is incredibly hard. Since muons decay, the measurement of their properties is not trivial. Muons are produced in the decays of other particles, called pions, that are created at Fermilab by smashing accelerated protons into targets. Once created, they are directed into a storage ring where they decay in a magnetic field giving out their spin information. The storage ring contains about 10,000 muons at the time going around the ring. To make the measurement, it is important to know the magnetic field in which those muons are moving with incredible precision. There is also an electric field that makes the muons going around the ring, whose effect is carefully removed by choosing how fast the muons fly. If all those (and other) effects are not accounted for, they would affect the result of the measurement! Their combined effect is usually referred to as systematic uncertainties. Most of the work done by the Muon g-2 collaboration at Fermilab was to reduce such effects, which eventually led to the acceptable level of those systematic uncertainties.

And here is the result (drum roll): the anomalous magnetic moment measured by the Muon g-2 collaboration is a=0.00116592061(41).

Ok, what does it all mean? First of all, the result is seemingly only ever so slightly different from the theoretical prediction. But it is not. What is more interesting is that if one combines this new result with the old result from the Brookhaven National Lab, one gets a very significant difference between the theoretical predictions and a combined result of two measurements: it is about 4.2 sigma. Sigmas measure the statistical significance of the result, 4.2 sigma means that the chance that the theoretical and experimental results agree — which is possible due to statistical fluctuations — is about 1 out 40,000! This is incredible!

The result might mean that there are particles that are not described by the Standard Model and the New Physics could be just around the corner! Come back here for more discoveries!