Hotly anticipated results from the first run of the muon g-2 experiment at Fermilab were announced today, increasing the tension between measurements and theoretical calculations. The last time this ultra-precise measurement was performed, in a sequence of results at Brookhaven National Laboratory in the late 1990s and early 2000s, it disagreed with the Standard Model (SM) by 3.7σ. After almost eight years of work rebuilding the Brookhaven experiment at Fermilab and analysing its first data, the muon’s anomalous magnetic moment has been measured to be 116 592 040(54)×10^{-11}. The result is in agreement with the Brookhaven measurement and is 3.3σ greater than the SM prediction: 116 591 810(43)×10^{-11}. Combined with the Brookhaven result, the world-average value for the anomalous magnetic moment of the muon is 116 592 061(41)×10^{-11}, representing a 4.2σ departure from the SM.

“Today is an extraordinary day, long awaited not only by us but by the whole international physics community,” says Graziano Venanzoni of the INFN, who is co-spokesperson of the Fermilab muon g-2 collaboration. “A large amount of credit goes to our young researchers who, with their talent, ideas and enthusiasm, have allowed us to achieve this incredible result.”

Today is an extraordinary day, long awaited not only by us but by the whole international physics community

Graziano Venanzoni

The Fermilab result was unblinded during a Zoom meeting on 25 February in the presence of around 200 collaborators from around the world. “We were all very excited to finally know our result and the meeting was very emotional,” says Venanzoni. The analysis took almost three years from data taking to the release of the result and the collaboration decided to unblind only when all the steps of the analysis were completed and there were no outstanding questions. Venanzoni adds that no further analysis was completed after the unblinding and the results are unchanged.

The previous Brookhaven measurement left physicists pondering whether the presence of unknown particles in loops could be affecting the muon’s behaviour. It was clear that further measurements were needed, but it turned out to be much cheaper to move the apparatus to Fermilab than to build a new, more precise experiment at Brookhaven. So in the summer of 2013, the experiment’s 14-m diameter, 1.45 T superconducting magnet was transported from Long Island to the suburbs of Chicago. The Fermilab team reassembled the magnet and spent a year “shimming” its field, making it three times more uniform than the one it created at Brookhaven. Along with a new beamline to deliver a purer muon beam, Fermilab’s muon g-2 reincarnation required entirely new instrumentation, along with new detectors and a control room.

When a muon travels through the strong external magnetic field of a storage ring, the direction of its magnetic moment precesses at a rate that depends on its strength g. The Dirac equation predicts that all fermions have a g-factor equal to two. But higher order loops add an “anomalous” moment, a_{μ} = (g-2)/2, which can be calculated extremely precisely. At Fermilab, muons with an energy of about 3.1 GeV are vertically focused in the storage ring via quadrupoles, and their precession frequency is determined from decays to electrons using 24 electromagnetic calorimeters located along the ring’s inner circumference. The intense polarised muon beam suppresses the pion contamination that challenged the Brookhaven measurement, while new calibration systems and simulations allow better control of systematic uncertainties.

It is so gratifying to finally be resolving this mystery

Chris Polly

The Fermilab muon g-2 collaboration took its first dataset in 2018, with over eight billion muon decays resulting in an overall uncertainty approximately 15% better than Brookhaven’s. Data analysis on the second and third runs is already under way, while a fourth run is ongoing and a fifth is planned. The collaboration is targeting a final precision of around 0.14 ppm – four times greater than the previous measurement.

“After the 20 years that have passed since the Brookhaven experiment ended, it is so gratifying to finally be resolving this mystery,” said Fermilab’s Chris Polly, a co-spokesperson for the current experiment and a graduate student on the Brookhaven experiment. “So far we have analysed less than 6% of the data that the experiment will eventually collect. Although these first results are telling us that there is an intriguing difference with the Standard Model, we will learn much more in the next couple of years.”

**Theory baseline
**Developments in the theory community are equally vital. The Fermilab muon g-2 collaboration takes as its theory baseline the value for a

_{μ}obtained last year by the Muon g-2 Theory Initiative. Uncertainties in the calculation are dominated by hadronic contributions, in particular a term called the hadronic vacuum polarization (HVP). The Theory Initiative incorporates the HVP value obtained by well-established “dispersive methods”, which combine fundamental properties of quantum field theory with experimental measurements of low-energy hadronic processes. An alternative approach gaining traction is to calculate the HVP contribution using lattice QCD. In a paper published in

*Nature*today, one group reports lattice calculations of HVP which, if included in the theory result, would significantly reduce the discrepancy between the experimental and theoretical values for a

_{μ}. The result is in 2σ tension with the value obtained from the dispersive approach, and is currently dominated by systematic uncertainties stemming from approximations used in the lattice calculations, say Muon g-2 Theory Initiative members.

“This being the first lattice result at sub-percent precision, it is premature to draw firm conclusions from this comparison,” reads a statement from the Muon g-2 Theory Initiative steering committee. “Indeed, given the complexity of the computations, independent results from different lattice groups with commensurate uncertainties are needed to test and check the lattice calculations against each other. Being entirely based on Standard Model theory, once the lattice results are well tested and precise enough, they will play an important role in understanding how new physics enters into the discrepancy.”