To see a world in a grain of sandAnd a heaven in a wild flower,Hold infinity in the palm of your handAnd eternity in an hour
It’s hard to keep these words, written by the poet William Blake in ‘Auguries of Innocence’, away when we are looking for clues about the fundamental nature of reality in the properties of subatomic particles.
In an astonishing feat of metrology, physicists recently reported measuring the electron’s magnetic moment with a precision of 0.13 parts per trillion (ppt). The resulting measurement is 2.2 times more accurate than the previous best, recorded 14 years ago. More importantly, it’s the most precise test so far of a theory that has both comforted and baffled physicists – the Standard Model of particle physics – and therein lies the rub.
What is the Standard Model?
The Standard Model (SM) is the theory that describes the properties of all subatomic particles, classifies them into different groups, and determines how they’re affected by three of the four fundamental forces of nature: strong-nuclear force, weak-nuclear force, and the electromagnetic force (it can’t explain gravity).
In the 1960s, physicists used SM to predict the existence of a particle called the Higgs boson; it was finally discovered in 2012. Similarly, the SM has allowed physicists to successfully predict the existence and properties of dozens of particles and is considered to be one of the most successful theories in the history of physics.
However, it still can’t explain why the universe has more matter than antimatter, what dark matter is, or what dark energy is. In one strategy to crack these still-open questions, physicists have tested different SM predictions to higher and higher limits and checked whether the predictions agree with observations.
So far, they have all agreed. This is good for the SM and not good for those looking for answers beyond the Standard Model.
How does the electron’s magnetic moment matter?
The SM’s most precise prediction is of the electron’s magnetic moment. Physically, the magnetic moment describes how willing an electron is to align itself in the direction of a magnetic field. Mathematically, it’s equal to –µ/µB. Here, µ (pronounced mew) is the electron’s magnetic moment (measured in amperes sq.-metres) and µB is a physical constant called the Bohr magneton. Together, –µ/µB is a dimensionless number.
In the new study, researchers in the U.S. suspended a single electron in a magnetic field at an ultra-cold temperature inside a vacuum chamber, and measured currents induced in nearby electrodes by the electron’s movement. They measured the value of –µ/µB to be 1.00115965218059, within 0.13 ppt.
They achieved such a precise result by closely controlling the electric fields that hold the electron in place, stabilising the magnetic field, and finely adjusting the physical properties of the hardware, thus subtracting the sources of uncertainty that can affect the data. To quote the physicists writing in their preprint paper,“The most precise prediction of the SM agrees with the most precise determination of a property of an elementary particle” to 1 ppt.
Is the result good for the SM?
Perhaps: the result is also affected by two open questions.
First, the electron and the muon are very similar particles, but the muon is around 207-times heavier. Multiple measurements until 2021 have found that the muon’s magnetic moment disagrees with the SM prediction by about 0.00000000251. If this is the handiwork of beyond-SM forces acting on the particle, their effects should be visible on the electron’s magnetic moment as well.
But because the electron is lighter, the effects will be 40,000-times weaker. By achieving such a highly precise result, the new result suggests that the physicists couldn’t find these signs.
Second, a series of mathematical calculations connect the data that physicists record in an experiment and the value of the electron’s magnetic moment. One of these calculations involves the fine structure constant (α) – a universal constant that specifies the strength with which electron couples to the electromagnetic field. (If it couples more strongly, the field will exert a greater force on the electron.)
Two studies published in 2018 and 2020 measured the value of α – and reached two distinct answers differing by 0.00000016. They should have reached the same answer since α is a constant. If this discrepancy is resolved, the physicists’ measurement can test the SM prediction to 10-times more precision.
Will we ever find evidence of beyond-SM forces?
It’s a billion-dollar question. Physicists will test as many of the SM’s predictions as they can, to the extent they can, to look for a crack in its façade. They already have some leads: the SM says neutrinos should be massless, but they aren’t; and of course the muon anomaly.
Physicists have also built detectors to look for different kinds of hypothetical dark-matter particles, are combing through astronomical data to make sense of dark energy, and are scrutinising each other’s calculations. Many of them are also debating whether they need an even larger supercollider to succeed the Large Hadron Collider.
The group that measured the electron’s magnetic moment itself has plans to upgrade its setup and repeat the measurement with the electron’s anti-particle, the positron.
All together, the community hopes that at least one of these efforts, guided by the principles they uncover in their theoretical studies, will reveal a glimpse of a world beyond the Standard Model.
