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Particle drag race leads to most precise estimate yet of the proton’s mass

Here’s an odd little story. Two physicists confined two ions in an electromagnetic trap and made them turn laps for weeks on end to compare their masses with exquisite precision. From that measurement and one borrowed from another team, they then derived the most precise estimate yet of the proton’s mass: 1.007276466574 atomic mass units (amu), plus or minus 10 trillionths of an amu. That small number may be a big deal, because knowing the proton’s mass precisely can help scientists search for new forces.

“It’s quite a beautiful technique,” says Matthew Redshaw, a nuclear physicist at Central Michigan University who was not involved in the work. Jeroen Koelemeij, an atomic and molecular physicist at the Free University of Amsterdam, agrees. “I credit them just for coming up with the idea.”

To determine the masses of light atomic nuclei such as the proton, scientists rely on physics familiar to high school students. Shoot a charged particle like a proton perpendicularly through a magnetic field, and the field will push it sideways so it circles at a frequency that reveals the particle’s mass. In practice, to improve the precision of the measurement, physicists compare the frequencies of two different types of particles to measure the ratio of their masses.

For example, in 2020, Edmund Myers and David Fink, atomic physicists at Florida State University, measured the ratio of the masses of a deuteron, an atomic nucleus consisting of a proton and a neutron, and an ionized molecule of hydrogen—two chemically bound protons that share a single electron. The two particles have identical charges and nearly equal masses, so they orbit at nearly the same frequency, increasing the precision of the measurement.

To make the deuteron and hydrogen ion orbit under the same conditions, Myers and Fink kept the two in the same electromagnetic trap for weeks at a time. They would park one in a large orbit 4 millimeters wide while they measured the other twirling in an orbit 40 micrometers across in the trap’s center, swapping them every 10 minutes. However, even that technique was not enough to ensure the measurements of the two particles were exactly comparable. “In those 10 minutes, the magnetic field can change,” Myers says.

Myers and Fink have now eliminated that problem. Resurrecting a technique developed 20 years ago at the Massachusetts Institute of Technology, they twirled the deuteron and the hydrogen ion in the center of their trap simultaneously, so they moved through the exact same magnetic field. The researchers compared the ions’ frequencies with four times greater precision than before. Using some theoretical results enabled them to determine the deuteron to proton mass ratio to 4.5 parts per trillion, they report in a paper in press at Physical Review Letters.

“Ed doesn’t like to blow his own trumpet but this is one of the most precise mass-ratio measurements to date,” Redshaw says.

Finally, to estimate the proton’s mass, Myers and Fink combined their ratio with an extremely precise measurement of the deuteron mass published last year by a collaboration led by physicists at the Max Planck Institute for Nuclear Physics. (That team used a trap to compare the orbital frequencies of a deuteron and a carbon-12 ion, and by definition a carbon-12 atom has a mass of exactly 12 amu.) The new proton mass estimate has one-fifth of the uncertainty of the official average value listed by the International Science Council’s Committee on Data (CODATA) and one-third of the Max Planck group’s world leading measurement. All three results agree.

So, is it time to pencil in a new value for the proton mass? Perhaps not yet, Myers says. He and Fink generated the trapped hydrogen ion by using an electron beam to knock an electron out of a hydrogen molecule. That violent process leaves the ion vibrating and rotating with internal energy. As Albert Einstein’s theory of relativity states, that energy is equivalent to mass—and slightly boosts the ion’s measured mass, an effect for which Myers and Fink had to correct.

According to quantum mechanics, the amount of vibrational or rotational energy in the ion comes in discrete steps. The experimenter could watch an ion’s mass decrease as it radiated away vibrational energy one step at a time. But to estimate how much rotational energy it had at each step, Myers and Fink relied on inferences based on theory, introducing some uncertainty.

Even if the team doesn’t have those assignments exactly right, the data suggest the uncertainty in its estimate of the proton mass likely isn’t bigger than about 16 parts per trillion, Redshaw says, leaving it the most precise value yet. Koelemeij says his team is using a laser to create and trap hydrogen ions in known vibrational and rotational states. That technique might be combined with Myers’s and Fink’s to further reduce the uncertainty, he says.

Ultraprecise measurements of the proton and deuteron masses can be used to predict the quantum states of a molecule made of a deuteron and a hydrogen atom, which can be probed by lasers. Any deviations from the predictions would be signs of new physical phenomena, such as an additional force of nature. Although unlikely, such a discovery would send all of physics into a whirl.

Source: Science Mag