Imagine waking up one morning to find that your meter stick had shrunk, overnight, by exactly four centimeters. That difference sounds small, yet it is still dramatic enough to thoroughly muck up basic calculations of motion and height. The shock of finding some basic property — one measured tens of thousands of times — suddenly shift dramatically would be upsetting to those who rely on the meter stick every day.
This hypothetical scenario is analogous to a physics whodunnit? currently playing out with the proton, the positively charged subatomic particle that, with neutrons and electrons, forms the basis of all the matter on the periodic table. 2020 will mark one hundred years since the proton was definitively discovered and named. In that span, the proton’s fundamental properties, like its mass and radius, have been confirmed experimentally thousands of times, perhaps more. Indeed, by 2010, the effective radius of the proton had been experimentally confirmed to be 0.8768 femtometers — a femtometer being one quadrillionth of one meter, or 10-15 meters.
So it was something of a shock when experimental physicists starting playing with protons in odd configurations and obtained a result for the proton's radius that deviated quite a bit from the widely accepted value. These peculiar results were observed by binding the proton with an unusual particle known as the muon.
Muve over, electrons
As you likely recall from high school science class, atoms are comprised of electrons (which are negatively charged), neutrons (neutral), and protons (positively charged). Electrons are electromagnetically bound to the atom by the presence of the proton(s), to which they eagerly adhere like fridge magnets. But electrons are not the only type of negatively charged leptons, the name for the class of singular particles that hover outside of atomic nuclei (rather than being bound within, à la protons and neutrons). There is a rarely seen, unstable lepton called a muon, with a mass two hundred times that of the electron, that has a negative charge just the same as the electron. Electrons and muons are the same breed (both leptons), but with masses two orders of magnitude apart; think of them like a Chihuahua and a Great Dane -- same species yet of variant sizes.
Being the same species, a muon can bind to a proton in a manner akin to an electron. The particles don't mind; if the proton is the fridge, the muon's just a bigger fridge magnet. Scientists call this substance “muonic hydrogen,” in that it’s a hydrogen atom, more or less, yet with a muon orbiting the nucleus instead of an electron.
The presence of the muon endows muonic hydrogen with some strange properties that make it a good candidate for studying fundaments of particle physics. “A muonic hydrogen atom is smaller by the ratio of the muon mass and the electron mass,” Dr. Michael Peskin, a professor of theoretical physics at the Stanford Linear Accelerator Center, told Salon by email. Peskin explained that this means that the wavefunction — the probability that the particle exists at any given point — is much smaller. The chihuahua-Great Dane analogy works here too: just as a tiny chihuahua (our metaphorical electron) is harder to spot as it excitedly rages about the room, the large Great Dane (our muon) is hard to miss. Making small things slightly more massive and therefore easier to track is a boon to studying this.
It was while experimenting with muonic hydrogen that physicists encountered a profoundly weird measurement for the proton's radius. Specifically, their result came up short: 0.83 femtometers, about 4 percent off of the aforementioned value.
When this peculiarity was first reported on in 2010, scientists were befuddled. "The [e]xperiment presents a puzzle with no obvious candidate for an explanation," Peter Mohr, a member of the international Committee on Data for Science and Technology, told a New Scientist reporter in 2010, after a team at the Max Planck Institute of Quantum Optics in Germany published the results of their measurements of the proton’s radius in experiments with muonic hydrogen. Both scientists to whom I spoke in 2018 had no definitive answer, only suggestions as to what may be happening.
After the Max Planck Institute's paper came out, theorists around the world began speculating as to what could be causing the discrepancy for a widely accepted value. The muon was immediately suspect. Could it be adding some new property to the muonic hydrogen system that researchers couldn’t account for? Indeed, beyond different masses, muons have other properties that differentiate them from their cousins the electrons. For one, muons are, unlike electrons, short-lived; “muons live only for 2 microseconds before they decay,” said Dr. Peskin. “This makes measuring their fundamental properties a bit harder, as they tend to die in a shower of electrons and neutrinos pretty quickly... In that short time, they have to be created, bind to a proton, and form a stable orbit,” he added.
Dr. Bruce Schumm, a physicist at the Santa Cruz Institute for Particle Physics and the author of a popular book on particle physics, also believed the oddity might have to do with the muon's tricks. “This is a different system than has been used before,” Schumm told Salon by email. “That leads to the possibility of mistakes in experimental technique, but also the possibility of new physical effects, since the coupling under study here is between a muon and a proton rather than, as in other studies, an electron and a proton.” Schumm was excited by the possibility that the results could hint at violations in “lepton universality” — a "difference in the behavior of electrons, muons and tau leptons other than that due to their differing masses,” as Schumm described it. “This is something we test whenever and wherever we can,” he said.
If the discrepancy in the proton widths turns out to be real — rather than an experimental error (which some suspect) — there are “many possibilities for what could produce such an effect,” Schumm added. Besides revealing violations in lepton universality, other possibilities abound.
“One interesting question that's raised in my mind is whether the effect in muonic atoms can be related to the effect in the magnetic strength of the muon,” Schumm said. Like anything with electric charge, the muon — like the electron — commands its own little magnetic field. Because it is so short-lived, the muon's magnetic strength is not well-measured; a study at Fermilab, currently under construction, is designed to find it more precisely.
Schumm explained that that the physical model that involves the muon's magnetic strength could involve supersymmetry, the idea that there are parallel (and undiscovered) fundamental particles that mirror the ones that we know already, and which may be involved in the muon's decay or existence; or extra dimensions, a theory that string theory fans might be familiar with that suggests that there are small, non-spatial dimensions beyond the ones we can move through that very small things like particles can wiggle in and out of.
New measurements in 2017 only heightened the mystery. An international group of physicists published a study in Science in 2017 sizing up regular hydrogen atoms (no muons here) using spectroscopy — in other words, stimulating the hydrogen and observing the wavelength of the photons they emit, which hint at the physical situation of the atom itself. “[We] obtained the size of the proton using very accurate spectroscopic measurements of regular hydrogen,” the scientists wrote in the abstract. “Unexpectedly, this value was inconsistent with the average value of previous measurements of the same type. Also unexpectedly, it was consistent with the size extracted from the muonic hydrogen experiments.”
Similar values don’t imply causation, of course, meaning the muon may yet lead us to new physics. Yet there are few such basic mysteries in modern physics that only get stranger as the results continue to stream in.
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