Essentially the most thrilling moments in a scientist’s life happen once you get a consequence that defies your expectations. Whether or not you’re a theorist that derives a consequence that conflicts with what’s experimentally or observationally recognized, or an experimentalist or observer who makes a measurement that provides a opposite consequence to your theoretical predictions, these “Eureka!” moments can go one in all two methods. Both they’re harbingers of a scientific revolution, exposing a crack within the foundations of what we had beforehand thought, or — to the chagrin of many — they merely consequence from an error.
The latter, sadly, has been the destiny of each experimental anomaly found in particle physics for the reason that discovery of the Higgs boson a decade in the past. There’s a significance threshold we’ve developed to forestall us from fooling ourselves: 5-sigma, comparable to solely a 1-in-3.5 million probability that no matter new factor we expect we’ve seen is a fluke. The first outcomes from Fermilab’s Muon g-2 experiment have simply come out, they usually rise to a 4.2-sigma significance: compelling, however not definitive. Nevertheless it’s not time to surrender on the Commonplace Mannequin simply but. Regardless of the suggestion of recent physics, there’s one other clarification. Let’s take a look at the complete suite of what we all know right now to search out out why.
What’s g? Think about you had a tiny, point-like particle, and that particle had an electrical cost to it. Even if there’s solely an electrical cost — and never a basic magnetic one — that particle goes to have magnetic properties, too. At any time when an electrically charged particle strikes, it generates a magnetic subject. If that particle both strikes round one other charged particle or spins on its axis, like an electron orbiting a proton, it’ll develop what we name a magnetic second: the place it behaves like a magnetic dipole.
Quantum mechanically, level particles don’t really spin on their axis, however quite behave like they’ve an intrinsic angular momentum to them: what we name quantum mechanical spin. The primary motivation for this got here in 1925, the place atomic spectra confirmed two totally different, very closely-spaced power states comparable to reverse spins of the electron. This hyperfine splitting was defined 3 years later, when Dirac efficiently wrote down the relativistic quantum mechanical equation describing the electron.
In the event you solely used classical physics, you’ll’ve anticipated that the spin magnetic second of some extent particle would simply equal one-half multiplied by the ratio of its electrical cost to its mass multiplied by its spin angular momentum. However, due to purely quantum results, all of it will get multiplied by a prefactor, which we name “g.” If the Universe had been purely quantum mechanical in nature, g would equal 2, precisely, as predicted by Dirac.
What’s g-2? As you might need guessed, g doesn’t equal 2 precisely, and which means the Universe isn’t purely quantum mechanical. As a substitute, not solely are the particles that exist within the Universe quantum in nature, however the fields that permeate the Universe — those related to every of the basic forces and interactions — are quantum in nature, too. For instance, an electron experiencing an electromagnetic pressure gained’t simply appeal to or repel from an interplay with an outdoor photon, however can trade arbitrary numbers of particles in response to the chances you’d calculate in quantum subject concept.
After we discuss “g-2,” we’re speaking about all of the contributions from all the things aside from the “pure Dirac” half: all the things related to the electromagnetic subject, the weak (and Higgs) subject, and the contributions from the sturdy subject. In 1948, Julian Schwinger — co-inventor of quantum subject concept — calculated the most important contribution to the electron and muon’s “g-2:” the contribution of an exchanged photon between the incoming and outgoing particle. This contribution, which equals the fine-structure fixed divided by 2π, was so essential that Schwinger had it engraved on his tombstone.
Why would we measure it for a muon? If you already know something about particle physics, you already know that electrons are mild, charged, and secure. At simply 1/1836 the mass of the proton, they’re straightforward to control and simple to measure. However as a result of the electron is so mild, its charge-to-mass ratio may be very low, which implies the results of “g-2” are dominated by the electromagnetic pressure. That’s very effectively understood, and so despite the fact that we’ve measured what “g-2” is for the electron to unbelievable precision — to 13 vital figures — it strains up with what concept predicts spectacularly. In line with Wikipedia (which is appropriate), the electron’s magnetic second is “probably the most precisely verified prediction within the historical past of physics.”
The muon, alternatively, may be unstable, but it surely’s 206 occasions as large because the electron. Not solely does this make its magnetic second a lot higher, but it surely implies that different contributions, significantly from the sturdy nuclear pressure, are far higher for the muon than the electron. Whereas the electron’s magnetic second reveals no mismatch between concept and experiment to raised than 1-part-in-a-trillion, results that will be imperceptible within the electron would present up in muon-containing experiments at concerning the 1-part-in-a-billion stage.
That’s exactly the impact the Muon g-2 experiment is in search of to measure to unprecedented precision.
What was recognized earlier than the Fermilab experiment? The g-2 experiment had its origin some 20 years in the past at Brookhaven. A beam of muons — unstable particles produced by decaying pions, which themselves are made out of fixed-target experiments — are fired at very excessive speeds right into a storage ring. Lining the ring are tons of of probes that measure how a lot every muon has precessed, which in flip permits us to deduce the magnetic second and, as soon as all of the evaluation is full, g-2 for the muon.
The storage ring is crammed with electromagnets that bend the muons right into a circle at very excessive, particular speeds, tuned to exactly 99.9416% the pace of sunshine. That’s the particular pace often called the “magic momentum,” the place electrical results don’t contribute to precession however magnetic ones do. Earlier than the experimental equipment was shipped cross-country to Fermilab, it operated at Brookhaven, the place the E821 experiment measured g-2 for the muon to 540 parts-per-billion precision.
The theoretical predictions we would arrived at, in the meantime, differed from Brookhaven’s worth by about ~3 normal deviations (3-sigma). Even with the substantial uncertainties, this mismatch spurred the group on to additional investigation.
How did the newly-released outcomes change that? Though the Fermilab experiment used the identical magnet because the E821 experiment, it represents a novel, unbiased, and higher-precision examine. In any experiment, there are three forms of uncertainties that may contribute:
- statistical uncertainties, the place as you are taking extra information, the uncertainty goes down,
- systematic uncertainties, the place these are errors that symbolize your lack-of-understanding of points inherent to your experiment,
- and enter uncertainties, the place stuff you don’t measure, however assume from prior research, must have their related uncertainties introduced alongside for the journey.
On April 7, 2021, the primary set of information from the Muon g-2 experiment was “unblinded,” after which introduced to the world. This was simply the “Run 1” information from the Muon g-2 experiment, with a minimum of 4 whole runs deliberate, however even with that, they had been capable of measure that “g-2” worth to be 0.00116592040, with an uncertainty within the final two digits of ±43 from statistics, ±16 from systematics, and ±03 from enter uncertainties. General, it agrees with the Brookhaven outcomes, and when the Fermilab and Brookhaven outcomes are mixed, it yields a internet worth of 0.00116592061, with a internet uncertainty of simply ±35 within the ultimate two digits. General, that is 4.2-sigma greater than the Commonplace Mannequin’s predictions.
Why would this suggest the existence of recent physics? The Commonplace Mannequin, in some ways, is our most profitable scientific concept of all-time. In virtually each occasion the place it’s made definitive predictions for what the Universe ought to ship, the Universe has delivered exactly that. There are a couple of exceptions — just like the existence of large neutrinos — however past that, nothing has crossed the “gold normal” threshold of 5-sigma to herald the arrival of recent physics that wasn’t later revealed to be a scientific error. 4.2-sigma is shut, but it surely’s not fairly the place we’d like it to be.
However what we’d wish to do on this scenario versus what we are able to do are two various things. Ideally, we’d wish to calculate all of the doable quantum subject concept contributions — what we name “greater loop-order corrections” — that make a distinction. This would come with from the electromagnetic, weak-and-Higgs, and robust pressure contributions. We will calculate these first two, however due to the actual properties of the sturdy nuclear pressure and the odd conduct of its coupling energy, we don’t calculate these contributions instantly. As a substitute, we estimate them from cross-section ratios in electron-positron collisions: one thing particle physicists have named “the R-ratio.” There may be at all times the priority, in doing this, that we would undergo from what I consider because the “Google translate impact.” In the event you translate from one language to a different after which again once more to the unique, you by no means fairly get again the identical factor you started with.
The theoretical outcomes we get from utilizing this methodology are constant, and preserve coming in considerably beneath the Brookhaven and Fermilab outcomes. If the mismatch is actual, this tells us there have to be contributions from exterior the Commonplace Mannequin which might be current. It will be implausible, compelling proof for brand new physics.
How assured are we of our theoretical calculations? As theorist Aida El-Khadra confirmed when the primary outcomes had been introduced, these sturdy pressure contributions symbolize probably the most unsure part of those calculations. In the event you settle for this R-ratio estimate, you get the quoted mismatch between concept and experiment: 4.2-sigma, the place the experimental uncertainties are dominant over the theoretical ones.
Whereas we positively can not carry out the “loop calculations” for the sturdy pressure the identical approach we carry out them for the opposite forces, there’s one other method that we may doubtlessly leverage: computing the sturdy pressure utilizing an method involving a quantum lattice. As a result of the sturdy pressure depends on shade, the quantum subject concept underlying it’s referred to as Quantum Chromodynamics: QCD.
The strategy of Lattice QCD, then, represents an unbiased solution to calculate the theoretical worth of “g-2” for the muon. Lattice QCD depends on high-performance computing, and has not too long ago develop into a rival to the R-ratio for the way we may doubtlessly compute theoretical estimates for what the Commonplace Mannequin predicts. What El-Khadra highlighted was a latest calculation displaying that sure Lattice QCD contributions don’t clarify the noticed discrepancy.
The elephant within the room: lattice QCD. However one other group — which calculated what’s recognized to be the dominant strong-force contribution to the muon’s magnetic second — discovered a major discrepancy. Because the above graph reveals, the R-ratio methodology and the Lattice QCD strategies disagree, they usually disagree at ranges which might be considerably higher than the uncertainties between them. The benefit of Lattice QCD is that it’s a purely theory-and-simulation-driven method to the issue, quite than leveraging experimental inputs to derive a secondary theoretical prediction; the drawback is that the errors are nonetheless fairly massive.
What’s outstanding, compelling, and troubling, nevertheless, is that the newest Lattice QCD outcomes favor the experimentally measured worth and never the theoretical R-ratio worth. As Zoltan Fodor, chief of the workforce that did the newest Lattice QCD analysis, put it, “the prospect of recent physics is at all times attractive, it’s additionally thrilling to see concept and experiment align. It demonstrates the depth of our understanding and opens up new alternatives for exploration.”
Whereas the Muon g-2 workforce is justifiably celebrating this momentous consequence, this discrepancy between two totally different strategies of predicting the Commonplace Mannequin’s anticipated worth — one in all which agrees with experiment and one in all which doesn’t — must be resolved earlier than any conclusions about “new physics” can responsibly be drawn.
So, what comes subsequent? Numerous actually glorious science, that’s what. On the theoretical entrance, not solely will the R-ratio and Lattice QCD groups proceed to refine and enhance their calculational outcomes, however they’ll try to know the origin of the mismatch between these two approaches. Different mismatches between the Commonplace Mannequin and experiments — though none of them have crossed the “gold normal” threshold for significance simply but — presently exist, and a few situations that might clarify these phenomena may additionally clarify the muon’s anomalous magnetic second; they are going to probably be explored in-depth.
However probably the most thrilling factor within the pipeline is healthier, extra improved information from the Muon g-2 collaboration. Runs 1, 2, and three are already full (Run 4 is in progress), and in a few 12 months we are able to anticipate the mixed evaluation of these first three runs — which ought to nearly quadruple the info, and therefore, halve the statistical uncertainties — to be printed. Moreover, Chris Polly introduced that the systematic uncertainties will enhance by nearly 50%. If the R-ratio outcomes maintain, we’ll have an opportunity to hit 5-sigma significance simply subsequent 12 months.
The Commonplace Mannequin is teetering, however nonetheless holds for now. The experimental outcomes are phenomenal, however till we perceive the theoretical predictions with out this current ambiguity, probably the most scientifically accountable course is to stay skeptical.