Probably the most thrilling moments in a scientist’s life happen if you get a outcome that defies your expectations. Whether or not you’re a theorist that derives a outcome that conflicts with what’s experimentally or observationally identified, or an experimentalist or observer who makes a measurement that provides a opposite outcome to your theoretical predictions, these “Eureka!” moments can go certainly one of 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 outcome from an error.

The latter, sadly, has been the destiny of each experimental anomaly found in particle physics because the 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, akin 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. But it surely’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 at this time 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 supposing there’s solely an electrical cost — and never a elementary magnetic one — that particle goes to have magnetic properties, too. Each time an electrically charged particle strikes, it generates a magnetic area. If that particle both strikes round one other charged particle or spins on its axis, like an electron orbiting a proton, it should develop what we name a magnetic second: the place it behaves like a magnetic dipole.

Quantum mechanically, level particles don’t truly spin on their axis, however reasonably 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 akin 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’d’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 an alternative, 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 elemental forces and interactions — are quantum in nature, too. For instance, an electron experiencing an electromagnetic drive received’t simply appeal to or repel from an interplay with an out of doors photon, however can change arbitrary numbers of particles in keeping with the possibilities you’d calculate in quantum area idea.

After we discuss “g-2,” we’re speaking about all of the contributions from every thing aside from the “pure Dirac” half: every thing related to the electromagnetic area, the weak (and Higgs) area, and the contributions from the robust area. In 1948, Julian Schwinger — co-inventor of quantum area idea — calculated the biggest 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 something about particle physics, that electrons are mild, charged, and secure. At simply 1/1836 the mass of the proton, they’re simple to govern and straightforward to measure. However as a result of the electron is so mild, its charge-to-mass ratio may be very low, which implies the consequences of “g-2” are dominated by the electromagnetic drive. That’s very nicely understood, and so although we’ve measured what “g-2” is for the electron to unimaginable precision — to 13 vital figures — it traces up with what idea predicts spectacularly. In line with Wikipedia (which is right), the electron’s magnetic second is “probably the most precisely verified prediction within the historical past of physics.”

The muon, alternatively, is likely to be unstable, but it surely’s 206 instances as large because the electron. Not solely does this make its magnetic second a lot better, but it surely signifies that different contributions, notably from the robust nuclear drive, are far better for the muon than the electron. Whereas the electron’s magnetic second reveals no mismatch between idea and experiment to raised than 1-part-in-a-trillion, results that may be imperceptible within the electron would present up in muon-containing experiments at in regards to the 1-part-in-a-billion degree.

That’s exactly the impact the Muon g-2 experiment is looking for to measure to unprecedented precision.

**What was identified 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 created from fixed-target experiments — are fired at very excessive speeds right into a storage ring. Lining the ring are a whole bunch 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 velocity of sunshine. That’s the particular velocity referred to as 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 neighborhood 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, impartial, and higher-precision examine. In any experiment, there are three sorts of uncertainties that may contribute:

- statistical uncertainties, the place as you’re taking extra information, the uncertainty goes down,
- systematic uncertainties, the place these are errors that signify 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, need to have their related uncertainties introduced alongside for the trip.

On April 7, 2021, the primary set of knowledge 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 in a position to 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. Total, 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 last two digits. Total, that is 4.2-sigma increased than the Commonplace Mannequin’s predictions.

**Why would this indicate the existence of recent physics?** The Commonplace Mannequin, in some ways, is our most profitable scientific idea 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 need to do on this scenario versus what we are able to do are two various things. Ideally, we’d need to calculate all of the potential quantum area idea contributions — what we name “increased loop-order corrections” — that make a distinction. This would come with from the electromagnetic, weak-and-Higgs, and robust drive contributions. We will calculate these first two, however due to the actual properties of the robust nuclear drive and the odd conduct of its coupling power, we don’t calculate these contributions instantly. As an alternative, we estimate them from cross-section ratios in electron-positron collisions: one thing particle physicists have named “the R-ratio.” There’s at all times the priority, in doing this, that we would endure 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 technique are constant, and maintain coming in considerably under the Brookhaven and Fermilab outcomes. If the mismatch is actual, this tells us there have to be contributions from exterior the Commonplace Mannequin which can be current. It might be improbable, 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 robust drive contributions signify probably the most unsure element of those calculations. In the event you settle for this R-ratio estimate, you get the quoted mismatch between idea and experiment: 4.2-sigma, the place the experimental uncertainties are dominant over the theoretical ones.

Whereas we positively can’t carry out the “loop calculations” for the robust drive the identical method we carry out them for the opposite forces, there’s one other approach that we may doubtlessly leverage: computing the robust drive utilizing an strategy involving a quantum lattice. As a result of the robust drive depends on shade, the quantum area idea underlying it’s referred to as Quantum Chromodynamics: QCD.

The strategy of Lattice QCD, then, represents an impartial solution to calculate the theoretical worth of “g-2” for the muon. Lattice QCD depends on high-performance computing, and has just lately turn out to be a rival to the R-ratio for a way we may doubtlessly compute theoretical estimates for what the Commonplace Mannequin predicts. What El-Khadra highlighted was a current calculation exhibiting 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 identified to be the dominant strong-force contribution to the muon’s magnetic second — discovered a big discrepancy. Because the above graph reveals, the R-ratio technique and the Lattice QCD strategies disagree, they usually disagree at ranges which can be considerably better than the uncertainties between them. The benefit of Lattice QCD is that it’s a purely theory-and-simulation-driven strategy to the issue, reasonably than leveraging experimental inputs to derive a secondary theoretical prediction; the drawback is that the errors are nonetheless fairly giant.

What’s outstanding, compelling, and troubling, nonetheless, is that the most recent 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 most recent Lattice QCD analysis, put it, “the prospect of recent physics is at all times engaging, it’s additionally thrilling to see idea 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 outcome, this discrepancy between two totally different strategies of predicting the Commonplace Mannequin’s anticipated worth — certainly one of which agrees with experiment and certainly one of which doesn’t — must be resolved earlier than any conclusions about “new physics” can responsibly be drawn.

**So, what comes subsequent?** A whole lot of really wonderful 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 grasp 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 would clarify these phenomena may additionally clarify the muon’s anomalous magnetic second; they may possible 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 count on the mixed evaluation of these first three runs — which ought to virtually quadruple the information, and therefore, halve the statistical uncertainties — to be printed. Moreover, Chris Polly introduced that the systematic uncertainties will enhance by virtually 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.