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  • richardmitnick 2:13 pm on October 20, 2020 Permalink | Reply
    Tags: , , , Muon g-2, ,   

    From Symmetry: “The many paths of muon math” 

    Symmetry Mag
    From Symmetry<

    Daniel Garisto

    Illustration by Sandbox Studio, Chicago with Ariel Davis.

    Here’s how physicists calculate g-2, the value that will determine whether the muon is giving us a sign of new physics.

    Like racecars on a track, thousands of particles called muons zip around an experiment’s giant 50-foot circular magnet at 99.9% of the speed of light. After making a few hundred laps in less than a millisecond, the muons decay and are soon replaced by another bunch.

    FNAL Muon g-2 studio.

    The goal of the experiment, Fermilab Muon g-2, is to better understand the properties of muons, which are essentially heavier versions of electrons, and use them to probe the limitations of the Standard Model of particle physics. Specifically, physicists want to know about the muons’ “magnetic moment”—that is, how much do they rotate on their axes in a powerful magnetic field— as they race around the magnet?

    In 2001, an experiment at the US Department of Energy’s Brookhaven National Lab found that the muons turned more than theory predicted.

    Brookhaven Muon g-2 ring.

    FNAL G-2 magnet from Brookhaven Lab finds a new home in the FNAL Muon G-2 experiment.

    The result surprised the physics community: If there really were a discrepancy, it could be a hint of new physics, like some as-yet-unknown particle influencing the muon. Two decades later, physicists hope to resolve the matter. Fermilab Muon g-2 aims to quadruple the precision of the 2001 finding and determine whether experiment really disagrees with theory.

    There’s another side to the search though—one that’s carried out not with particle accelerators and giant magnets, but with equations on blackboards and computer simulations. Since 2016, another group of physicists has been trying to update the theoretical prediction of the muon’s magnetic moment by combining the efforts of several groups.

    In June, the Muon g-2 Theory Initiative, which comprises 132 physicists across 82 institutions, published its first prediction: They calculated the muon’s anomalous magnetic moment, or αµ, to be 116,591,810×10-11. The value differs subtly, but significantly from the 2001 experiment, which found αµ to be 116,592,089×10-11. (That’s a difference of 279 parts in a million, for those keeping score at home.)

    “This is the first time that the entire community has come together and reached a consensus on the Standard Model prediction of this quantity,” says Aida X. El-Khadra, a physicist at the University of Illinois Urbana-Champaign and cofounder of the Theory Initiative. Previously, individual groups produced their own predictions of αµ, which differed slightly from one another.

    By combining their efforts, physicists in the Theory Initiative hope that they’ll be able to come up with an ultra-precise prediction to complement the forthcoming result from the Fermilab Muon g-2 experiment. Both the experiment and the theory initiative receive support from DOE’s Office of Science.

    But just how do physicists predict something like the muon’s magnetic moment, and why does it take 132 of them?

    The path to g-2

    The first calculations of particle magnetic moments came in the 1920s, when physicists were just beginning to develop relativistic quantum mechanics. British theoretical physicist Paul Dirac, building on the work of Llewellyn Thomas and others, found the ultimate equation describing the electron and its spin—then conceived of as the electron’s internal rotation—and its magnetic moment. Dirac predicted this number, called “g,” to be exactly 2.

    But atomic spectroscopy experiments soon found that g differed from that prediction by about 0.1%—a so-called “anomalous” magnetic moment, αe. In 1947, Julian Schwinger developed a theoretical explanation: The electron could emit and then reabsorb a virtual photon, which slightly changed its interaction with a magnetic field.

    “Every way that something can happen in nature will happen,” says Tom Blum, a theoretical physicist at the University of Connecticut. “If a particle starts from here and gets to there, it can take all possible paths to get from there to there. And what quantum field theory tells us is how to weight those paths.”

    The emission and absorption of a single virtual photon is just the most straightforward of these possible particle paths. Since Schwinger, physicists have been working to calculate increasingly unlikely possible paths that a particle can take. Ironically, the way they think about these paths is with a tool of Schwinger’s rival, Richard Feynman. To illustrate the paths and calculate their probabilities, Feynman developed his eponymously named diagrams.

    Here, the Feynman diagram represents a muon (the Greek letter mu) moving left to right in a magnetic field (the squiggly line, which also denotes a photon).


    The Feynman diagram for Schwinger’s path is slightly more complicated—this time there’s a squiggly blue line, the virtual photon being emitted and absorbed by the muon. This contributes approximately 0.00116 to αµ. This is the vast majority of muon’s anomalous magnetic moment.


    To make the task manageable, the Theory Initiative segmented the task of calculating the muon’s magnetic moment into each component. To get down to a precision of about 100 parts in a billion, physicists have had to calculate a lot more than just a single virtual photon.

    “Contributions to the anomalous magnetic moment come from the three different interactions— the strong interaction, the weak interaction and quantum electrodynamics all contribute,” Blum says.

    There was at one point some thought that gravity would have an impact, but further investigation proved its role was too small.

    Quantum electrodynamics, or QED, covers all the possible ways a photon can interact with a muon. To get better precision, physicists can account for more virtual photons. Each additional virtual photon has about 1/137th the chance of being produced and reabsorbed, so a Feynman diagram with two virtual photons contributes about 1 / 137 * 137 to αµ, three virtual photons contribute 1 / 137 * 137 * 137, and so on. Physicists have even gone all the way to five virtual photons.

    With five virtual photons, there are more than 10,000 possible paths, so there are a corresponding number of Feynman diagrams to calculate. Possibilities abound because virtual photons can split into a virtual electron and a virtual positron (the antimatter counterpart to an electron). This virtual pair can then annihilate back into a virtual photon. Describing these complex paths requires loops and squiggles that arc over each other. Five-photon Feynman diagrams look less like a traditional particle physics schematic and more like abstract art.


    The weak force and the strong force

    The weak force, which governs the radioactive decay of nuclei, also plays a role in influencing the muon’s magnetic moment. Unlike QED, which is mediated by the massless photon, the weak force is mediated by the massive W and Z bosons, which each weigh about 90 times the mass of a proton. The fact that the bosons are heavy makes it extremely unlikely that the muon would emit and absorb a virtual W or Z boson. But occasionally, it does happen.


    Both QED and the contribution from the weak force can be calculated to extremely high precision. The process is arduous, but physicists can calculate a good deal of the interactions simply by hand. That’s not the case with contributions from particles bound together by the strong force called hadrons, which represent the majority of uncertainty in the calculation of the muon’s anomalous magnetic moment.

    Gluons, the particles that mediate the strong force, are described by the rules of quantum chromodynamics, or QCD. Unlike photons in QED, gluons can interact with one another. Trying to calculate QCD processes by hand is effectively impossible, because the self-interacting gluons throw everything out of whack.

    “The reason why we need a collaborative effort is because the hadronic corrections cannot be calculated from first principle QCD on a blackboard,” says El-Khadra.

    There are two main types of hadronic corrections: “vacuum polarization” corrections and “light by light” corrections. In vacuum polarization, the muon emits a virtual photon, which decays into a quark and antiquark. These quarks and antiquarks exchange gluons, turning into a frothing blob of hadronic matter such as pions and kaons. Finally, the virtual blob of hadronic matter ends when a quark and antiquark annihilate back into a virtual photon, which is finally absorbed by the muon.


    Light by light contributions are perhaps some of the strangest. From the outside, it looks as if two virtual photons are emitted by a muon, interact, and are then absorbed. What’s going on here?

    “When we look around us… the reason why we can see very well is because photons—to a large degree—don’t interact with each other,” says Christoph Lehner, a physicist at Brookhaven National Lab and cofounder of the Theory Initiative.

    But if the two virtual photons get caught in a quark loop, each converting to a virtual quark and virtual antiquark, they can form a blob of hadronic matter. If the virtual quarks and virtual antiquarks annihilate back into virtual photons, the two will appear to have bounced off of one another, interacting in a forbidden way.

    Traditionally, hadronic corrections to αµ were calculated using so-called “dispersion relations.” Physicists modeling the virtual blob of hadronic matter would turn to experiments where real blobs of hadronic matter were created. Real blobs are produced in experiments where electrons collide with positrons, creating a spray of hadronic matter. Experiments like BaBar, KLOE and now Belle II all provide this kind of data, which physicists have scoured to better understand the virtual blobs.

    A contribution from supercomputing

    Recently, another method for calculating messy hadronic blobs has become viable, thanks to increasingly powerful computers and improved algorithms. Lattice QCD is a method for essentially simulating the blob from the ground up. Physicists write in the properties of the particles and the forces that govern them, set up a giant sandbox (a lattice) that the system can evolve in, and let it run. Lattice QCD is hugely computationally intensive—to produce a precise simulation, supercomputers have to calculate all of the gluon interchanges, a task that was impossible by hand.

    Because it’s a simulation of the real world from first principles, “it’s in that sense very similar to an experiment,” according to Lehner.

    One benefit is that physicists can be confident that their approach provides an answer to the question. The downsides, as in any experiment, are systematic errors—and the amount of resources required. Finding computer time is easier said than done, but at the end of the day, lattice QCD is approaching the precision of the dispersion relation method.

    Contribution—————————————–Value (x10-11)
    QED ———————————————116,584,718.931±.104
    Weak force——————————————-153.6±1.0
    Hadronic vacuum polarization (dispersive)————6,845±40
    NOT USED (Lattice hadronic vacuum polarization)——7116±184
    Hadronic light-by-light (dispersive+lattice)———92±18
    Total Standard Model Value ————————–116,591,810±43
    Difference from 2001 experiment———————-279±76

    Putting it all together

    In February, a lattice QCD group claimed to have a result for hadronic contributions in serious conflict with the predictions of dispersive relations. Almost immediately, a flurry of other publications discussing and challenging the result followed. The June paper from the Theory Initiative does not address the potential inconsistency, but lattice QCD researchers are hard at work trying to replicate the result.

    At the end of the day, when the experimentalists finish analyzing the data from the Muon g-2 experiment, they’ll compare against the theoretical value to see if there’s still a significant discrepancy. The hope, for many, is that they continue to disagree, opening a window for new physics.

    See the full article here .


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    Symmetry is a joint Fermilab/SLAC publication.

  • richardmitnick 4:37 pm on February 6, 2018 Permalink | Reply
    Tags: , Fermilab’s Muon g-2 experiment officially starts up, , , Muon g-2, , ,   

    From FNAL: “Fermilab’s Muon g-2 experiment officially starts up” 

    FNAL II photo

    FNAL Art Image
    FNAL Art Image by Angela Gonzales

    Fermilab is an enduring source of strength for the US contribution to scientific research world wide.

    February 6, 2018
    Bruno Martin

    FNAL Muon g-2 studio

    Fermilab’s Muon g-2 experiment has officially begun taking data. Pictured here is the centerpiece of the experiment, a 50-foot-wide electromagnet ring, which generates a uniform magnetic field so scientists can make measurements of particles called muons with immense precision. Photo: Reidar Hahn

    The Muon g-2 experiment at Fermilab, which has been six years in the making, is officially up and running after reaching its final construction milestone. The U.S. Department of Energy on Jan. 16 granted the last of five approval stages to the project, Critical Decision 4 (CD-4), formally allowing its transition into operations.

    “We laid down the plans for Muon g-2 early on and have stuck to that through four years of construction,” said Fermilab’s Chris Polly, the experiment’s co-spokesperson and former project manager. “We’ve come out on schedule and under budget, which sets a good precedent for all the other projects.”

    The experiment will send particles called muons — heavier cousins of the electron — around a 50-foot-wide muon storage ring that was relocated from Brookhaven National Laboratory in New York state in 2013. The uniform magnetic field inside the ring exerts a torque that affects the muons’ own spins, causing them to wobble. In the early 2000s, scientists at Brookhaven found the value of this wobble, called magnetic precession, to be different from the “g-2” value predicted by theory.

    At Fermilab, the Muon g-2 experiment aims to confirm or refute this intriguing discrepancy with theory by repeating the measurements with a fourfold improvement in accuracy, up to 140 parts per billion. That’s like measuring the length of a football field with a margin of error that is only one-tenth the thickness of a human hair. If the experimental deviation from theory turns out to be real, it would mean that undiscovered forces or particles beyond the Standard Model — the theoretical framework that describes how the universe works — are appearing and disappearing from the vacuum to disturb the muons’ magnetic moment.

    And if it isn’t?

    “Well, if we find the measurement is consistent with theory, it will allow us to narrow our search for new physics, since it will rule out some current models that would no longer be viable,” Polly said.

    For example, Polly added, there are theories positing the existence of supersymmetric particles — superheavy partners to those in the Standard Model — and new categories of particles that could be the constituents of the mysterious dark matter, which makes up 80 percent of the universe’s mass. Some of these theories would no longer be valid.

    “That’s the value of a null result,” Polly said. “It helps us make sure that the theories that we would use to try to understand these other bigger questions are consistent.”

    All that’s left now is to finish fine-tuning the instruments so the experiment can start its several-year run of data collection.

    “For most of the team, this was the first project we’ve worked on,” said Fermilab physicist Mary Convery, who served as the experiment’s deputy project manager. “To see it through from design to construction and now to operations has been very rewarding.”

    Muon g-2 operations got a head start in June 2017, when the team fired up the particle beam to start calibrating the detectors and tweaking components that required additional work.

    “Since the accelerator turned back on in November, we have been commissioning the beamlines, the storage ring and the rest of the experiment,” said University of Washington physicist David Hertzog, Muon g-2 co-spokesperson.

    As early as next month, Muon g-2 will be ready to start collecting physics-quality data at Fermilab and explore the nature of the previously measured g-2 discrepancy.

    “We’ve set ourselves the goal of collecting three times the amount of data that they had in Brookhaven’s three-year run during this first spring season,” Hertzog said. “But this is just the very beginning: The experiment will run with higher intensity next year. The ultimate goal is to collect 21 times the Brookhaven statistics.”

    See the full article here .

    Please help promote STEM in your local schools.

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    FNAL Icon

    Fermi National Accelerator Laboratory (Fermilab), located just outside Batavia, Illinois, near Chicago, is a US Department of Energy national laboratory specializing in high-energy particle physics. Fermilab is America’s premier laboratory for particle physics and accelerator research, funded by the U.S. Department of Energy. Thousands of scientists from universities and laboratories around the world
    collaborate at Fermilab on experiments at the frontiers of discovery.

  • richardmitnick 2:44 pm on January 30, 2018 Permalink | Reply
    Tags: , , Muon g-2, ,   

    From FNAL: “Muon machine makes milestone magnetic map” 

    FNAL II photo

    FNAL Art Image
    FNAL Art Image by Angela Gonzales

    Fermilab is an enduring source of strength for the US contribution to scientific research world wide.

    January 29, 2018
    Tom Barratt

    David Flay holds one of the probes that Muon g-2 scientists will use to map the magnetic field inside the experiment’s storage ring. Photo: Reidar Hahn.

    Muons are mysterious, and scientists are diving deep into the particle to get a handle on a property that might render it — and the universe — a little less mysterious.

    Like electrons – muons’ lighter siblings – they are particles with a sort of natural internal magnet. They also have an angular momentum called spin, kind of like a spinning top. The combination of the spin and internal magnet of a particle is called the gyromagnetic ratio, dubbed “g,” but previous attempts at measuring it for muons have thrown up intriguing surprises.

    The goal of the Muon g-2 experiment at Fermilab is to measure it more precisely than ever before.

    FNAL Muon g-2 studio

    To reach these remarkable levels of precision, scientists have to keep very careful tabs on a few parts of the experiment, one of which is how strong its magnetic field is. The team has been measuring and tweaking the magnetic field for months and is now very close to achieving a stable field before experiments can properly begin.

    “We’re in the experiment’s commissioning period right now, where we’re basically learning how our systems behave and making sure everything works properly before we transition into stable running,” said David Flay, a University of Massachusetts scientist working on the calibration of the magnetic field for Muon g-2.

    Muon mystery

    Muon g-2 is following up on an intriguing result seen at Brookhaven National Laboratory in New York in the early 2000s, when the experiment made observations of muons that didn’t match with theoretical predictions. The experiment’s 15-meter-diameter circular magnet, called a storage ring, was shipped to Illinois across land and sea in 2013, and the measurement is now being conducted at Fermilab with four times the precision.

    When Brookhaven carried out the experiment, the result was surprising: The muon value of g differed significantly from what calculations said it should be, and no one is quite sure why. It’s possible the experiment itself was flawed and the result was false, but it also opens the door to the possibility of exotic new particles and theories. With its four-fold increase in precision, Muon g-2 will shed more light on the situation.

    To measure g, beams of muons circulating inside the experiment’s storage ring are subjected to an intense magnetic field – about 30,000 times the strength of Earth’s natural field. This causes the muons to rotate around the magnetic field, or precess, in a particular way. By measuring this precession, it is possible to precisely extract the value of g.

    The strength of magnetic field to which the muons are exposed directly affects how they precess, so it’s absolutely crucial to make extremely precise measurements of the field strength and maintain its uniformity throughout the ring – not an easy task.

    If Muon g-2 backs up Brookhaven’s result, it would be huge news. The Standard Model would need rethinking and it would open up a whole new chapter of particle physics.

    A leading theory to explain the intriguing results are new kinds of virtual particles, quantum phenomena that flit in and out of existence, even in an otherwise empty vacuum. All known particles do this, but their total effect doesn’t quite account for Brookhaven’s results. Scientists are therefore predicting one or more new, undiscovered kinds, whose additional ephemeral presence could be providing the strange muon observations.

    “The biggest challenge so far has been dealing with the unexpected,” said Joe Grange, scientist at Argonne National Laboratory working on Muon g-2’s magnetic field. “When a mystery pops up that needs to be solved relatively quickly, things can get hectic. But it’s also one of the more fun parts of our work.”

    Probing the field

    The magnetic field strength measurements are made using small, sensitive electronic devices called probes. Three types of probes – fixed, trolley and plunging – work together to build up a 3-D map of the magnetic field inside the experiment. The field can drift over time, and things like temperature changes in the experiment’s building can subtly affect the ring’s shape, so roughly 400 fixed probes are positioned just above and below the storage ring to keep a constant eye on the field inside. Because these probes are always watching, the scientists know when and by how much to tweak the field to keep it uniform.

    For these measurements, and every few days when the experiments is paused and the muon beam is stopped, a 0.5-meter-long, curved cylindrical trolley on rails containing 17 probes is sent around the ring to take a precise field map in the region where the muons are stored. Each orbit takes a couple of hours. The trolley probes are themselves calibrated by a plunging probe, which can move in and out of its own chamber at a specific location in the ring when needed.

    The fixed probes have been installed and working since fall 2016, while the 17 trolley probes have recently been removed, upgraded and reinstalled.

    “The probes are inside the ring where we can’t see them,” Flay said. “So matching up their positions to get an accurate calibration between them is not an easy thing to do.”

    The team developed some innovative solutions to tackle this problem, including a barcode-style system inside the ring, which the trolley scans to relay where it is as it moves around.

    Global g-2

    Muon g-2 is an international collaboration hosted by Fermilab. Together with scientists from Fermilab, Argonne, and Brookhaven, several universities across the U.S. work with international collaborators from countries as wide-ranging as South Korea, Italy and the UK. In total, around 30 institutions and 150 people work on the experiment.

    “It’s the detailed efforts of the Argonne, University of Washington, University of Massachusetts and University of Michigan teams that have produced these reliable, quality tools that give us a complete picture of the magnetic field,” said Brendan Kiburg, Fermilab scientist working on Muon g-2. “It has taken years of meticulous work.”

    The team is working to finish the main field strength measurement part of the commissioning process by early 2018, before going on to analyze exactly how the muons experience the generated field. The experiment is planned to begin in full in February 2018.

    See the full article here .

    Please help promote STEM in your local schools.

    STEM Icon

    Stem Education Coalition

    FNAL Icon

    Fermi National Accelerator Laboratory (Fermilab), located just outside Batavia, Illinois, near Chicago, is a US Department of Energy national laboratory specializing in high-energy particle physics. Fermilab is America’s premier laboratory for particle physics and accelerator research, funded by the U.S. Department of Energy. Thousands of scientists from universities and laboratories around the world
    collaborate at Fermilab on experiments at the frontiers of discovery.

  • richardmitnick 1:13 pm on January 25, 2018 Permalink | Reply
    Tags: , , Muon g-2, , ,   

    From Science: “Renewed measurements of muon’s magnetism could open door to new physics” 

    Science Magazine

    Jan. 25, 2018
    Adrian Cho

    The magnetism of muons is measured as the short-lived particles circulate in a 700-ton ring. FNAL.

    Next week, physicists will pick up an old quest for new physics. A team of 190 researchers at Fermi National Accelerator Laboratory (Fermilab) in Batavia, Illinois, will begin measuring to exquisite precision the magnetism of a fleeting particle called the muon. They hope to firm up tantalizing hints from an earlier incarnation of the experiment, which suggested that the particle is ever so slightly more magnetic than predicted by the prevailing standard model of particle physics. That would give researchers something they have desired for decades: proof of physics beyond the standard model.

    “Physics could use a little shot of love from nature right now,” says David Hertzog, a physicist at the University of Washington in Seattle and co-spokesperson for the experiment, which is known as Muon g-2 (pronounced “gee minus two”). Physicists are feeling increasingly stymied because the world’s biggest atom smasher, the Large Hadron Collider (LHC) near Geneva, Switzerland, has yet to blast out particles beyond those in the standard model. However, g-2 could provide indirect evidence of particles too heavy to be produced by the LHC.

    The muon is a heavier, unstable cousin of the electron. Because it is charged, it will circle in a magnetic field. Each muon is also magnetized like a miniature bar magnet. Place a muon in a magnetic field perpendicular to the orientation of its magnetization, and its magnetic polarity will turn, or precess, just like a twirling compass needle.

    At first glance, theory predicts that in a magnetic field a muon’s magnetism should precess at the same rate as the particle itself circulates, so that if it starts out polarized in the direction it’s flying, it will remain locked that way throughout its orbit. Thanks to quantum uncertainty, however, the muon continually emits and reabsorbs other particles. That haze of particles popping in and out of existence increases the muon’s magnetism and make it precess slightly faster than it circulates.

    Because the muon can emit and reabsorb any particle, its magnetism tallies all possible particles—even new ones too massive for the LHC to make. Other charged particles could also sample this unseen zoo, says Aida El-Khadra, a theorist at the University of Illinois in Urbana. But, she adds, “The muon hits the sweet spot of being light enough to be long-lived and heavy enough to be sensitive to new physics.”

    From 1997 to 2001, researchers on the original g-2 experiment at Brookhaven National Laboratory in Upton, New York, tested this promise by shooting the particles by the thousands into a ring-shaped vacuum chamber 45 meters in diameter, sandwiched between superconducting magnets.

    Over hundreds of microseconds, the positively charged muons decay into positrons, which tend to be spat out in the direction of the muons’ polarization. Physicists can track the muons’ precession by watching for positrons with detectors lining the edge of the ring.

    The g-2 team first reported a slight excess in the muon’s magnetism in 2001. That result quickly faded as theorists found a simple math mistake in the standard model prediction (Science, 21 December 2001, p. 2449). Still, by the time the team reported on the last of its Brookhaven data in 2004, the discrepancy had re-emerged. Since then, the result has grown, as theorists improved their standard model calculations. They had struggled to account for the process in which the muon emits and reabsorbs particles called hadrons, says Michel Davier, a theorist at the University of Paris-South in Orsay, France. By using data from electron-positron colliders, he says, the theorists managed to reduce this largest uncertainty.

    Physicists measure the strength of signals in multiples of the experimental uncertainty, σ, and the discrepancy now stands at 3.5 σ—short of the 5 σ needed to claim a discovery, but interesting enough to warrant trying again.

    In 2013, the g-2 team lugged the experiment on a 5000-kilometer odyssey from Brookhaven to Fermilab, taking the ring by barge around the U.S. eastern seaboard and up the Mississippi River. Since then, they have made the magnetic field three times more uniform, and at Fermilab, they can generate far purer muon beams. “It’s really a whole new experiment,” says Lee Roberts, a g-2 physicist at Boston University. “Everything is better.”

    Over 3 years, the team aims to collect 21 times more data than during its time at Brookhaven, Roberts says. By next year, Hertzog says, the team hopes to have enough data for a first result, which could push the discrepancy above 5 σ.

    Will the muon end up being a portal to new physics? JoAnne Hewett, a theorist at SLAC National Accelerator Laboratory in Menlo Park, California, hesitates to wager. “In my physics lifetime, every 3-σ deviation from the standard model has gone away,” she says. “If it weren’t for that baggage, I’d be cautiously optimistic.”

    The magnetism of muons is measured as the short-lived particles circulate in a 700-ton ring.

    See the full article here .

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