How do neutrinos get their mass?

For decades, scientists studying the muon have been puzzled by a strange pattern in the way muons rotate in magnetic fields, one that left physicists wondering if it can be explained by the Standard Model — the best tool physicists have to understand the universe.

This week, an international team of more than 170 physicists published the most reliable prediction so far for the theoretical value of the muon’s anomalous magnetic moment, which would account for its particular rotation, or precession. The magnetic moment of subatomic particles is generally expressed in terms of the dimensionless Landé factor, called g. While a number of international groups have worked separately on the calculation, this publication marks the first time the global theoretical physics community has come together to publish a consensus value for the muon’s magnetic moment.

The result differs from the most recent experimental measurement, which was performed at Brookhaven National Laboratory in 2004, but not significantly enough to unambiguously answer this question.

Now the world awaits the result from Fermilab’s current Muon g-2 experiment. In the upcoming months, physicists working on the experiment will unveil their preliminary measurement for the value. Depending on how much the Standard Model theoretical calculation differs from the upcoming experimental measurement, physicists may be one step closer to determining whether the muon’s magnetic interactions are hinting at particles or forces that have yet to be discovered.

In the late 1960s at CERN laboratory, scientists began using a large circular magnetic ring to test the theory that described how muons should “wobble” when moving through a magnetic field. Since then, experimenters have continued to quantify that wobble, making more and more precise measurements of the muon’s anomalous magnetic moment.

The decades-long effort eventually led to an experiment at Brookhaven National Laboratory and its successor at Fermilab, as well as plans for a new experiment in Japan. At the same time, theorists worked to improve the precision of their calculations and fine-tune their predictions.

The theoretical value of the anomalous magnetic moment of the muon, published today, is:

a = (g-2)/2 (muon, theory) = 116 591 810(43) x 10^-11

The most precise experimental result available so far is:

a = (g-2)/2 (muon, expmt) = 116 592 089(63) x 10^-11

Again, the slight discrepancy between the experimental measurements and the predicted value has persisted, and again it is just beneath the threshold to make a definitive statement.

This theoretical value, published in the arXiv, is the result of over three years of work by 130 physicists from 78 institutions in 21 countries.

“We’ve not had a theory effort like this before in which all the different evaluations are combined into a single Standard Model prediction,” said Aida El-Khadra, a physicist at the University of Illinois and co-chair of the Steering Committee for the Muon g-2 Theory Initiative, the name of the group of scientists who worked on the calculation.

Their work builds on a single equation published in 1928 that simultaneously started the field of quantum electrodynamics and laid the foundations for the Muon g-2 experiment.

An elegant theory

If you were to ask physicists what they considered the most accurate and successful equation in their field, chances are more than a few would say it’s Dirac’s equation, which describes the relativistic quantum theory of the electron. Published in 1928, Dirac described the spin motion of electrons, and his equation bridged the gap between Einstein’s theory of relativity and the theory of quantum mechanics, and unintentionally predicted the existence of antimatter with only a single equation.

Dirac was also able to calculate something called the magnetic moment of the electron, which he described as being “an unexpected bonus.”

Electrons can be thought of as tiny spinning tops that rotate on their axis, an intrinsic property that makes each electron act like a tiny magnet. When placed in a magnetic field, such as the ones generated in particle accelerators, electrons will precess — or wobble on their axis — in a specific and predictable pattern. This wobble is an effect of the particle’s magnetic moment, and it applies to more than electrons. Every electrically charged particle with ½ spin (spin is quantified in half units) behaves in the same way, including particles called muons, which have the same properties as electrons but are more than 200 times as massive.

Dirac’s equation, which did not take into account the effects of quantum fluctuations, predicted that g would equal 2. Experiment has shown that the actual value differs from that simple expectation — hence the name “muon g-2.”

Physicists now have a much better understanding of what those quantum fluctuations are and how they behave at subatomic scales, but precisely calculating how they affect the muon’s path is no easy task.

“Calculating the effects of these quantum fluctuations at the precision level demanded by modern experiment isn’t something that one brilliant person can do alone,” El-Khadra said. “It really takes the whole village.”

Meeting of the minds

With so many physicists working on the latest developments to the theory around the world, El-Khadra and her colleagues at Fermilab knew the best way to facilitate interactions between the groups was to bring them all together. So, starting in 2016, El-Khadra and her colleagues in the Fermilab Theory Group, together with Brookhaven National Laboratory scientist Christoph Lehner, Theory Initiative co-chair, and several other international collaborators reached out to the leaders in the global community of physicists working on this problem to put together a new initiative, the Muon g-2 Theory Initiative. The initiative, led by a nine-person Steering Committee that includes leaders of all the major efforts in both theory and experiment, organized a series of workshops around the world, including in the U.S., Japan and Germany, the first of which was hosted at Fermilab in 2017.

“We had some very intense discussions,” El-Khadra said, “That led to more detailed comparisons and a better understanding of the pros and cons of the various approaches.”

The establishment of the Muon g-2 Theory Initiative was the first coherent international effort to bring together all of the parties working on the Standard Model value of the muon’s anomalous magnetic moment.

“Before this initiative began, there were a number of evaluations in the literature of the Standard Model value, each of which differed slightly from the others,” said Boston University scientist Lee Roberts, co-founder of the Fermilab experiment and a member of the initiative’s Steering Committee. “The remarkable thing is that this worldwide community was able to come together and to agree on the ‘best’ value for each of the contributions to the value of the muon’s magnetic moment.”

Quantum calculations

“Muons and other spin-½ particles are never really alone in the universe,” said Fermilab scientist Chris Polly, who is one of Muon g-2’s spokespersons, along with University of Manchester physicist Mark Lancaster. “They interact with a whole entourage of particles that are constantly popping into and out of existence.”

The two main sources of uncertainty are hadronic vacuum polarization and light-by-light scattering — in which a muon emits and reabsorbs photons after they have traveled through a bubble of quarks and gluons. Both of these factors combine to make up less than 0.01% of the effect on the muon’s wobble yet make up the main source of uncertainty in the theory calculation.

Calculating the light-by-light scattering part of the hadronic contribution has proven to be especially difficult, and before the start of the Muon g-2 Theory Initiative, physicists had not yet produced reliable estimates of its effects. The best they could manage were rough approximations that led some to wonder whether these evaluations of the light-by-light scattering might be the source of the difference between the muon’s calculated anomalous magnetic moment and the experimentally measured value.

But theorists are now confident that they can lay these doubts to rest. Thanks to heroic efforts in recent years within the theory community, not just one, but two independent evaluations are now available, each with reliably estimated uncertainties, which are included in the total error of the Standard Model prediction listed above.

“We’ve now quantified the light-by-light scattering contribution to the extent that it can no longer be used as an explanation to save the Standard Model if the experimental value turns out to differ significantly from the theoretical prediction,” said Brookhaven National Laboratory physicist Christoph Lehner, Theory Initiative co-chair.

And with so much riding on the line, El-Khadra and other members of the Theory Initiative have left nothing to chance.

“We have strongly emphasized the importance of including evaluations based on several different methods in our construction of the Standard Model prediction of the anomalous magnetic moment of the muon,” El-Khadra said. “Because if we find that the Fermilab experiment’s measurement is inconsistent with the Standard Model, we want to be sure.”

Aida El-Khadra will present the results of the white paper in a special Fermilab seminar on June 18 at 10:30 a.m.

The Fermilab Muon g-2 experiment is supported by the DOE Office of Science.

Fermilab is supported by the Office of Science of the U.S. Department of Energy. The Office of Science is the single largest supporter of basic research in the physical sciences in the United States and is working to address some of the most pressing challenges of our time. For more information, visit science.energy.gov.

With people around the world working from home during these unprecedented times, many Fermilab employees are working remotely, and this includes work on the design of Fermilab’s PIP-II accelerator. While certain aspects of the accelerator project can be carried out only in a laboratory, such as making and testing components, the international team of engineers and scientists can advance other aspects, like component design and working on the machine’s detailed blueprints, from their home offices.

In many ways, years of videoconferencing with their international partners has prepared the team to continue making progress from home.

This is especially true for those who are designing the PIP-II cryomodules, large metal structures that keep superconducting accelerator components chilled to just a few degrees above absolute zero as they propel protons to close to the speed of light. Researchers and engineers from five countries have been collaborating on the design and construction of these cryomodules, work that has remained relatively uninterrupted during the lab’s teleworking period.

Ramping up energy, cooling down cavities, working across borders

Cryomodules are the largest components of a superconducting particle accelerator. They house structures called superconducting accelerator cavities, which are lined up end-to-end inside the cryomodule. These cavities boost the energy of a particle beam as it travels through one after the next.

PIP-II’s accelerator cavities are made of niobium, a material that becomes superconducting at ultracold temperatures. Like a high-tech refrigerator, the cryomodules that house the PIP-II cavities cool the cavities down to minus 271 degrees Celsius and keep them at that temperature.

The new accelerator will help generate the world’s most powerful neutrino beam for the international Deep Underground Neutrino Experiment, hosted by Fermilab. It will also provide intense proton beams for the lab’s future experimental programs.

A truly global effort, PIP-II is the first particle accelerator project in the U.S. with significant international contribution. Engineers from France, India, Italy, the United Kingdom and United States are working together to design and build the cryomodules, and engineers from Poland are working on the cryogenics distribution system for the new accelerator.

When complete, the entire 700-foot-long PIP-II accelerator will have a total of 23 cryomodules. Each of the accelerator’s five cryomodule designs will boost the energy of the protons, finally achieving 800 million electronvolts and propelling the particles to 84% of the speed of light. After exiting the PIP-II accelerator, the beam will enter the Fermilab accelerator chain for further acceleration, and then the protons will smash into a target to produce neutrinos.

The new accelerator is analogous to an airport runway. When a plane takes off, passengers experience an initial jolt of acceleration, after which the plane continuously ramps up in speed. Similarly, the ion source and front end of the PIP-II accelerator provide the initial acceleration for the particle beam, which then enters the string of 23 cryomodules, each one providing a set boost.

Engineering from home

The first cryomodule houses a cavity known as the HWR (half-wave resonator), a type of accelerating structure used in the early stages of particle acceleration. The only one of its kind in the PIP-II accelerator, the cryomodule was developed by Argonne National Laboratory and is currently scheduled to undergo testing at Fermilab. The next stage of acceleration deploys a cryomodule that houses a different type of cavity called the SSR1 (single-spoke resonator 1). It was recently completed at Fermilab with the help of collaborators from India.

“We were about to begin testing of the SSR1 cryomodule, but all hands-on activities are currently paused,” said Fermilab engineer Donato Passarelli.

Instead, engineers on the project have focused their current efforts on the design and planning activities. They have learned to adapt to the challenges of doing design work remotely.

“As mechanical engineers, we usually print all of our design drawings and edit them directly,” said Fermilab engineer Vincent Roger. “It’s now necessary to scan the edited drawings to send the corrections to the drafter as well. It makes the process slightly longer, but it’s still an efficient way to keep track of changes.”

The nature of international collaboration has also allowed the team to more easily transition into a remote work schedule. Colleagues on the project from different countries rarely get to interact in person and so typically interact through email or online meetings.

“Of course, it’s always easier when my colleagues are in the same corridor,” Roger said. “During this period, we’ve adjusted by organizing more meetings, many of which are very short. Sometimes it’s just a five-minute meeting to share a concept and get feedback.”

The first two PIP-II cryomodules have been installed at a PIP-II prototype test facility awaiting testing. First beam is expected later this year, and the installation of all cryomodules in their final location is planned to be complete in the mid-2020s, when the PIP-II accelerator is also scheduled to come online.

“As partners in an international project, PIP-II collaborators are fluent in online coordination, so we’re well-equipped to carry on the work of cryomodule design remotely,” said PIP-II Project Director Lia Merminga of Fermilab. “Every day brings us closer to the moment when we’ll realize this world-class accelerator, and that will not only be an achievement for Fermilab and its partners, but also a testament to the fruits of global cooperation.”

Work on the PIP-II project is supported by the Department of Energy Office of Science and receives contributions from partners in France, India, Italy, Poland, the United Kingdom and United States.

Fermilab is supported by the Office of Science of the U.S. Department of Energy. The Office of Science is the single largest supporter of basic research in the physical sciences in the United States and is working to address some of the most pressing challenges of our time. For more information, visit science.energy.gov.

 

 

Fermilab regularly makes fundamental science discoveries and is a world leader in quantum physics. In 2019, it launched the Fermilab Quantum Institute, which conducts world-class research at the leading edge of quantum computing and information science, laying the groundwork for critical physics calculations to be performed on quantum computers. As such, Fermilab is an ideal place to bring together particle physics and quantum computing as two complementary fields.

During the summer of 2018, three of us in the Fermilab Theoretical Physics Department applied to mentor two high school teachers, Anastasia Perry and Ranbel Sun. With STEM education in mind, we thought this was an ideal opportunity to share the exciting and disruptive technology of quantum computing.

After surveying the available resources on quantum computing, we discovered that while popular science articles and advanced textbooks existed in abundance, the material for high school students was decidedly lacking.

We decided to fill the gap: During the summer, Anastasia and Ranbel met with us several times a week to discuss the foundations of quantum mechanics, quantum computing and how to best present this information to a high school level audience. They read a vast amount of quantum computing material, distilled it to the simplest parts and created the module at an appropriate comprehension level. Together, we decided students should learn about quantum concepts including superposition, qubits, encryption, quantum measurement, entanglement, teleportation and their real-world applications.

Once the summer was over, all of us continued to work on the material, creating attractive figures, improving readability and adding information on recent quantum computing developments (research really does change that quickly!). Finally, the information was collected into a single book. Working together with such a motivated and intelligent group ensured the whole process was exciting and fun.

Our group developed a course, “Quantum Computing as a High School Module,” which is available on the open-access archive arXiv. The course is the first on quantum computing designed for U.S. high school students, but it is also useful for a quantum-computing-curious public. The teachers ensured that the material is at the appropriate level, and we ensured that the science is sound.

We created the course to guide students through various aspects of quantum computing without relying on prior knowledge of quantum mechanics. Conceptual ideas are reinforced with active learning techniques, such as interactive problem sets and simulation-based labs at various levels. We’ve heard that the walkthrough exercises that use IBM’s real quantum computer to build a Schroedinger’s worm (equivalent to the cat) have been a real hit.

We tested the material through trial runs and received positive feedback from multiple sources. In the trial runs, we conducted surveys before and after the students took the course and found that they successfully learned about quantum computing and had a high level of enthusiasm for it. One student even commented “we should replace special relativity with quantum computing next year.”

This spring, we submitted to journal The Physics Teacher an article in which we analyze student feedback.

The course has seen remarkable success since its inception. We have been contacted by people from all over the world, including high school teachers in Brazil and education researchers in the Netherlands. The American Association of Physics Teachers is excited to collaborate with us on future quantum computing pedagogy workshops and to create nationwide impact in quantum computing education for high schoolers.

Quantum computing will affect the future of every area of science, so the need for a quantum-fluent workforce is great. With this quantum computing course, Fermilab scientists are breaking new ground in both quantum computing research and ensuring the competitiveness of the STEM workforce in the quantum era.

Ciaran Hughes, Joshua Isaacson and Jessica Turner are theoretical physicists at Fermilab.

 

What makes for a good dark matter detector? It has a lot in common with a good teleconference setup: You need a sensitive microphone and a quiet room.

Scientists working on the SENSEI experiment at the Department of Energy’s Fermilab now have demonstrated for the first time a particle detector — based on charge-coupled device, or CCD, technology — with both the sensitivity and reduced background rates needed for an effective search for low-mass particles of dark matter, the mysterious substance that accounts for about 80 percent of all matter in the universe.

The demonstration is important in two ways. First, the background rates measured by the SENSEI detector are record lows for a silicon detector. They set the world’s strongest limits on dark matter interactions with electrons, across a wide range of models. Second, it shows the high quality of the detectors that will be used in the full-scale SENSEI experiment under construction. SENSEI will run at the Canadian SNOLAB deep underground laboratory.

The SENSEI detector is a 5.4-megapixel CCD made of 2 grams of silicon currently operating about 100 meters underground at Fermilab. If a dark matter particle collides with one of the electrons in the silicon, the energy transferred to the electron may be enough to liberate it from the crystal structure of the silicon. If there is enough energy, additional electrons will be freed. This charge is the signal SENSEI scientists are looking for. The smaller the signal SENSEI can detect, the broader the range of dark matter models it can test.

To observe small dark matter signals, the first thing scientists need is a sensitive detector. In other words, they must be able to detect a small signal and consistently distinguish it from a truly empty detector. As demonstrated in previous work, SENSEI’s skipper-CCDs, designed by Lawrence Berkeley National Laboratory, can count the exact number of electrons in each pixel.

Second, scientists need low background — the rate of signal-like events from causes other than dark matter has to be small. A sensitive detector with high background is like a studio microphone in a noisy room. Even if the microphone can pick up a whisper, your soft voice might be drowned out by the noise of the washing machine in the background. The only way to improve the recording is to eliminate the noise of the washing machine.

The SENSEI collaboration now has demonstrated for the first time that it has a sensitive dark matter detector and can reduce background rates. It’s important to demonstrate that a detector can achieve low background rates before you scale up to a larger experiment with the same technology, because otherwise you are just going to scale up your background rate. Previous dark matter searches by SENSEI used prototype CCDs, which had high sensitivity but also high backgrounds because they were not made with the highest-quality silicon.

SENSEI’s new dark matter search has yielded the first result from its new science-grade CCDs, which were fabricated in a dedicated production run for SENSEI with high-quality silicon. The collaboration also reduced the amount of radiation that hits the CCD by adding extra shielding around the experiment. The result was a decrease in background event rates compared to the previous search with a prototype CCD. The rate of single-electron events decreased from 33,000 to 450 events/gram-day, and we see fewer two-electron events (five, down from 21) in a much larger exposure (2.09 gram-days, up from 0.043). We also see no three- or four-electron events — just as in the previous search, but with a larger exposure.

The science-grade CCDs work as well as could have been hoped, and SENSEI expects background rates to be even lower at SNOLAB. There will likely be more great science from SENSEI in the near future!

Learn more from SENSEI’s preprint or the collaboration’s presentation at a seminar at Fermilab.

Sho Uemura of the SENSEI collaboration is a scientist at Tel Aviv University and is supported in part by the Zuckerman STEM Leadership Program.

U.S. work on SENSEI is supported by the DOE Office of Science. This work is also funded by the Heising-Simons Foundation.

Fermilab is supported by the Office of Science of the U.S. Department of Energy. The Office of Science is the single largest supporter of basic research in the physical sciences in the United States and is working to address some of the most pressing challenges of our time. For more information, visit science.energy.gov.