Magnetic-field measurement and analysis for the Muon g − 2 Experiment at Fermilab

The Fermi National Accelerator Laboratory (FNAL) Muon g - 2 Experiment has measured the anomalous precession frequency a_{μ}(g_{μ} - 2)/2 of the muon to a combined precision of 0.46 parts per million with data collected during its first physics run in 2018. This paper documents the measurement of the magnetic field in the muon storage ring. The magnetic field is monitored by systems and calibrated in terms of the equivalent proton spin precession frequency in a spherical water sample at 34.7C. The measured field is weighted by the muon distribution resulting in \tilde{ω}'_{p}, the denominator in the ratio \tilde{ω}_{a}/\tilde{ω}'_{p} that together with known fundamental constants yields aμ. The reported uncertainty on \tilde{ω}'_{p} for the Run-1 data set is 114 ppb consisting of uncertainty contributions from frequency extraction, calibration, mapping, tracking, and averaging of 56 ppb, and contributions from fast transient fields of 99 ppb

Measurement of the Positive Muon Anomalous Magnetic Moment to 0.20 ppm

We present a new measurement of the positive muon magnetic anomaly, a_{μ}≡(g_{μ}-2)/2, from the Fermilab Muon g-2 Experiment using data collected in 2019 and 2020. We have analyzed more than 4 times the number of positrons from muon decay than in our previous result from 2018 data. The systematic error is reduced by more than a factor of 2 due to better running conditions, a more stable beam, and improved knowledge of the magnetic field weighted by the muon distribution, ω[over ˜]_{p}^{'}, and of the anomalous precession frequency corrected for beam dynamics effects, ω_{a}. From the ratio ω_{a}/ω[over ˜]_{p}^{'}, together with precisely determined external parameters, we determine a_{μ}=116 592 057(25)×10^{-11} (0.21 ppm). Combining this result with our previous result from the 2018 data, we obtain a_{μ}(FNAL)=116 592 055(24)×10^{-11} (0.20 ppm). The new experimental world average is a_{μ}(exp)=116 592 059(22)×10^{-11} (0.19 ppm), which represents a factor of 2 improvement in precision

Beam dynamics corrections to the Run-1 measurement of the muon anomalous magnetic moment at Fermilab

This paper presents the beam dynamics systematic corrections and their uncertainties for the Run-1 data set of the Fermilab Muon g-2 Experiment. Two corrections to the measured muon precession frequency $\omega_a^m$ are associated with well-known effects owing to the use of electrostatic quadrupole (ESQ) vertical focusing in the storage ring. An average vertically oriented motional magnetic field is felt by relativistic muons passing transversely through the radial electric field components created by the ESQ system. The correction depends on the stored momentum distribution and the tunes of the ring, which has relatively weak vertical focusing. Vertical betatron motions imply that the muons do not orbit the ring in a plane exactly orthogonal to the vertical magnetic field direction. A correction is necessary to account for an average pitch angle associated with their trajectories. A third small correction is necessary because muons that escape the ring during the storage time are slightly biased in initial spin phase compared to the parent distribution. Finally, because two high-voltage resistors in the ESQ network had longer than designed RC time constants, the vertical and horizontal centroids and envelopes of the stored muon beam drifted slightly, but coherently, during each storage ring fill. This led to the discovery of an important phase-acceptance relationship that requires a correction. The sum of the corrections to $\omega_a^m$ is 0.50 $\pm$ 0.09 ppm; the uncertainty is small compared to the 0.43 ppm statistical precision of $\omega_a^m$

Measurement of the anomalous precession frequency of the muon in the Fermilab Muon g-2 Experiment

The Muon g-2 Experiment at Fermi National Accelerator Laboratory (FNAL) has measured the muon anomalous precession frequency $\omega_a$ to an uncertainty of 434 parts per billion (ppb), statistical, and 56 ppb, systematic, with data collected in four storage ring configurations during its first physics run in 2018. When combined with a precision measurement of the magnetic field of the experiment's muon storage ring, the precession frequency measurement determines a muon magnetic anomaly of $a_{\mu}({\rm FNAL}) = 116\,592\,040(54) \times 10^{-11}$ (0.46 ppm). This article describes the multiple techniques employed in the reconstruction, analysis and fitting of the data to measure the precession frequency. It also presents the averaging of the results from the eleven separate determinations of \omega_a, and the systematic uncertainties on the result.Comment: 29 pages, 19 figures. Published in Physical Review

Magnetic Field Measurement and Analysis for the Muon g-2 Experiment at Fermilab

The Fermi National Accelerator Laboratory has measured the anomalous precession frequency $a^{}_\mu = (g^{}_\mu-2)/2$ of the muon to a combined precision of 0.46 parts per million with data collected during its first physics run in 2018. This paper documents the measurement of the magnetic field in the muon storage ring. The magnetic field is monitored by nuclear magnetic resonance systems and calibrated in terms of the equivalent proton spin precession frequency in a spherical water sample at 34.7$^\circ$C. The measured field is weighted by the muon distribution resulting in $\tilde{\omega}'^{}_p$, the denominator in the ratio $\omega^{}_a$/$\tilde{\omega}'^{}_p$ that together with known fundamental constants yields $a^{}_\mu$. The reported uncertainty on $\tilde{\omega}'^{}_p$ for the Run-1 data set is 114 ppb consisting of uncertainty contributions from frequency extraction, calibration, mapping, tracking, and averaging of 56 ppb, and contributions from fast transient fields of 99 ppb

Beam dynamics corrections to the Run-1 measurement of the muon anomalous magnetic moment at Fermilab

This paper presents the beam dynamics systematic corrections and their uncertainties for the Run-1 data set of the Fermilab Muon g-2 Experiment. Two corrections to the measured muon precession frequency $\omega_a^m$ are associated with well-known effects owing to the use of electrostatic quadrupole (ESQ) vertical focusing in the storage ring. An average vertically oriented motional magnetic field is felt by relativistic muons passing transversely through the radial electric field components created by the ESQ system. The correction depends on the stored momentum distribution and the tunes of the ring, which has relatively weak vertical focusing. Vertical betatron motions imply that the muons do not orbit the ring in a plane exactly orthogonal to the vertical magnetic field direction. A correction is necessary to account for an average pitch angle associated with their trajectories. A third small correction is necessary because muons that escape the ring during the storage time are slightly biased in initial spin phase compared to the parent distribution. Finally, because two high-voltage resistors in the ESQ network had longer than designed RC time constants, the vertical and horizontal centroids and envelopes of the stored muon beam drifted slightly, but coherently, during each storage ring fill. This led to the discovery of an important phase-acceptance relationship that requires a correction. The sum of the corrections to $\omega_a^m$ is 0.50 $\pm$ 0.09 ppm; the uncertainty is small compared to the 0.43 ppm statistical precision of $\omega_a^m$

Magnetic-field measurement and analysis for the Muon g − 2 Experiment at Fermilab

The Fermi National Accelerator Laboratory (FNAL) Muon g-2 Experiment has measured the anomalous precession frequency aμ(gμ-2)/2 of the muon to a combined precision of 0.46 parts per million with data collected during its first physics run in 2018. This paper documents the measurement of the magnetic field in the muon storage ring. The magnetic field is monitored by systems and calibrated in terms of the equivalent proton spin precession frequency in a spherical water sample at 34.7C. The measured field is weighted by the muon distribution resulting in ωp′, the denominator in the ratio ωa/ωp′ that together with known fundamental constants yields aμ. The reported uncertainty on ωp′ for the Run-1 data set is 114 ppb consisting of uncertainty contributions from frequency extraction, calibration, mapping, tracking, and averaging of 56 ppb, and contributions from fast transient fields of 99 ppb

Measurement of the Positive Muon Anomalous Magnetic Moment to 0.20 ppm.

We present a new measurement of the positive muon magnetic anomaly, a_{μ}≡(g_{μ}-2)/2, from the Fermilab Muon g-2 Experiment using data collected in 2019 and 2020. We have analyzed more than 4 times the number of positrons from muon decay than in our previous result from 2018 data. The systematic error is reduced by more than a factor of 2 due to better running conditions, a more stable beam, and improved knowledge of the magnetic field weighted by the muon distribution, ω[over ˜]_{p}^{'}, and of the anomalous precession frequency corrected for beam dynamics effects, ω_{a}. From the ratio ω_{a}/ω[over ˜]_{p}^{'}, together with precisely determined external parameters, we determine a_{μ}=116 592 057(25)×10^{-11} (0.21 ppm). Combining this result with our previous result from the 2018 data, we obtain a_{μ}(FNAL)=116 592 055(24)×10^{-11} (0.20 ppm). The new experimental world average is a_{μ}(exp)=116 592 059(22)×10^{-11} (0.19 ppm), which represents a factor of 2 improvement in precision

Introduction STATE OF THE CLIMATE IN 2022

Abstract —J. BLUNDEN, T. BOYER, AND E. BARTOW-GILLIES Earth’s global climate system is vast, complex, and intricately interrelated. Many areas are influenced by global-scale phenomena, including the “triple dip” La Niña conditions that prevailed in the eastern Pacific Ocean nearly continuously from mid-2020 through all of 2022; by regional phenomena such as the positive winter and summer North Atlantic Oscillation that impacted weather in parts the Northern Hemisphere and the negative Indian Ocean dipole that impacted weather in parts of the Southern Hemisphere; and by more localized systems such as high-pressure heat domes that caused extreme heat in different areas of the world. Underlying all these natural short-term variabilities are long-term climate trends due to continuous increases since the beginning of the Industrial Revolution in the atmospheric concentrations of Earth’s major greenhouse gases. In 2022, the annual global average carbon dioxide concentration in the atmosphere rose to 417.1±0.1 ppm, which is 50% greater than the pre-industrial level. Global mean tropospheric methane abundance was 165% higher than its pre-industrial level, and nitrous oxide was 24% higher. All three gases set new record-high atmospheric concentration levels in 2022. Sea-surface temperature patterns in the tropical Pacific characteristic of La Niña and attendant atmospheric patterns tend to mitigate atmospheric heat gain at the global scale, but the annual global surface temperature across land and oceans was still among the six highest in records dating as far back as the mid-1800s. It was the warmest La Niña year on record. Many areas observed record or near-record heat. Europe as a whole observed its second-warmest year on record, with sixteen individual countries observing record warmth at the national scale. Records were shattered across the continent during the summer months as heatwaves plagued the region. On 18 July, 104 stations in France broke their all-time records. One day later, England recorded a temperature of 40°C for the first time ever. China experienced its second-warmest year and warmest summer on record. In the Southern Hemisphere, the average temperature across New Zealand reached a record high for the second year in a row. While Australia’s annual temperature was slightly below the 1991–2020 average, Onslow Airport in Western Australia reached 50.7°C on 13 January, equaling Australia's highest temperature on record. While fewer in number and locations than record-high temperatures, record cold was also observed during the year. Southern Africa had its coldest August on record, with minimum temperatures as much as 5°C below normal over Angola, western Zambia, and northern Namibia. Cold outbreaks in the first half of December led to many record-low daily minimum temperature records in eastern Australia. The effects of rising temperatures and extreme heat were apparent across the Northern Hemisphere, where snow-cover extent by June 2022 was the third smallest in the 56-year record, and the seasonal duration of lake ice cover was the fourth shortest since 1980. More frequent and intense heatwaves contributed to the second-greatest average mass balance loss for Alpine glaciers around the world since the start of the record in 1970. Glaciers in the Swiss Alps lost a record 6% of their volume. In South America, the combination of drought and heat left many central Andean glaciers snow free by mid-summer in early 2022; glacial ice has a much lower albedo than snow, leading to accelerated heating of the glacier. Across the global cryosphere, permafrost temperatures continued to reach record highs at many high-latitude and mountain locations. In the high northern latitudes, the annual surface-air temperature across the Arctic was the fifth highest in the 123-year record. The seasonal Arctic minimum sea-ice extent, typically reached in September, was the 11th-smallest in the 43-year record; however, the amount of multiyear ice—ice that survives at least one summer melt season—remaining in the Arctic continued to decline. Since 2012, the Arctic has been nearly devoid of ice more than four years old. In Antarctica, an unusually large amount of snow and ice fell over the continent in 2022 due to several landfalling atmospheric rivers, which contributed to the highest annual surface mass balance, 15% to 16% above the 1991–2020 normal, since the start of two reanalyses records dating to 1980. It was the second-warmest year on record for all five of the long-term staffed weather stations on the Antarctic Peninsula. In East Antarctica, a heatwave event led to a new all-time record-high temperature of −9.4°C—44°C above the March average—on 18 March at Dome C. This was followed by the collapse of the critically unstable Conger Ice Shelf. More than 100 daily low sea-ice extent and sea-ice area records were set in 2022, including two new all-time annual record lows in net sea-ice extent and area in February. Across the world’s oceans, global mean sea level was record high for the 11th consecutive year, reaching 101.2 mm above the 1993 average when satellite altimetry measurements began, an increase of 3.3±0.7 over 2021. Globally-averaged ocean heat content was also record high in 2022, while the global sea-surface temperature was the sixth highest on record, equal with 2018. Approximately 58% of the ocean surface experienced at least one marine heatwave in 2022. In the Bay of Plenty, New Zealand’s longest continuous marine heatwave was recorded. A total of 85 named tropical storms were observed during the Northern and Southern Hemisphere storm seasons, close to the 1991–2020 average of 87. There were three Category 5 tropical cyclones across the globe—two in the western North Pacific and one in the North Atlantic. This was the fewest Category 5 storms globally since 2017. Globally, the accumulated cyclone energy was the lowest since reliable records began in 1981. Regardless, some storms caused massive damage. In the North Atlantic, Hurricane Fiona became the most intense and most destructive tropical or post-tropical cyclone in Atlantic Canada’s history, while major Hurricane Ian killed more than 100 people and became the third costliest disaster in the United States, causing damage estimated at $113 billion U.S. dollars. In the South Indian Ocean, Tropical Cyclone Batsirai dropped 2044 mm of rain at Commerson Crater in Réunion. The storm also impacted Madagascar, where 121 fatalities were reported. As is typical, some areas around the world were notably dry in 2022 and some were notably wet. In August, record high areas of land across the globe (6.2%) were experiencing extreme drought. Overall, 29% of land experienced moderate or worse categories of drought during the year. The largest drought footprint in the contiguous United States since 2012 (63%) was observed in late October. The record-breaking megadrought of central Chile continued in its 13th consecutive year, and 80-year record-low river levels in northern Argentina and Paraguay disrupted fluvial transport. In China, the Yangtze River reached record-low values. Much of equatorial eastern Africa had five consecutive below-normal rainy seasons by the end of 2022, with some areas receiving record-low precipitation totals for the year. This ongoing 2.5-year drought is the most extensive and persistent drought event in decades, and led to crop failure, millions of livestock deaths, water scarcity, and inflated prices for staple food items. In South Asia, Pakistan received around three times its normal volume of monsoon precipitation in August, with some regions receiving up to eight times their expected monthly totals. Resulting floods affected over 30 million people, caused over 1700 fatalities, led to major crop and property losses, and was recorded as one of the world’s costliest natural disasters of all time. Near Rio de Janeiro, Brazil, Petrópolis received 530 mm in 24 hours on 15 February, about 2.5 times the monthly February average, leading to the worst disaster in the city since 1931 with over 230 fatalities. On 14–15 January, the Hunga Tonga-Hunga Ha'apai submarine volcano in the South Pacific erupted multiple times. The injection of water into the atmosphere was unprecedented in both magnitude—far exceeding any previous values in the 17-year satellite record—and altitude as it penetrated into the mesosphere. The amount of water injected into the stratosphere is estimated to be 146±5 Terragrams, or ∼10% of the total amount in the stratosphere. It may take several years for the water plume to dissipate, and it is currently unknown whether this eruption will have any long-term climate effect.</jats:p