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{{Short description|Particle physics experiment}}
{{Italic title|string=g}}
{{Use mdy dates|date=December 2022}}
{{Use American English|date=December 2022}}
[[File:Fermilab g-2 (E989) ring.jpg|thumb|The {{mvar|g}}{{nnbsp}}−{{nnbsp}}2 storage-ring magnet at [[Fermilab]], which was originally designed for the Brookhaven {{mvar|g}}{{nnbsp}}−{{nnbsp}}2 experiment. The geometry allows for a very uniform magnetic field to be established in the ring.]] 

'''Muon {{mvar|g}}{{nnbsp}}−{{nnbsp}}2''' (pronounced "gee minus two") is a [[particle physics]] experiment at [[Fermilab]] to measure the [[anomalous magnetic dipole moment]] of a [[muon]] to a precision of 0.14&nbsp;[[Parts per million|ppm]],<ref>{{cite web |title=Muon {{mvar|g}} − 2 Experiment |type=main page |publisher=Fermilab |lang=en |url=http://muon-g-2.fnal.gov/ |access-date=April 26, 2017}}</ref> which is a sensitive test of the [[Standard Model]].<ref>{{Cite journal |last1=Keshavarzi |first1=Alex |last2=Khaw |first2=Kim Siang |last3=Yoshioka |first3=Tamaki |date=2022-01-22 |title=Muon g{{nnbsp}}−{{nnbsp}}2: A review |url=https://linkinghub.elsevier.com/retrieve/pii/S0550321322000268 |journal=Nuclear Physics B |language=en |volume=975 |pages=115675 |doi=10.1016/j.nuclphysb.2022.115675|arxiv=2106.06723 |bibcode=2022NuPhB.97515675K |s2cid=245880824 }}</ref> It might also provide evidence of the existence of new particles.<ref>{{cite journal |last=Gibney |first=Elizabeth |date=April 13, 2017 |title=Muons' big moment could fuel new physics |journal=Nature |lang=en |volume=544 |issue=7649 |pages=145–146 |doi=10.1038/544145a |pmid=28406224 |bibcode=2017Natur.544..145G|s2cid=4400589 |doi-access=free }}</ref><ref name="NYT-20230810">{{cite news |last=Miller |first=Katrina |title=Physicists Move One Step Closer to a Theoretical Showdown – The deviance of a tiny particle called the muon might prove that one of the most well-tested theories in physics is incomplete. + comment |url=https://www.nytimes.com/2023/08/10/science/physics-muons-g2-fermilab.html |date=10 August 2023 |work=[[The New York Times]] |url-status=bot: unknown |archiveurl=https://web.archive.org/web/20230811153709/https://www.nytimes.com/2023/08/10/science/physics-muons-g2-fermilab.html#permid=126945707 |archivedate=August 11, 2023 |accessdate=11 August 2023 }}</ref><ref name="nature 2023Aug10" />

The muon, like its lighter sibling the electron, acts like a tiny magnet. The parameter known as the "[[g-factor (physics)|{{mvar|g}}&nbsp;factor]]" indicates how strong the magnet is and the rate of its [[gyration]] in an externally applied magnetic field. It is this rate of gyration that is indirectly measured in the Muon ''g''{{nnbsp}}−{{nnbsp}}2 experiment. 

The value of {{mvar|g}} is slightly larger than&nbsp;2, hence the name of the experiment. This difference from&nbsp;2 (the "anomalous" part) is caused by higher-order contributions from [[quantum field theory]]. In measuring {{mvar|g}}{{nnbsp}}−{{nnbsp}}2 with high precision and comparing its value to the theoretical prediction, physicists will discover whether the experiment agrees with theory. Any deviation would point to as yet undiscovered subatomic particles that exist in nature.<ref>{{cite press release |title=Muon {{mvar|g}}{{nnbsp}}−{{nnbsp}}2 Collaboration to solve mystery |website=Muon {{mvar|g}}{{nnbsp}}−{{nnbsp}}2 Experiment |publisher=Fermilab |lang=en |url=http://muon-g-2.fnal.gov/1-muon-g-2-collaboration-to-solve-mystery.html |access-date=April 30, 2017 |archive-date=July 1, 2017 |archive-url=https://web.archive.org/web/20170701180929/http://muon-g-2.fnal.gov/1-muon-g-2-collaboration-to-solve-mystery.html |url-status=dead }}</ref>

On July 9, 2023 the Fermilab collaboration concluded the experiment after six years of data collection.<ref name="endofdatataking"/> The initial results (based on data from the first year of the experiment's operation) were released on April&nbsp;7, 2021.<ref>{{ cite press release |title=First results from the Muon {{mvar|g}}{{nnbsp}}−{{nnbsp}}2 experiment at Fermilab |date=March 7, 2021 |publisher=Fermilab |url=https://theory.fnal.gov/events/event/first-results-from-the-muon-g-2-experiment-at-fermilab/ }}</ref><ref name="NYT-20210407">{{cite news |last=Overbye |first=Dennis |author-link=Dennis Overbye |date=April 7, 2021 |title=Finding from particle research could break known laws of physics |newspaper=[[The New York Times]] |quote=It's not the next Higgs boson – yet. But the best explanation, physicists say, involves forms of matter and energy not currently known to science. |url=https://www.nytimes.com/2021/04/07/science/particle-physics-muon-fermilab-brookhaven.html |access-date=April 7, 2021 }}</ref><ref name="FL-20210407">{{cite press release |last=Marc |first=Tracy |date=April 7, 2021 |title=First results from Fermilab's Muon {{mvar|g}} − 2 experiment strengthen evidence of new physics |publisher=[[Fermilab]] |url=https://news.fnal.gov/2021/04/first-results-from-fermilabs-muon-g-2-experiment-strengthen-evidence-of-new-physics/ |access-date=April 7, 2021 }}</ref> The results from the first three years of data-taking were announced in August 2023.<ref name="NYT-20230810" /><ref name="nature 2023Aug10" /> The final results, based on the full six years of data-taking, are planned to be released in 2025.<ref name="endofdatataking"/>

== Timeline ==

=== Muon ''g'' − 2 at CERN ===
[[File:Storage ring.jpg|thumb|The storage ring of the muon {{mvar|g}}{{nnbsp}}−{{nnbsp}}2 experiment at CERN]]
The first muon {{mvar|g}}{{nnbsp}}−{{nnbsp}}2 experiments began at [[CERN]] in 1959 at the initiative of [[Leon M. Lederman]].<ref>{{Cite journal |last=Crease |first=Robert P. |date=2024-04-17 |title=Francis James Macdonald Farley. 13 October 1920—16 July 2018 |url=https://royalsocietypublishing.org/doi/10.1098/rsbm.2023.0037 |journal=Biographical Memoirs of Fellows of the Royal Society |language=en |doi=10.1098/rsbm.2023.0037 |issn=0080-4606|doi-access=free }}</ref><ref name=Farley-2004>{{cite book |last=Farley |first=Francis |author-link=Francis Farley |year=2004 |chapter=The dark side of the muon |editor=Álvarez-Gaumé, Luis |editor-link=Luis Álvarez-Gaumé |title=Infinitely CERN: Memories of fifty years of research, 1954–2004 |pages=38–41 |publisher=Editions Suzanne Hurter |location=Geneva, CH |isbn=978-2-940031-33-7 |oclc=606546795}}</ref><ref>{{cite web |title=Archives of Muon {{mvar|g}}{{nnbsp}}−{{nnbsp}}2 experiment |year=2007 |website=CERN Archive |url=http://library.cern/archives/CERN_archive/guide/experimental_physics/SC/isamuon |access-date=March 4, 2020}}</ref> A group of six physicists formed the first experiment, using the [[Synchro-Cyclotron (CERN)|Synchrocyclotron]] at CERN. The first results were published in 1961,<ref name="Cabibbo1994">{{cite book |last1=Charpak |first1=Georges |author-link1=Georges Charpak |last2=Garwin |first2=Richard L. |last3=Farley |first3=Francis J.M. |author-link3=Francis Farley |last4=Müller |first4=T. |year=1994 |chapter=Results of the {{mvar|g}}{{nnbsp}}−{{nnbsp}}2 experiment |editor1-last=Cabibbo |editor1-first=N. |editor1-link=Nicola Cabibbo |title=Lepton Physics at CERN and Frascati |chapter-url={{google books |plainurl=y |id=QixQ1Khsy_0C|page=34}} |publisher=World Scientific |isbn=9789810220785 |pages=34 ff}}</ref> with a 2% precision with respect to the theoretical value, and then the second ones with this time a 0.4% precision, hence validating the quantum electrodynamics theory.

A second experiment started in 1966 with a new group, working this time with the [[Proton Synchrotron]], also at CERN. The results were then 25&nbsp;times more precise than the previous ones and showed a quantitative discrepancy between the experimental values and the theoretical ones, and thus required the physicists to recalculate their theoretical model.

The third experiment, which started in 1969, published its final results in 1979,<ref name="CombleyFarley1981">{{cite journal |last1=Combley |first1=F. |last2=Farley |first2=F.J.M. |last3=Picasso |first3=E. |year=1981 |title=The CERN muon ({{mvar|g}} − 2) experiments |journal=Physics Reports |volume=68 |issue=2 |pages=93–119 |issn=0370-1573 |doi=10.1016/0370-1573(81)90028-4 |bibcode=1981PhR....68...93C |url=https://cds.cern.ch/record/134110}}</ref> confirming the theory with a precision of 0.0007%.

The United States took over the {{mvar|g}}{{nnbsp}}−{{nnbsp}}2 experiment in 1984.<ref name=muong2_CERN_website>{{cite press release |title=Enigma of the muon |publisher=[[European Organization for Nuclear Research]] (CERN) |url=http://public-archive.web.cern.ch/public-archive/en/research/G2-en.html |access-date=July 19, 2018 }}</ref>

=== Muon ''g'' − 2 at Brookhaven National Laboratory ===
The next stage of muon {{mvar|g}}{{nnbsp}}−{{nnbsp}}2 research was conducted at the [[Brookhaven National Laboratory]] (BNL) [[Alternating Gradient Synchrotron]]; the experiment was known as ('''BNL''') '''Muon E821''' experiment,<ref name="halfresults"/> but it has also been called "muon experiment at BNL" or "(muon) ''g'' − 2 at BNL" etc.<ref name="endofdatataking"/> Brookhaven's Muon ''g'' − 2 experiment was constructed from 1989 to 1996 and collected data from 1997 to 2001.<ref>{{ cite web |url=https://www.bnl.gov/science/g-2/ |title=Muon ''g'' − 2 Experiment |website=bnl.gov |date=11 August 2023 }}</ref>

The experiment was done similarly to the last of the CERN experiments with the goal of having 20&nbsp;times better precision. The technique involved storing 3.094&nbsp;[[GeV]] muons in a uniform measured magnetic field and observing the difference of the muon spin precession and rotation frequency via detection of the muon decay electrons. The advance in precision relied crucially on a much more intense beam than was available at CERN and the injection of muons into the storage ring, whereas the previous CERN experiments had injected pions into the storage ring, of which only a small fraction decay into muons that are stored. The experiment used a much more uniform magnetic field using a superferric superconducting storage ring magnet, a passive superconducting inflector magnet, fast muon kickers to deflect the injected muons onto stored orbits, a beam tube NMR trolley that could map the magnetic field in the storage region, and numerous other experimental advances.  The experiment took data with positive and negative muons between 1997 and 2001. Its final result is {{nobr| {{mvar|a}}{{sub|μ}} {{=}} ({{mvar|g}}{{nnbsp}}−{{nnbsp}}2)/2 {{=}} 11659208.0(5.4)(3.3) × {{10^|−10}} }} obtained by combination of consistent results with similar precision from positive and negative muons.<ref>{{cite journal |last1=Bennett |first1=G.W. |last2=Bousquet |first2=B. |last3=Brown |first3=H.N. |last4=Bunce |first4=G. |last5=Carey |first5=R.M. |last6=Cushman |first6=P. |last7=Danby |first7=G.T. |last8=Debevec |first8=P.T. |last9=Deile |first9=M. |last10=Deng |first10=H. |collaboration=Muon {{mvar|g}} − 2 Collaboration |display-authors=6 |date=April 7, 2006 |title=Final report of the E821 muon anomalous magnetic moment measurement at BNL |journal=Physical Review&nbsp;D |volume=73 |issue=7 |page=072003 |arxiv=hep-ex/0602035 |bibcode=2006PhRvD..73g2003B |s2cid=53539306 |doi=10.1103/PhysRevD.73.072003 |url=https://link.aps.org/doi/10.1103/PhysRevD.73.072003}}</ref>

=== Muon ''g'' − 2 at Fermilab ===
[[Fermilab]] is continuing the experiment conducted at Brookhaven<ref name="Farley2004">{{cite journal |last1=Farley |first1=F. |year=2004 |title=The 47&nbsp;years of muon {{mvar|g}} − 2 |journal=Progress in Particle and Nuclear Physics |volume=52 |issue=1 |pages=1–83 |issn=0146-6410 |doi=10.1016/j.ppnp.2003.09.004 |bibcode=2004PrPNP..52....1F}}</ref> to measure the [[anomalous magnetic dipole moment]] of the [[muon]]. The Brookhaven experiment ended in 2001, but ten years later Fermilab, which is able to produce a purer beam of muons than Brookhaven, acquired the equipment.<ref>{{Cite web |last=Cho |first=Adrian |date=2021-04-07 |title=Particle mystery deepens, as physicists confirm that the muon is more magnetic than predicted |url=https://www.science.org/content/article/particle-mystery-deepens-physicists-confirm-muon-more-magnetic-predicted |archive-url=https://archive.today/20230518134726/https://www.science.org/content/article/particle-mystery-deepens-physicists-confirm-muon-more-magnetic-predicted |archive-date=2023-05-18 |access-date=2023-05-18 |website=www.science.org |language=en}}</ref> The goal is to make a more accurate measurement (smaller ''[[Confidence interval|σ]]'') which will either eliminate the discrepancy between Brookhaven's results and theory predictions or confirm it as an experimentally observable example of [[physics beyond the Standard Model]].

The magnet was refurbished and powered on in September&nbsp;2015, and has been confirmed to have the same 1.3&nbsp;[[Parts per million|ppm]] basic magnetic field uniformity that it had before the move.

As of October&nbsp;2016 the magnet has been rebuilt and carefully [[shim (magnetism)|shimmed]] to produce a highly uniform magnetic field. New efforts at Fermilab have resulted in a three-fold improved overall uniformity, which is important for the new measurement at its higher precision goal.<ref>{{cite conference |book-title=Proceedings, 12th&nbsp;International Conference on Beauty, Charm, and Hyperons in Hadronic Interactions (BEACH 2016): Fairfax, Virginia, USA, June 12–18, 2016 |conference=XIIth International Conference on Beauty, Charm, and Hyperons in Hadronic Interactions |conference-url=http://beach2016.gmu.edu/ |last=Holzbauer |first=J. L. |date=December 9, 2016 |title=The Muon {{mvar|g}} − 2 Experiment Overview and Status as of June 2016 |journal=J. Phys. Conf. Ser. |volume=770 |page=012038 |doi=10.1088/1742-6596/770/1/012038 |arxiv=1610.10069 }} {{cite web |url=https://inspirehep.net/record/1495244 |title=alt. source |via=inSPIRE}}</ref>

In April&nbsp;2017 the collaboration was preparing the experiment for the first production run with protons – to calibrate detector systems. The magnet received its first beam of muons in its new location on May&nbsp;31, 2017.<ref>{{cite press release |title=Muon magnet's moment has arrived |date=May 31, 2017 |publisher=Fermilab |url=http://news.fnal.gov/2017/05/muon-magnets-moment-arrived/}}</ref> Data taking was planned to run until 2020.<ref>{{cite conference |book-title= 18th&nbsp;International Workshop on Neutrino Factories and Future Neutrino Facilities Search (NuFact16) Quy Nhon, Vietnam, August 21–27, 2016 |last1=Gohn |first1=W. |display-authors=etal |collaboration=Muon {{mvar|g}} − 2 Collaboration |date=November 15, 2016 |title=The muon {{mvar|g}} − 2 experiment at Fermilab |arxiv=1611.04964 }} {{cite web |url=http://inspirehep.net/record/1498085 |via=inSPIRE |title=alt source}}</ref>

On April 7, 2021, the result from run 1 experiment were published: {{nowrap|1={{math|''a''}}{{sub|μ}} = {{val|0.00116592040|(54)}}}}. The new experimental world-average results announced by the Muon {{mvar|g}}{{nnbsp}}−{{nnbsp}}2 collaboration are: {{mvar|g}}-factor: {{val|2.00233184122|(82)}}, anomalous magnetic moment: {{val|0.00116592061|(41)}}. The combined results from Fermilab and Brookhaven show a difference with theory at a significance of 4.2&nbsp;sigma (or standard deviations), slightly under the 5&nbsp;sigma that particle physicists require to claim a discovery, but still evidence of new physics. The chance that a statistical fluctuation would produce equally striking results is about {{nobr|1 in 40,000.}}<ref name="FL-20210407"/>

Data-taking came to an end on July 9, 2023, when the collaboration shut off the muon beam, concluding the experiment after six years of data collection. On August 10, 2023, the results from run 1, 2 and 3 (that is, the first three years of data-taking) were announced, giving a new world average of {{nowrap|1={{math|''a''}}{{sub|μ}} = {{val|0.00116592059|(22)}}}}, representing an improvement of two in the error factor from the 2021 results.<ref name="halfresults">{{cite journal|last1=Aguillard|first1=D.P.|authorlink1=|display-authors=etal|date=10 August 2023|title=Measurement of the Positive Muon Anomalous Magnetic Moment to 0.20 PPM|url=https://muon-g-2.fnal.gov/result2023.pdf|journal=Physical Review Letters|volume=131|issue=16|page=161802|doi=10.1103/PhysRevLett.131.161802|pmid=37925710|arxiv=2308.06230|bibcode=2023PhRvL.131p1802A |s2cid=260781819|access-date=}}</ref> Although this experimental result is 5.1 sigma deviation from the 2020 Standard Model theory prediction, it differs only by roughly 1 sigma from the prediction yielded by recent lattice calculations. This discrepancy between the experiment and theory is under further study.<ref name="NYT-20230810" /><ref name="nature 2023Aug10">{{cite journal |last1=Castelvecchi |first1=Davide |title=Dreams of new physics fade with latest muon magnetism result: Precision test of particle's magnetism confirms earlier shocking findings — but theory might not need a rethink after all |url=https://www.nature.com/articles/d41586-023-02532-6?WT.ec_id=NATURE-20230817&sap-outbound-id=9B10F0EF8BC6DF9D543FAA7A7CC105D46DB71C66 |access-date=17 August 2023 |journal=Nature |volume=620 |issue=7974|doi=10.1038/d41586-023-02532-6 |date=10 August 2023|pages=473–474 |pmid=37563473 |s2cid=260807806 }}</ref> 

The Fermilab experiment will reach its final, most precise measurement of the muon magnetic moment once scientists incorporate all six years of data in their analysis; the plan is to release their final result in 2025.<ref name="endofdatataking">{{cite press release |title=Muon ''g'' − 2 doubles down with latest measurement, explores uncharted territory in search of new physics |date=August 10, 2023 |publisher=Fermilab |url=https://news.fnal.gov/2023/08/muon-g-2-doubles-down-with-latest-measurement/ }}</ref>

== Theory of magnetic moments ==
The {{mvar|g}}&nbsp;factor of a charged lepton ([[electron]], [[muon]], or [[Tau (particle)|tau]]) is very nearly&nbsp;2. The difference from 2 (the "anomalous" part) depends on the lepton, and can be computed quite precisely based on the current [[Standard Model of particle physics]]. Measurements of the electron's {{mvar|g}}&nbsp;factor are in excellent agreement with this computation. The Brookhaven experiment did this measurement for muons, a much more technically difficult measurement due to their short lifetime, and detected a tantalizing, but not definitive, discrepancy between the measured value and the prediction of the Standard Model.<ref>{{cite press release |title=Physicists publish worldwide consensus of muon magnetic moment calculation |date=June 11, 2020 |publisher=Fermilab |url=https://news.fnal.gov/2020/06/physicists-publish-worldwide-consensus-of-muon-magnetic-moment-calculation/}}</ref>

The computation of the Standard Model prediction of the muon's {{mvar|g}}&nbsp;factor is extremely complicated, and several different approaches exist. The main difficulty is that the value is affected by [[Virtual particle|virtual]] [[Hadron|hadrons]].<ref>{{Cite web |date=2020-11-18 |title=The Many Paths of Muon Math |url=https://www.bnl.gov/newsroom/news.php?a=217530 |access-date=2023-05-18 |website=Brookhaven National Laboratory |language=en}}</ref> 

In 2020, the Muon ''g'' − 2 Theory Initiative published their computed consensus value of the muon's {{mvar|g}}&nbsp;factor, based on perturbative methods.<ref>{{Cite journal |last=Muon g-2 Theory Initiative |date=2020-12-03 |title=The anomalous magnetic moment of the muon in the Standard Model |url=https://www.sciencedirect.com/science/article/pii/S0370157320302556 |journal=Physics Reports |series= |language=en |volume=887 |pages=1–166 |doi=10.1016/j.physrep.2020.07.006 |arxiv= 2006.04822|bibcode= 2020PhR...887....1A|s2cid= 219559166|issn=}}</ref><ref>{{Cite web |title=Home {{!}} Muon ''g'' − 2 Theory |url=https://muon-gm2-theory.illinois.edu/ |access-date=2023-03-14 |website=muon-gm2-theory.illinois.edu}}</ref> In 2021, the Budapest–Marseille–Wuppertal (BMW) collaboration published results of [[lattice QCD]] computations of the {{mvar|g}}&nbsp;factor<ref>{{Cite journal |last1=Borsanyi |first1=Sz. |last2=Fodor |first2=Z. |last3=Guenther |first3=J. N. |last4=Hoelbling |first4=C. |last5=Katz |first5=S. D. |last6=Lellouch |first6=L. |last7=Lippert |first7=T. |last8=Miura |first8=K. |last9=Parato |first9=L. |last10=Szabo |first10=K. K. |last11=Stokes |first11=F. |last12=Toth |first12=B. C. |last13=Torok |first13=Cs. |last14=Varnhorst |first14=L. |date=2021-05-06 |title=Leading hadronic contribution to the muon magnetic moment from lattice QCD |url=https://www.nature.com/articles/s41586-021-03418-1 |journal=Nature |language=en |volume=593 |issue=7857 |pages=51–55 |arxiv=2002.12347 |bibcode=2021Natur.593...51B |doi=10.1038/s41586-021-03418-1 |issn=0028-0836 |pmid=33828303 |s2cid=221151004}}</ref><ref>{{Cite web |title=Budapest–Marseille–Wuppertal Collaboration |url=http://www.bmw.uni-wuppertal.de/ |access-date= |website=www.bmw.uni-wuppertal.de}}</ref> which stood between the experimental value obtained at Fermilab and the theoretical value calculated by the Muon ''g'' − 2 Theory Initiative. Subsequent works by the Coordinated Lattice Simulations (CLS) group<ref>{{Cite journal |last1=Cè |first1=M. |last2=Gérardin |first2=A. |last3=von Hippel |first3=G. |last4=Hudspith |first4=R. J. |last5=Kuberski |first5=S. |last6=Meyer |first6=H. B. |last7=Miura |first7=K. |last8=Mohler |first8=D. |last9=Ottnad |first9=K. |last10=Paul |first10=S. |last11=Risch |first11=A. |last12=San José |first12=T. |last13=Wittig |first13=H. |date=2022-12-13 |title=Window observable for the hadronic vacuum polarization contribution to the muon $g\ensuremath{-}2$ from lattice QCD |journal=Physical Review D |volume=106 |issue=11 |pages=114502 |doi=10.1103/PhysRevD.106.114502 |s2cid=56285714|doi-access=free |arxiv=2206.06582 }}</ref><ref>{{Cite web |title=Coordinated Lattice Simulations |url=https://wiki-zeuthen.desy.de/CLS/ |website=DESY}}</ref> and the European Twisted Mass Collaboration (ETMC)<ref>{{Cite arXiv |eprint=2212.10490 |class=hep-ph |first1=Constantia |last1=Alexandrou|author1-link=Constantia Alexandrou |first2=Simone |last2=Bacchio |title=Short \& intermediate distance HVP contributions to muon ''g'' − 2: SM (lattice) prediction versus e<sup>+</sup>e<sup>−</sup> annihilation data |date=2022-12-20 |last3=Dimopoulos |first3=Petros |last4=Finkenrath |first4=Jacob |last5=Frezzotti |first5=Roberto |last6=Gagliardi |first6=Giuseppe |last7=Garofalo |first7=Marco |last8=Hadjiyiannakou |first8=Kyriakos |last9=Kostrzewa |first9=Bartosz |last10=Jansen |first10=Karl |last11=Lubicz |first11=Vittorio |last12=Petschlies |first12=Marcus |last13=Sanfilippo |first13=Francesco |last14=Simula |first14=Silvano |last15=Urbach |first15=Carsten}}</ref><ref>{{Cite web |title=European Twisted Mass Collaboration |url=https://www-zeuthen.desy.de/~kjansen/etmc/ |access-date=2023-03-14 |website=www-zeuthen.desy.de}}</ref> have come closer each to the theoretical value, suggesting there could be systematical errors in the estimation of the [[R (cross section ratio)|R-ratio]] of the [[QCD vacuum|hadronic vacuum]] [[Vacuum polarization|polarization]] used by Fermilab.<ref>{{Cite journal |arxiv=2212.08467 |first1=Constantia |last1=Alexandrou |first2=Simone |last2=Bacchio |title=Probing the Energy-Smeared <math>R</math> Ratio Using Lattice QCD |date=2023 |last3=De Santis |first3=Alessandro |last4=Dimopoulos |first4=Petros |last5=Finkenrath |first5=Jacob |last6=Frezzotti |first6=Roberto |last7=Gagliardi |first7=Giuseppe |last8=Garofalo |first8=Marco |last9=Hadjiyiannakou |first9=Kyriakos |last10=Kostrzewa |first10=Bartosz |last11=Jansen |first11=Karl |last12=Lubicz |first12=Vittorio |last13=Petschlies |first13=Marcus |last14=Sanfilippo |first14=Francesco |last15=Simula |first15=Silvano|journal=Physical Review Letters |volume=130 |issue=24 |page=241901 |doi=10.1103/PhysRevLett.130.241901 |pmid=37390427 |bibcode=2023PhRvL.130x1901A |s2cid=258823484 }}</ref>

== Design ==
[[File:Littlemove5-hr.jpg|right|thumb|The {{mvar|g}}{{nnbsp}}−{{nnbsp}}2 ring arriving at its final destination{{snd}}the experimental hall (MC1) at Fermilab{{snd}}on July&nbsp;30, 2014]]

=== Magnet ===
Central to the experiment is a {{convert|50|foot|m|adj=on}}-diameter [[superconducting magnet]] with an exceptionally uniform magnetic field, used as a [[storage ring]]. This was transported, in one piece, from Brookhaven in [[Long Island]], New York, to Fermilab in the summer of 2013. The move traversed {{convert|3200|mi|km}} over 35&nbsp;days,<ref>{{cite news |first1=David |last1=Hertzog |first2=Lee |last2=Roberts |date=October 27, 2014 |title=Muon {{mvar|g}} − 2 storage ring starts a new life |website=CERN Courier |lang=en-GB |url=http://cerncourier.com/cws/article/cern/58931 |access-date=April 26, 2017}}</ref> mostly on a barge down the [[East Coast of the United States|East Coast]] and through [[Mobile, Alabama]], to the [[Tennessee–Tombigbee Waterway]] and then briefly on the [[Mississippi River|Mississippi]]. The initial and final legs were on a special truck traveling closed highways at night.

The Muon {{mvar|g}}{{nnbsp}}−{{nnbsp}}2 experiment injected 3.1 GeV/c polarized muons produced at the Fermilab Muon Campus into the storage ring that was significantly upgraded from the Brookhaven experiment.

[[File:PbF2 Crystal SIPM.png|left|thumb|Sample 25&nbsp;mm × 25&nbsp;mm × 140&nbsp;mm [[lead(II) fluoride|PbF{{sub|2}}]] crystals (bare and wrapped in Millipore paper) are pictured together with a 16&nbsp;channel monolithic Hamamatsu SiPM.]]

=== Detectors ===
The magnetic moment measurement is realized by 24&nbsp;electromagnetic [[Calorimeter (particle physics)|calorimetric detectors]], which are distributed uniformly on the inside of the storage ring. The calorimeters measure the energy and time of arrival (relative to the injection time) of the decay positrons (and their count) from the muon [[Particle decay|decay]] in the storage ring. After a muon decays into a positron and two neutrinos, the positron ends up with less energy than the original muon. Thus, the magnetic field curls it inward where it hits a segmented [[lead(II) fluoride]] (PbF{{sub|2}}) calorimeter read out by silicon [[Photomultiplier|photo-multipliers]] (SiPM).<ref name="TDR">{{cite report |last1=Grange |first1=J. |last2=Guarino |first2=V. |last3=Winter |first3=P. |last4=Wood |first4=K. |last5=Zhao |first5=H. |last6=Carey |first6=R.M. |last7=Gastler |first7=D. |last8=Hazen |first8=E. |last9=Kinnaird |first9=N. |collaboration=Muon {{mvar|g}} − 2 Collaboration |display-authors=6 |date=January 27, 2015 |title=Muon ({{mvar|g}} − 2) Technical Design Report |arxiv=1501.06858 |bibcode=2015arXiv150106858G }} {{cite web |url=http://inspirehep.net/record/1341289 |title=alt. source |via=inSPIRE}}</ref>

The [[Particle detector|tracking detectors]] register the trajectory of the positrons from the muon decay in the storage ring. The tracker can provide a muon [[electric dipole moment]] measurement, but not directly the magnetic moment measurement. The main purpose of the tracker is to measure the muon beam profile, as well as resolution of pile-up of events (for reduction of the systematic uncertainty in the calorimeter measurement).<ref name=TDR/>

[[File:Tracker g-2.jpg|thumb|One of the 4&nbsp;rows of 32&nbsp;straws is shown. A straw (length of 100&nbsp;mm, and diameter of 5&nbsp;mm) acts like an [[ionisation chamber]] filled with 1:1 [[argon]]:[[ethane]], with a central cathode wire at +1.6&nbsp;kV.]]

=== Magnetic field ===
To measure the magnetic moment to [[Parts-per notation|ppb]] level of precision requires a uniform average magnetic field to be of the same level precision. The experimental goal of {{mvar|g}}{{nnbsp}}−{{nnbsp}}2 is to achieve an uncertainty level on the magnetic field to 70&nbsp;ppb averaged over time and muon distribution. A uniform field of {{val|1.45|ul=T}} is created in the storage ring using superconducting magnets, and the field value will be actively mapped throughout the ring using an [[NMR]] probe on a mobile trolley (without breaking the vacuum). Calibration of the trolley is referenced to the [[Larmor frequency]] of a proton in a spherical water sample at a reference temperature (34.7&nbsp;°C), and is cross-calibrated to a novel [[helium-3]] magnetometer.<ref name=TDR/>

=== Data acquisition ===
An essential component of the experiment is the [[data acquisition]] (DAQ) system, which manages the data flow from the detector electronics. The requirement for the experiment is to acquire raw data at a rate of 18&nbsp;GB/s. This is accomplished by employing parallel data-processing architecture using 24&nbsp;high-speed [[Graphics processing unit|GPUs]] (NVIDIA Tesla K40) to process data from 12&nbsp;bit waveform digitisers. The set-up is controlled by the MIDAS DAQ software framework. The DAQ system processes data from 1296&nbsp;calorimeter channels, 3&nbsp;straw tracker stations, and auxiliary detectors (e.g. entrance muon counters). The total data output of the experiment is estimated at 2&nbsp;[[byte|PB]].<ref>{{cite conference |last=Gohn |first=W. |collaboration=Muon {{mvar|g}} − 2 Collaboration |display-authors=etal |date=November 15, 2016 |title=Data acquisition with GPUs: The DAQ for the muon {{mvar|g}} − 2 experiment at Fermilab |book-title=Proceedings, 38th International Conference on High Energy Physics (ICHEP 2016): Chicago, Illinois, USA, August 3–10, 2016 |page=174 |arxiv=1611.04959 |doi=10.22323/1.282.0174 |bibcode=2016arXiv161104959G |doi-access=free }} {{cite web |url=http://inspirehep.net/record/1498145 |title=alt. source |via=inSPIRE}}</ref>
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== Collaboration ==
The following universities, laboratories, and companies are participating in the experiment:<ref>{{cite web |title=Muon {{mvar|g}} − 2 Collaboration |website=Muon {{mvar|g}} − 2 Experiment |publisher=Fermilab |lang=en |url=http://muon-g-2.fnal.gov/collaboration.html |access-date=April 26, 2017}}</ref>
{{div col|colwidth=22em}}

=== Universities ===
* [[Boston University]]
* [[Cornell University]]
* [[Johannes Gutenberg University Mainz]]
* [[University of Chicago]]
* [[University of Illinois at Urbana-Champaign]]
* [[James Madison University]]
* Korea Advanced Institute of Science and Technology ([[KAIST]])
* [[University of Kentucky]]
* [[University of Liverpool]]
* [[Lancaster University]]
* [[University College London]]
* [[University of Manchester]]
* [[University of Massachusetts]]
* [[Michigan State University]]
* [[University of Michigan]]
* [[University of Mississippi]]
* [[University of Molise|Università del Molise]]
* [[University of Naples Federico II|Università degli Studi di Napoli Federico II]]
* [[North Central College]]
* [[Northern Illinois University]]
* [[Regis University]]
* [[Shanghai Jiao Tong University]]
* [[Technische Universitat Dresden]]
* [[University of Udine|Università di Udine]]
* [[University of Virginia]]
* [[University of Washington]]

=== Laboratories ===
* [[Argonne National Laboratory]]
* [[Brookhaven National Laboratory]]
* [[Fermi National Accelerator Laboratory]]
* [[Budker Institute of Nuclear Physics]]
* [[Istituto Nazionale di Fisica Nucleare]]
* [[Joint Institute for Nuclear Research|Joint Institute for Nuclear Research, Dubna]]
* [[Laboratori Nazionali di Frascati]]
* [[Istituto Nazionale di Fisica Nucleare|INFN, Sezione di Napoli]]
* [[Istituto Nazionale di Fisica Nucleare|INFN, Sezione di Pisa]]
* [[Istituto Nazionale di Fisica Nucleare|INFN, Sezione di Roma Tor Vergata]]
* [[Institute for Basic Science]], S. Korea
{{div col end}}

== References ==
{{reflist|25em}}

== External links ==
* {{Official website}}
* {{cite web |url=https://www.reddit.com/r/IAmA/comments/mvi5im/i_am_muon_g2_group_at_argonne_we_are_part_of_the/ |title=Muon {{mvar|g}} − 2 group at Argonne |date=April 21, 2021 |website=[[Reddit]] – Ask Me Anything |publisher= |via=}}
* {{cite web |url=https://inspirehep.net/experiments/1108252 |title=Record for Muon {{mvar|g}} − 2 Experiment Record |via=[[INSPIRE-HEP]]}}

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