Final Report on the Measurement of the Positive Muon… — Plain-Language Explanation

Original authors: 2 Collaboration, D. P. Aguillard (University of Michigan, Ann Arbor, Michigan, USA), T. Albahri (University of Liverpool, Liverpool, United Kingdom), D. Allspach (Fermi National Accelerator Laboratory2 Collaboration, D. P. Aguillard (University of Michigan, Ann Arbor, Michigan, USA), T. Albahri (University of Liverpool, Liverpool, United Kingdom), D. Allspach (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), J. Annala (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), K. Badgley (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), S. Baeßler (University of Virginia, Charlottesville, Virginia, USA), L. Bailey (Department of Physics and Astronomy, University College London, London, United Kingdom), E. Barlas-Yucel (University of Illinois at Urbana-Champaign, Urbana, Illinois, USA), T. Barrett (Cornell University, Ithaca, New York, USA), E. Barzi (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), F. Bedeschi (INFN, Sezione di Pisa, Pisa, Italy), M. Berz (Michigan State University, East Lansing, Michigan, USA), M. Bhattacharya (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), H. P. Binney (University of Washington, Seattle, Washington, USA), P. Bloom (North Central College, Naperville, Illinois, USA), J. Bono (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), E. Bottalico (University of Liverpool, Liverpool, United Kingdom), T. Bowcock (University of Liverpool, Liverpool, United Kingdom), S. Braun (University of Washington, Seattle, Washington, USA), M. Bressler (Department of Physics, University of Massachusetts, Amherst, Massachusetts, USA), G. Cantatore (INFN, Sezione di Trieste, Trieste, Italy), R. M. Carey (Boston University, Boston, Massachusetts, USA), B. C. K. Casey (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), D. Cauz (Università di Udine, Udine, Italy), R. Chakraborty (University of Kentucky, Lexington, Kentucky, USA), A. Chapelain (Cornell University, Ithaca, New York, USA), S. Chappa (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), S. Charity (University of Liverpool, Liverpool, United Kingdom), C. Chen (Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai, China, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China), M. Cheng (University of Illinois at Urbana-Champaign, Urbana, Illinois, USA), R. Chislett (Department of Physics and Astronomy, University College London, London, United Kingdom), Z. Chu (School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China), T. E. Chupp (University of Michigan, Ann Arbor, Michigan, USA), C. Claessens (University of Washington, Seattle, Washington, USA), F. Confortini (INFN, Sezione di Napoli, Naples, Italy), M. E. Convery (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), S. Corrodi (Argonne National Laboratory, Lemont, Illinois, USA), L. Cotrozzi (University of Liverpool, Liverpool, United Kingdom), J. D. Crnkovic (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), S. Dabagov (INFN, Laboratori Nazionali di Frascati, Frascati, Italy), P. T. Debevec (University of Illinois at Urbana-Champaign, Urbana, Illinois, USA), S. Di Falco (INFN, Sezione di Pisa, Pisa, Italy), G. Di Sciascio (INFN, Sezione di Roma Tor Vergata, Rome, Italy), S. Donati (INFN, Sezione di Pisa, Pisa, Italy), B. Drendel (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), A. Driutti (INFN, Sezione di Pisa, Pisa, Italy, University of Kentucky, Lexington, Kentucky, USA), M. Eads (Northern Illinois University, DeKalb, Illinois, USA), A. Edmonds (Boston University, Boston, Massachusetts, USA, City University of New York at York College, Jamaica, New York, USA), J. Esquivel (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), M. Farooq (University of Michigan, Ann Arbor, Michigan, USA), R. Fatemi (University of Kentucky, Lexington, Kentucky, USA), K. Ferraby (University of Liverpool, Liverpool, United Kingdom), C. Ferrari (INFN, Sezione di Pisa, Pisa, Italy), M. Fertl (Institute of Physics and Cluster of Excellence PRISMA++, Johannes Gutenberg University Mainz, Mainz, Germany), A. T. Fienberg (University of Washington, Seattle, Washington, USA), A. Fioretti (INFN, Sezione di Pisa, Pisa, Italy), D. Flay (Department of Physics, University of Massachusetts, Amherst, Massachusetts, USA), S. B. Foster (University of Kentucky, Lexington, Kentucky, USA, Boston University, Boston, Massachusetts, USA), H. Friedsam (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), N. S. Froemming (Northern Illinois University, DeKalb, Illinois, USA), C. Gabbanini (INFN, Sezione di Pisa, Pisa, Italy), I. Gaines (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), S. Ganguly (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), J. George (Department of Physics, University of Massachusetts, Amherst, Massachusetts, USA), L. K. Gibbons (Cornell University, Ithaca, New York, USA), A. Gioiosa (Università del Molise, Campobasso, Italy), K. L. Giovanetti (Department of Physics and Astronomy, James Madison University, Harrisonburg, Virginia, USA), P. Girotti (INFN, Sezione di Pisa, Pisa, Italy), W. Gohn (University of Kentucky, Lexington, Kentucky, USA), L. Goodenough (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), T. Gorringe (University of Kentucky, Lexington, Kentucky, USA), J. Grange (University of Michigan, Ann Arbor, Michigan, USA), S. Grant (Argonne National Laboratory, Lemont, Illinois, USA, Department of Physics and Astronomy, University College London, London, United Kingdom), F. Gray (Regis University, Denver, Colorado, USA), S. Haciomeroglu (Center for Axion and Precision Physics), T. Halewood-Leagas (University of Liverpool, Liverpool, United Kingdom), D. Hampai (INFN, Laboratori Nazionali di Frascati, Frascati, Italy), F. Han (University of Kentucky, Lexington, Kentucky, USA), J. Hempstead (University of Washington, Seattle, Washington, USA), D. W. Hertzog (University of Washington, Seattle, Washington, USA), G. Hesketh (Department of Physics and Astronomy, University College London, London, United Kingdom), E. Hess (INFN, Sezione di Pisa, Pisa, Italy), A. Hibbert (University of Liverpool, Liverpool, United Kingdom), Z. Hodge (University of Washington, Seattle, Washington, USA), S. Y. Hoh (Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai, China, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China), K. W. Hong (University of Virginia, Charlottesville, Virginia, USA), R. Hong (Argonne National Laboratory, Lemont, Illinois, USA, University of Kentucky, Lexington, Kentucky, USA), T. Hu (Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai, China, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China), Y. Hu (School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China), M. Iacovacci (INFN, Sezione di Napoli, Naples, Italy), M. Incagli (INFN, Sezione di Pisa, Pisa, Italy), S. Israel (Boston University, Boston, Massachusetts, USA, Department of Physics, University of Massachusetts, Amherst, Massachusetts, USA), P. Kammel (University of Washington, Seattle, Washington, USA), M. Kargiantoulakis (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), M. Karuza (INFN, Sezione di Trieste, Trieste, Italy), J. Kaspar (University of Washington, Seattle, Washington, USA), D. Kawall (Department of Physics, University of Massachusetts, Amherst, Massachusetts, USA), L. Kelton (University of Kentucky, Lexington, Kentucky, USA, Department of Physics and Astronomy, Trinity University, San Antonio, Texas, USA), A. Keshavarzi (Department of Physics and Astronomy, University College London, London, United Kingdom), D. S. Kessler (Department of Physics, University of Massachusetts, Amherst, Massachusetts, USA), K. S. Khaw (Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai, China, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China), Z. Khechadoorian (Cornell University, Ithaca, New York, USA), B. Kiburg (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), M. Kiburg (Fermi National Accelerator Laboratory, Batavia, Illinois, USA, North Central College, Naperville, Illinois, USA), O. Kim (University of Mississippi, University, Mississippi, USA), N. Kinnaird (Boston University, Boston, Massachusetts, USA), E. Kraegeloh (University of Michigan, Ann Arbor, Michigan, USA), J. LaBounty (University of Washington, Seattle, Washington, USA), K. R. Labe (Cornell University, Ithaca, New York, USA), M. Lancaster (Department of Physics and Astronomy, University of Manchester, Manchester, United Kingdom), S. Lee (Center for Axion and Precision Physics), B. Li (School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China), D. Li (School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China), L. Li (School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China), I. Logashenko (Budker Institute of Nuclear Physics, Novosibirsk, Russia), A. Lorente Campos (University of Kentucky, Lexington, Kentucky, USA), Z. Lu (School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China), A. Lucà (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), G. Lukicov (Department of Physics and Astronomy, University College London, London, United Kingdom), A. Lusiani (INFN, Sezione di Pisa, Pisa, Italy), A. L. Lyon (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), B. MacCoy (University of Washington, Seattle, Washington, USA), R. Madrak (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), K. Makino (Michigan State University, East Lansing, Michigan, USA), S. Mastroianni (INFN, Sezione di Napoli, Naples, Italy), R. McCarthy (Boston University, Boston, Massachusetts, USA), J. P. Miller (Boston University, Boston, Massachusetts, USA), S. Miozzi (INFN, Sezione di Roma Tor Vergata, Rome, Italy), B. Mitra (University of Mississippi, University, Mississippi, USA), J. P. Morgan (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), W. M. Morse (Brookhaven National Laboratory, Upton, New York, USA), J. Mott (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), A. Nath (INFN, Sezione di Napoli, Naples, Italy), J. K. Ng (Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai, China, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China), H. Nguyen (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), Y. Oksuzian (Argonne National Laboratory, Lemont, Illinois, USA), Z. Omarov (Korea Advanced Institute of Science and Technology, Center for Axion and Precision Physics), W. Osar (Cornell University, Ithaca, New York, USA), R. Osofsky (University of Washington, Seattle, Washington, USA), S. Park (Center for Axion and Precision Physics), G. Pauletta (Università di Udine, Udine, Italy), J. Peck (University of Kentucky, Lexington, Kentucky, USA), G. M. Piacentino (Università del Molise, Campobasso, Italy), R. N. Pilato (University of Liverpool, Liverpool, United Kingdom), K. T. Pitts (University of Illinois at Urbana-Champaign, Urbana, Illinois, USA), B. Plaster (University of Kentucky, Lexington, Kentucky, USA), N. Pohlman (Northern Illinois University, DeKalb, Illinois, USA), C. C. Polly (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), D. Počanić (University of Virginia, Charlottesville, Virginia, USA), J. Price (University of Liverpool, Liverpool, United Kingdom), B. Quinn (University of Mississippi, University, Mississippi, USA), M. U. H. Qureshi (Institute of Physics and Cluster of Excellence PRISMA++, Johannes Gutenberg University Mainz, Mainz, Germany), G. Rakness (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), S. Ramachandran (Argonne National Laboratory, Lemont, Illinois, USA), E. Ramberg (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), R. Reimann (Institute of Physics and Cluster of Excellence PRISMA++, Johannes Gutenberg University Mainz, Mainz, Germany), B. L. Roberts (Boston University, Boston, Massachusetts, USA), D. L. Rubin (Cornell University, Ithaca, New York, USA), M. Sakurai (Department of Physics and Astronomy, University College London, London, United Kingdom), L. Santi (Università di Udine, Udine, Italy), C. Schlesier (University of Illinois at Urbana-Champaign, Urbana, Illinois, USA), A. Schreckenberger (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), Y. K. Semertzidis (Center for Axion and Precision Physics, Korea Advanced Institute of Science and Technology), A. K. Soha (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), M. Sorbara (INFN, Sezione di Roma Tor Vergata, Rome, Italy), J. Stapleton (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), D. Still (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), C. Stoughton (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), D. Stratakis (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), D. Stöckinger (Institut für Kern- und Teilchenphysik, Technische Universität Dresden, Dresden, Germany), H. E. Swanson (University of Washington, Seattle, Washington, USA), G. Sweetmore (Department of Physics and Astronomy, University of Manchester, Manchester, United Kingdom), D. A. Sweigart (Cornell University, Ithaca, New York, USA), M. J. Syphers (Northern Illinois University, DeKalb, Illinois, USA), Y. Takeuchi (Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai, China, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China), D. A. Tarazona (Cornell University, Ithaca, New York, USA), T. Teubner (University of Liverpool, Liverpool, United Kingdom), A. E. Tewsley-Booth (University of Kentucky, Lexington, Kentucky, USA, University of Michigan, Ann Arbor, Michigan, USA), V. Tishchenko (Brookhaven National Laboratory, Upton, New York, USA), N. H. Tran (Boston University, Boston, Massachusetts, USA), W. Turner (University of Liverpool, Liverpool, United Kingdom), E. Valetov (Michigan State University, East Lansing, Michigan, USA), D. Vasilkova (University of Liverpool, Liverpool, United Kingdom), G. Venanzoni (University of Liverpool, Liverpool, United Kingdom), T. Walton (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), A. Weisskopf (Michigan State University, East Lansing, Michigan, USA), L. Welty-Rieger (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), P. Winter (Argonne National Laboratory, Lemont, Illinois, USA), Y. Wu (Argonne National Laboratory, Lemont, Illinois, USA), B. Yu (University of Mississippi, University, Mississippi, USA), M. Yucel (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), E. Zaid (University of Liverpool, Liverpool, United Kingdom), Y. Zeng (Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai, China, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China), C. Zhang (University of Liverpool, Liverpool, United Kingdom)

Published 2026-06-17

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Original authors: 2 Collaboration, D. P. Aguillard (University of Michigan, Ann Arbor, Michigan, USA), T. Albahri (University of Liverpool, Liverpool, United Kingdom), D. Allspach (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), J. Annala (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), K. Badgley (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), S. Baeßler (University of Virginia, Charlottesville, Virginia, USA), L. Bailey (Department of Physics and Astronomy, University College London, London, United Kingdom), E. Barlas-Yucel (University of Illinois at Urbana-Champaign, Urbana, Illinois, USA), T. Barrett (Cornell University, Ithaca, New York, USA), E. Barzi (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), F. Bedeschi (INFN, Sezione di Pisa, Pisa, Italy), M. Berz (Michigan State University, East Lansing, Michigan, USA), M. Bhattacharya (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), H. P. Binney (University of Washington, Seattle, Washington, USA), P. Bloom (North Central College, Naperville, Illinois, USA), J. Bono (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), E. Bottalico (University of Liverpool, Liverpool, United Kingdom), T. Bowcock (University of Liverpool, Liverpool, United Kingdom), S. Braun (University of Washington, Seattle, Washington, USA), M. Bressler (Department of Physics, University of Massachusetts, Amherst, Massachusetts, USA), G. Cantatore (INFN, Sezione di Trieste, Trieste, Italy), R. M. Carey (Boston University, Boston, Massachusetts, USA), B. C. K. Casey (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), D. Cauz (Università di Udine, Udine, Italy), R. Chakraborty (University of Kentucky, Lexington, Kentucky, USA), A. Chapelain (Cornell University, Ithaca, New York, USA), S. Chappa (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), S. Charity (University of Liverpool, Liverpool, United Kingdom), C. Chen (Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai, China, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China), M. Cheng (University of Illinois at Urbana-Champaign, Urbana, Illinois, USA), R. Chislett (Department of Physics and Astronomy, University College London, London, United Kingdom), Z. Chu (School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China), T. E. Chupp (University of Michigan, Ann Arbor, Michigan, USA), C. Claessens (University of Washington, Seattle, Washington, USA), F. Confortini (INFN, Sezione di Napoli, Naples, Italy), M. E. Convery (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), S. Corrodi (Argonne National Laboratory, Lemont, Illinois, USA), L. Cotrozzi (University of Liverpool, Liverpool, United Kingdom), J. D. Crnkovic (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), S. Dabagov (INFN, Laboratori Nazionali di Frascati, Frascati, Italy), P. T. Debevec (University of Illinois at Urbana-Champaign, Urbana, Illinois, USA), S. Di Falco (INFN, Sezione di Pisa, Pisa, Italy), G. Di Sciascio (INFN, Sezione di Roma Tor Vergata, Rome, Italy), S. Donati (INFN, Sezione di Pisa, Pisa, Italy), B. Drendel (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), A. Driutti (INFN, Sezione di Pisa, Pisa, Italy, University of Kentucky, Lexington, Kentucky, USA), M. Eads (Northern Illinois University, DeKalb, Illinois, USA), A. Edmonds (Boston University, Boston, Massachusetts, USA, City University of New York at York College, Jamaica, New York, USA), J. Esquivel (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), M. Farooq (University of Michigan, Ann Arbor, Michigan, USA), R. Fatemi (University of Kentucky, Lexington, Kentucky, USA), K. Ferraby (University of Liverpool, Liverpool, United Kingdom), C. Ferrari (INFN, Sezione di Pisa, Pisa, Italy), M. Fertl (Institute of Physics and Cluster of Excellence PRISMA++, Johannes Gutenberg University Mainz, Mainz, Germany), A. T. Fienberg (University of Washington, Seattle, Washington, USA), A. Fioretti (INFN, Sezione di Pisa, Pisa, Italy), D. Flay (Department of Physics, University of Massachusetts, Amherst, Massachusetts, USA), S. B. Foster (University of Kentucky, Lexington, Kentucky, USA, Boston University, Boston, Massachusetts, USA), H. Friedsam (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), N. S. Froemming (Northern Illinois University, DeKalb, Illinois, USA), C. Gabbanini (INFN, Sezione di Pisa, Pisa, Italy), I. Gaines (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), S. Ganguly (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), J. George (Department of Physics, University of Massachusetts, Amherst, Massachusetts, USA), L. K. Gibbons (Cornell University, Ithaca, New York, USA), A. Gioiosa (Università del Molise, Campobasso, Italy), K. L. Giovanetti (Department of Physics and Astronomy, James Madison University, Harrisonburg, Virginia, USA), P. Girotti (INFN, Sezione di Pisa, Pisa, Italy), W. Gohn (University of Kentucky, Lexington, Kentucky, USA), L. Goodenough (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), T. Gorringe (University of Kentucky, Lexington, Kentucky, USA), J. Grange (University of Michigan, Ann Arbor, Michigan, USA), S. Grant (Argonne National Laboratory, Lemont, Illinois, USA, Department of Physics and Astronomy, University College London, London, United Kingdom), F. Gray (Regis University, Denver, Colorado, USA), S. Haciomeroglu (Center for Axion and Precision Physics), T. Halewood-Leagas (University of Liverpool, Liverpool, United Kingdom), D. Hampai (INFN, Laboratori Nazionali di Frascati, Frascati, Italy), F. Han (University of Kentucky, Lexington, Kentucky, USA), J. Hempstead (University of Washington, Seattle, Washington, USA), D. W. Hertzog (University of Washington, Seattle, Washington, USA), G. Hesketh (Department of Physics and Astronomy, University College London, London, United Kingdom), E. Hess (INFN, Sezione di Pisa, Pisa, Italy), A. Hibbert (University of Liverpool, Liverpool, United Kingdom), Z. Hodge (University of Washington, Seattle, Washington, USA), S. Y. Hoh (Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai, China, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China), K. W. Hong (University of Virginia, Charlottesville, Virginia, USA), R. Hong (Argonne National Laboratory, Lemont, Illinois, USA, University of Kentucky, Lexington, Kentucky, USA), T. Hu (Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai, China, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China), Y. Hu (School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China), M. Iacovacci (INFN, Sezione di Napoli, Naples, Italy), M. Incagli (INFN, Sezione di Pisa, Pisa, Italy), S. Israel (Boston University, Boston, Massachusetts, USA, Department of Physics, University of Massachusetts, Amherst, Massachusetts, USA), P. Kammel (University of Washington, Seattle, Washington, USA), M. Kargiantoulakis (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), M. Karuza (INFN, Sezione di Trieste, Trieste, Italy), J. Kaspar (University of Washington, Seattle, Washington, USA), D. Kawall (Department of Physics, University of Massachusetts, Amherst, Massachusetts, USA), L. Kelton (University of Kentucky, Lexington, Kentucky, USA, Department of Physics and Astronomy, Trinity University, San Antonio, Texas, USA), A. Keshavarzi (Department of Physics and Astronomy, University College London, London, United Kingdom), D. S. Kessler (Department of Physics, University of Massachusetts, Amherst, Massachusetts, USA), K. S. Khaw (Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai, China, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China), Z. Khechadoorian (Cornell University, Ithaca, New York, USA), B. Kiburg (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), M. Kiburg (Fermi National Accelerator Laboratory, Batavia, Illinois, USA, North Central College, Naperville, Illinois, USA), O. Kim (University of Mississippi, University, Mississippi, USA), N. Kinnaird (Boston University, Boston, Massachusetts, USA), E. Kraegeloh (University of Michigan, Ann Arbor, Michigan, USA), J. LaBounty (University of Washington, Seattle, Washington, USA), K. R. Labe (Cornell University, Ithaca, New York, USA), M. Lancaster (Department of Physics and Astronomy, University of Manchester, Manchester, United Kingdom), S. Lee (Center for Axion and Precision Physics), B. Li (School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China), D. Li (School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China), L. Li (School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China), I. Logashenko (Budker Institute of Nuclear Physics, Novosibirsk, Russia), A. Lorente Campos (University of Kentucky, Lexington, Kentucky, USA), Z. Lu (School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China), A. Lucà (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), G. Lukicov (Department of Physics and Astronomy, University College London, London, United Kingdom), A. Lusiani (INFN, Sezione di Pisa, Pisa, Italy), A. L. Lyon (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), B. MacCoy (University of Washington, Seattle, Washington, USA), R. Madrak (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), K. Makino (Michigan State University, East Lansing, Michigan, USA), S. Mastroianni (INFN, Sezione di Napoli, Naples, Italy), R. McCarthy (Boston University, Boston, Massachusetts, USA), J. P. Miller (Boston University, Boston, Massachusetts, USA), S. Miozzi (INFN, Sezione di Roma Tor Vergata, Rome, Italy), B. Mitra (University of Mississippi, University, Mississippi, USA), J. P. Morgan (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), W. M. Morse (Brookhaven National Laboratory, Upton, New York, USA), J. Mott (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), A. Nath (INFN, Sezione di Napoli, Naples, Italy), J. K. Ng (Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai, China, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China), H. Nguyen (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), Y. Oksuzian (Argonne National Laboratory, Lemont, Illinois, USA), Z. Omarov (Korea Advanced Institute of Science and Technology, Center for Axion and Precision Physics), W. Osar (Cornell University, Ithaca, New York, USA), R. Osofsky (University of Washington, Seattle, Washington, USA), S. Park (Center for Axion and Precision Physics), G. Pauletta (Università di Udine, Udine, Italy), J. Peck (University of Kentucky, Lexington, Kentucky, USA), G. M. Piacentino (Università del Molise, Campobasso, Italy), R. N. Pilato (University of Liverpool, Liverpool, United Kingdom), K. T. Pitts (University of Illinois at Urbana-Champaign, Urbana, Illinois, USA), B. Plaster (University of Kentucky, Lexington, Kentucky, USA), N. Pohlman (Northern Illinois University, DeKalb, Illinois, USA), C. C. Polly (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), D. Počanić (University of Virginia, Charlottesville, Virginia, USA), J. Price (University of Liverpool, Liverpool, United Kingdom), B. Quinn (University of Mississippi, University, Mississippi, USA), M. U. H. Qureshi (Institute of Physics and Cluster of Excellence PRISMA++, Johannes Gutenberg University Mainz, Mainz, Germany), G. Rakness (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), S. Ramachandran (Argonne National Laboratory, Lemont, Illinois, USA), E. Ramberg (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), R. Reimann (Institute of Physics and Cluster of Excellence PRISMA++, Johannes Gutenberg University Mainz, Mainz, Germany), B. L. Roberts (Boston University, Boston, Massachusetts, USA), D. L. Rubin (Cornell University, Ithaca, New York, USA), M. Sakurai (Department of Physics and Astronomy, University College London, London, United Kingdom), L. Santi (Università di Udine, Udine, Italy), C. Schlesier (University of Illinois at Urbana-Champaign, Urbana, Illinois, USA), A. Schreckenberger (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), Y. K. Semertzidis (Center for Axion and Precision Physics, Korea Advanced Institute of Science and Technology), A. K. Soha (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), M. Sorbara (INFN, Sezione di Roma Tor Vergata, Rome, Italy), J. Stapleton (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), D. Still (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), C. Stoughton (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), D. Stratakis (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), D. Stöckinger (Institut für Kern- und Teilchenphysik, Technische Universität Dresden, Dresden, Germany), H. E. Swanson (University of Washington, Seattle, Washington, USA), G. Sweetmore (Department of Physics and Astronomy, University of Manchester, Manchester, United Kingdom), D. A. Sweigart (Cornell University, Ithaca, New York, USA), M. J. Syphers (Northern Illinois University, DeKalb, Illinois, USA), Y. Takeuchi (Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai, China, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China), D. A. Tarazona (Cornell University, Ithaca, New York, USA), T. Teubner (University of Liverpool, Liverpool, United Kingdom), A. E. Tewsley-Booth (University of Kentucky, Lexington, Kentucky, USA, University of Michigan, Ann Arbor, Michigan, USA), V. Tishchenko (Brookhaven National Laboratory, Upton, New York, USA), N. H. Tran (Boston University, Boston, Massachusetts, USA), W. Turner (University of Liverpool, Liverpool, United Kingdom), E. Valetov (Michigan State University, East Lansing, Michigan, USA), D. Vasilkova (University of Liverpool, Liverpool, United Kingdom), G. Venanzoni (University of Liverpool, Liverpool, United Kingdom), T. Walton (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), A. Weisskopf (Michigan State University, East Lansing, Michigan, USA), L. Welty-Rieger (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), P. Winter (Argonne National Laboratory, Lemont, Illinois, USA), Y. Wu (Argonne National Laboratory, Lemont, Illinois, USA), B. Yu (University of Mississippi, University, Mississippi, USA), M. Yucel (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), E. Zaid (University of Liverpool, Liverpool, United Kingdom), Y. Zeng (Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai, China, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China), C. Zhang (University of Liverpool, Liverpool, United Kingdom)

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe is a giant, invisible rulebook called the Standard Model. For decades, physicists have been trying to read every page of this book to understand how the smallest particles in existence behave. One of the most important characters in this story is the muon, a particle that is essentially a heavy, unstable cousin of the electron.

This paper is the final report from a massive experiment at Fermilab (a giant particle accelerator in Illinois) that measured the muon's "magnetic personality" with unprecedented precision. Here is what they found, explained simply.

The Muon as a Spinning Top

Think of a muon not just as a tiny ball, but as a spinning top with a tiny magnet attached to it. Because it has a charge and a spin, it acts like a tiny bar magnet.

According to the "rulebook" (the Standard Model), if you put this spinning top in a magnetic field, it should wobble (precess) at a very specific, predictable speed. Scientists call this the g-factor. For a perfect, simple top, the math says it should wobble at exactly 2.

However, quantum physics tells us the vacuum of space isn't empty. It's a bubbling soup of "virtual particles" popping in and out of existence. These virtual particles interact with the muon, slightly changing how it wobbles. This tiny change is called the anomalous magnetic moment (or "the anomaly"). It's like the spinning top is wobbling slightly faster or slower than the rulebook predicted because it's bumping into invisible ghosts in the room.

The Experiment: A Cosmic Race Track

To measure this tiny wobble, the scientists built a storage ring, which is essentially a giant, super-stable racetrack made of magnets.

The Racers: They shot millions of muons into this ring.
The Track: The muons circled around the ring at nearly the speed of light, held in place by a perfectly uniform magnetic field.
The Finish Line: As the muons circled, they eventually decayed (died), shooting out high-energy particles called positrons. By counting these positrons over time, the scientists could see the rhythm of the muon's wobble.

It's like trying to measure the wobble of a spinning top by listening to the sound it makes as it slows down. The louder and more frequent the "clicks" (positrons), the more they could hear the rhythm.

The Challenge: A Symphony of Noise

Measuring this wobble is incredibly hard because the "track" isn't perfectly smooth, and the "top" isn't perfectly stable.

The Jitter: The muons don't just circle perfectly; they wiggle up and down and side-to-side (like a car swerving slightly while driving in a straight line).
The Noise: The detectors that catch the positrons have their own quirks, like a microphone that gets slightly quieter as the battery drains.
The Ghosts: The magnetic field isn't perfectly static; it has tiny ripples caused by the machinery turning on and off.

To get the answer, the team had to build a super-complex mathematical model to subtract all this "noise" and "jitter" to hear the pure wobble of the muon. They used six different teams of scientists, each using different methods to analyze the data, to ensure they weren't all making the same mistake. It's like having six different chefs taste a soup to make sure the salt level is right.

The Result: A Crack in the Rulebook?

After analyzing data collected from 2021 to 2023 (which is 2.5 times more data than their previous attempts), they calculated the value of the muon's wobble with a precision of 127 parts per billion. That is like measuring the distance from the Earth to the Moon and being off by less than the width of a human hair.

The Big Discovery:
The value they measured does not match the value predicted by the Standard Model.

The Prediction: The rulebook says the wobble should be X.
The Reality: The experiment says the wobble is Y.
The Gap: The difference is about 4 to 5 standard deviations. In the world of physics, this is a "shout." It means there is a very high probability that the rulebook is missing a chapter.

What Does This Mean?

The paper concludes that the Standard Model is likely incomplete. The "invisible ghosts" (virtual particles) interacting with the muon might include new, undiscovered particles that the current rulebook doesn't know about.

Think of it like this: For years, we thought the universe was a puzzle with 1,000 pieces. We had a picture of what the finished puzzle should look like. But when we actually put the pieces together, we found a few pieces that didn't fit the picture. This experiment confirms that those pieces are definitely there, suggesting there are new pieces of the puzzle (new physics) waiting to be found.

Summary

This paper is the final, most precise measurement of the muon's magnetic wobble to date. It confirms a long-standing mystery: the muon behaves slightly differently than our current best theories predict. This isn't a mistake in the math; it's a signal that nature is more complex and interesting than we thought, hinting at the existence of new particles or forces that we haven't discovered yet.

Technical Summary: Final Report on the Measurement of the Positive Muon Anomalous Magnetic Moment at Fermilab to 127 ppb

Problem and Motivation
The measurement of the magnetic moment of the muon, specifically the anomalous magnetic moment $a_\mu = (g_\mu - 2)/2$ , serves as a critical precision test of the Standard Model (SM) of particle physics. While the electron anomaly is dominated by Quantum Electrodynamics (QED) and used to determine the fine-structure constant, the muon's larger mass ( $m_\mu \approx 207 m_e$ ) enhances its sensitivity to Beyond the Standard Model (BSM) physics by a factor of $m_\mu^2/m_e^2 \approx 43,000$ . Previous measurements, notably by the Brookhaven National Laboratory (BNL) E821 experiment, revealed a tension with SM predictions that grew to approximately 3.5 standard deviations with improved theoretical calculations. The Muon $g-2$ Experiment at Fermi National Accelerator Laboratory (FNAL) was designed to improve experimental precision by a factor of four compared to BNL to provide a conclusive statement on these hints of new physics.

Methodology
The experiment measures $a_\mu$ by storing polarized positive muons with a "magic momentum" of 3.094 GeV/c ( $\gamma = 29.3$ ) in a highly uniform vertical magnetic field ( $\vec{B}$ ). At this momentum, the electric field focusing term in the spin precession equation vanishes to first order. The anomalous precession frequency $\omega_a$ is determined from the time distribution of decay positrons, while the magnetic field strength is characterized by the Larmor frequency of shielded protons, $\omega'_p$ . The anomaly is derived from the ratio $R'_\mu = \omega_a / \omega'_p$ , combined with precisely known constants.

The analysis utilizes data collected from 2018 to 2023 across six running periods (Run-1 through Run-6). The final report focuses on the Run-4/5/6 dataset, which comprises approximately 70% of the total statistics (over 2.5 times the statistics of previous results). Key methodological components include:

Positron Reconstruction and $\omega_a$ Determination: Decay positrons are detected by 24 electromagnetic calorimeters. The analysis employs four distinct reconstruction methods (Local I, Local II, Global, and Energy Flow) and ten variations of fitting strategies to extract $\omega_a$ . These methods utilize different approaches to handle pileup, beam dynamics, and gain variations. The data is hardware-blinded and analyzed by independent teams to ensure robustness.
Beam Dynamics Corrections: The measured frequency $\omega^m_a$ $ω_{a}^{m}$ requires corrections for non-ideal beam behavior. Significant improvements in Run-4/5/6 include the commissioning of a Radio Frequency (RF) system on the Electrostatic Quadrupoles (ESQ) to damp coherent betatron oscillations (CBO). Corrections are applied for:
- Electric Field ( $C_e$ ): Accounting for momentum spread deviations from the magic momentum.
- Pitch ( $C_p$ ): Correcting for vertical betatron oscillations.
- Time-Varying Ensemble: Corrections for phase-acceptance ( $C_{pa}$ ), differential decay ( $C_{dd}$ ), and muon loss ( $C_{ml}$ ).
Magnetic Field Measurement ( $\omega_p$ ): The field is mapped using a mobile trolley with 17 Nuclear Magnetic Resonance (NMR) probes and monitored by ~400 fixed NMR probes. A rigorous calibration chain links the trolley probes to a spherical water sample at a reference temperature of 25°C, updated to align with CODATA 2022 recommendations. Corrections are applied for probe-specific effects, environmental factors (e.g., magnetic images, oxygen), and transient fields from kickers and ESQs.

Key Contributions and Improvements
This report details the final measurement using the full Run-4/5/6 dataset, introducing several technical advancements over previous results:

RF System Operation: The implementation of horizontal and vertical RF fields on the ESQs reduced CBO amplitudes and muon losses by a factor of five, significantly lowering systematic uncertainties related to beam dynamics.
Enhanced Momentum Distribution Analysis: The electric field correction ( $C_e$ ) was refined using a new $\chi^2$ -based Fast-Rotation analysis that accounts for time-momentum correlations, alongside a positron-tracking analysis validated by a Minimally Intrusive Scintillating Fiber (MiniSciFi) detector.
Differential Decay Correction: The analysis combined direct and transverse injection components into a single injection term evaluated via simulation, addressing complex mixing during the injection process.
Calibration Updates: The magnetic field calibration adopted a reference temperature of 25°C and included extensive cross-checks against J-PARC calibration probes and a $^3$ He-based NMR probe, leading to an inflation of uncertainties in specific cross-check terms to ensure consistency.
Blinding and Cross-Checks: The analysis utilized a multi-team approach with independent blinding offsets and extensive closure tests, including histogram swapping and start-time stability scans, to validate the robustness of the results.

Results
The final measurement yields the following values for the positive muon anomalous magnetic moment:

Run-4/5/6 Dataset: $a_\mu = 116,592,0710(162) \times 10^{-12}$ (139 ppb).
Combined with Previous Results: When combined with Run-1 and Run-2/3 data, the result is $a_\mu = 116,592,0705(148) \times 10^{-12}$ (127 ppb).
Experimental World Average: The new experimental world average, dominated by the FNAL measurements, is $a_\mu^{\text{Exp}} = 116,592,0715(145) \times 10^{-12}$ (124 ppb).

The total uncertainty is reduced to 127 ppb, surpassing the experiment's design goal by 10%. The statistical uncertainty is 98 ppb, and the total systematic uncertainty is 78 ppb.

Significance
The paper claims that this result provides the most precise measurement of the muon magnetic anomaly to date. The achieved precision and the stability of the experimental result over decades serve as a fundamental benchmark for any future extension to the Standard Model. The report emphasizes that the consistency of the result across different datasets, reconstruction methods, and beam conditions validates the experimental technique and the rigorous treatment of systematic uncertainties. The paper concludes by noting that this measurement, combined with the Muon $g-2$ Theory Initiative's efforts, continues to test the completeness of the Standard Model, though the specific comparison to theory and the resulting tension are discussed in a separate section of the report rather than as a primary claim of this measurement document itself.

Final Report on the Measurement of the Positive Muon Anomalous Magnetic Moment at Fermilab to 127 ppb