⚛️ nuclear experiments

An improved direct limit on the muon electric dipole moment

Using data from the Fermilab Muon g-2 Experiment collected between 2019 and 2020, researchers established a new direct 95% confidence level limit on the muon electric dipole moment of $|d_\mu|<1.10\times10^{-19}~e\cdot$ cm, finding the measured value consistent with zero.

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 (27,a), 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 (31,a), G. Cantatore (12,b), R. M. Carey (Boston University, Boston, Massachusetts, USA), B. C. K. Casey (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), D. Cauz (25,c), 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 (20,21,d), 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 (20,d), T. E. Chupp (University of Michigan, Ann Arbor, Michigan, USA), C. Claessens (University of Washington, Seattle, Washington, USA), F. Confortini (9,e), 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 (8,f), 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 (10,g), 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 (10,h), 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 (10,h), D. Flay (Department of Physics, University of Massachusetts, Amherst, Massachusetts, USA), S. B. Foster (2,28,i), H. Friedsam (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), N. S. Froemming (18,j), C. Gabbanini (10,h), I. Gaines (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), S. Ganguly (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), J. George (31,k), L. K. Gibbons (Cornell University, Ithaca, New York, USA), A. Gioiosa (24,l), K. L. Giovanetti (Department of Physics and Astronomy, James Madison University, Harrisonburg, Virginia, USA), P. Girotti (10,m), 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 (19,n), S. Haciomeroglu (5,o), 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 (10,p), A. Hibbert (University of Liverpool, Liverpool, United Kingdom), Z. Hodge (University of Washington, Seattle, Washington, USA), S. Y. Hoh (20,21,q), 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 (20,21,d), Y. Hu (20,d), M. Iacovacci (9,e), 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 (12,p), J. Kaspar (University of Washington, Seattle, Washington, USA), D. Kawall (Department of Physics, University of Massachusetts, Amherst, Massachusetts, USA), L. Kelton (Department of Physics and Astronomy, Trinity University, San Antonio, Texas, USA, University of Kentucky, Lexington, Kentucky, 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 (20,21,d), 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 (33,n), 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 (20,r), D. Li (20,s), L. Li (20,d), I. Logashenko (4,t), A. Lorente Campos (University of Kentucky, Lexington, Kentucky, USA), Z. Lu (20,d), A. Lucà (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), G. Lukicov (Department of Physics and Astronomy, University College London, London, United Kingdom), A. Lusiani (10,u), 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 (2,v), J. P. Miller (Boston University, Boston, Massachusetts, USA), S. Miozzi (INFN, Sezione di Roma Tor Vergata, Rome, Italy), B. Mitra (33,w), 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 (9,e), J. K. Ng (20,21,d), H. Nguyen (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), Y. Oksuzian (Argonne National Laboratory, Lemont, Illinois, USA), Z. Omarov (Center for Axion and Precision Physics, Korea Advanced Institute of Science and Technology), 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 (25,c), J. Peck (University of Kentucky, Lexington, Kentucky, USA), G. M. Piacentino (24,l), R. N. Pilato (University of Liverpool, Liverpool, United Kingdom), K. T. Pitts (27,x), 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 (1,k), E. Ramberg (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), R. Reimann (14,y), 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 (25,c), C. Schlesier (27,z), A. Schreckenberger (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), Y. K. Semertzidis (5,15,aa), A. K. Soha (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), M. Sorbara (11,bb), 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 (20,21,d), 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 (16,cc), D. Vasilkova (University of Liverpool, Liverpool, United Kingdom), G. Venanzoni (29,dd), 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 (1,ee), 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 (20,21,d), C. Zhang (University of Liverpool, Liverpool, United Kingdom)

Published 2026-08-12

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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 (27,a), 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 (31,a), G. Cantatore (12,b), R. M. Carey (Boston University, Boston, Massachusetts, USA), B. C. K. Casey (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), D. Cauz (25,c), 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 (20,21,d), 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 (20,d), T. E. Chupp (University of Michigan, Ann Arbor, Michigan, USA), C. Claessens (University of Washington, Seattle, Washington, USA), F. Confortini (9,e), 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 (8,f), 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 (10,g), 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 (10,h), 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 (10,h), D. Flay (Department of Physics, University of Massachusetts, Amherst, Massachusetts, USA), S. B. Foster (2,28,i), H. Friedsam (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), N. S. Froemming (18,j), C. Gabbanini (10,h), I. Gaines (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), S. Ganguly (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), J. George (31,k), L. K. Gibbons (Cornell University, Ithaca, New York, USA), A. Gioiosa (24,l), K. L. Giovanetti (Department of Physics and Astronomy, James Madison University, Harrisonburg, Virginia, USA), P. Girotti (10,m), 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 (19,n), S. Haciomeroglu (5,o), 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 (10,p), A. Hibbert (University of Liverpool, Liverpool, United Kingdom), Z. Hodge (University of Washington, Seattle, Washington, USA), S. Y. Hoh (20,21,q), 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 (20,21,d), Y. Hu (20,d), M. Iacovacci (9,e), 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 (12,p), J. Kaspar (University of Washington, Seattle, Washington, USA), D. Kawall (Department of Physics, University of Massachusetts, Amherst, Massachusetts, USA), L. Kelton (Department of Physics and Astronomy, Trinity University, San Antonio, Texas, USA, University of Kentucky, Lexington, Kentucky, 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 (20,21,d), 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 (33,n), 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 (20,r), D. Li (20,s), L. Li (20,d), I. Logashenko (4,t), A. Lorente Campos (University of Kentucky, Lexington, Kentucky, USA), Z. Lu (20,d), A. Lucà (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), G. Lukicov (Department of Physics and Astronomy, University College London, London, United Kingdom), A. Lusiani (10,u), 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 (2,v), J. P. Miller (Boston University, Boston, Massachusetts, USA), S. Miozzi (INFN, Sezione di Roma Tor Vergata, Rome, Italy), B. Mitra (33,w), 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 (9,e), J. K. Ng (20,21,d), H. Nguyen (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), Y. Oksuzian (Argonne National Laboratory, Lemont, Illinois, USA), Z. Omarov (Center for Axion and Precision Physics, Korea Advanced Institute of Science and Technology), 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 (25,c), J. Peck (University of Kentucky, Lexington, Kentucky, USA), G. M. Piacentino (24,l), R. N. Pilato (University of Liverpool, Liverpool, United Kingdom), K. T. Pitts (27,x), 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 (1,k), E. Ramberg (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), R. Reimann (14,y), 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 (25,c), C. Schlesier (27,z), A. Schreckenberger (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), Y. K. Semertzidis (5,15,aa), A. K. Soha (Fermi National Accelerator Laboratory, Batavia, Illinois, USA), M. Sorbara (11,bb), 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 (20,21,d), 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 (16,cc), D. Vasilkova (University of Liverpool, Liverpool, United Kingdom), G. Venanzoni (29,dd), 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 (1,ee), 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 (20,21,d), 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

The Cosmic Detective Story: Hunting for a Tiny Tilt

Imagine the universe as a giant, invisible dance floor where every particle has its own unique rhythm. For decades, physicists have been trying to figure out why the universe is made mostly of matter, with very little antimatter left over. According to the best rules we have (the Standard Model), matter and antimatter should have been created in equal amounts and then annihilated each other, leaving nothing behind. But here we are, so something must have tipped the scales.

To find the culprit, scientists look for "symmetry breaking." Think of a perfect spinning top. If it spins perfectly upright, it looks the same from every angle. But if it wobbles or tilts, that symmetry is broken. In the world of subatomic particles, there are two main ways a particle can "wobble": it can have a magnetic dipole moment (like a tiny bar magnet) or an electric dipole moment (EDM). The magnetic one is like a compass needle; we know it exists. The electric one, however, is the ghost in the machine. If a particle has an EDM, it means its positive and negative charges are slightly separated, creating a tiny electric "tilt" that violates the rules of time and space symmetry. Finding this tilt would be like discovering a secret ingredient in the cosmic recipe that explains why we exist. But so far, this ingredient has been incredibly hard to find, hiding in the shadows of our most sensitive experiments.

The Search for the Invisible Tilt

In this latest chapter of the hunt, the Muon g-2 Collaboration at Fermilab has taken a fresh look at the muon, a heavy cousin of the electron. They wanted to see if the muon has this elusive electric dipole moment. Imagine a muon as a tiny, hyper-fast gyroscope spinning inside a giant, magnetic racetrack. As it zooms around, its spin usually wobbles in a predictable horizontal circle, like a spinning top precessing on a table.

The team's big idea was simple but clever: if the muon has an electric dipole moment, the electric forces inside the lab would push on its "electric charge separation," causing its spin axis to tilt slightly up or down, out of the flat racetrack. It's like if you were spinning a top on a table, and someone gently blew air from the side, causing the top to lean over. The researchers didn't look for the lean directly; instead, they watched the muons as they decayed into positrons (anti-electrons). Because of the way muons decay, the positrons shoot out in a specific direction relative to the muon's spin. If the spin is tilted, the positrons will, on average, fly out at a slightly different vertical angle than expected.

The team analyzed data from 2019 and 2020, tracking billions of these decay events. They used a special set of "straw trackers"—essentially a ring of hollow tubes that act like high-tech eyes to catch the positrons and measure their paths with incredible precision. By measuring the average vertical angle of these positrons over time, they could see if there was a rhythmic wobble that matched the signature of an electric dipole moment.

The Result: A Very Flat Spin

After crunching the numbers and running through a rigorous process to ensure no hidden errors were skewing the results, the answer came back: the muon didn't tilt. The data showed that the average vertical angle of the positrons was consistent with zero tilt. The measured value for the muon's electric dipole moment is $d_\mu = (-0.35 \pm 0.19_{\text{stat}} \pm 0.34_{\text{sys}}) \times 10^{-19} \text{ e}\cdot\text{cm}$ .

Because this number is so close to zero and the uncertainty range includes zero, the team concluded that they did not find a permanent electric dipole moment. Instead, they set a new, stricter limit on how big it could possibly be. They stated that with 95% confidence, the muon's electric dipole moment is smaller than $1.10 \times 10^{-19} \text{ e}\cdot\text{cm}$ .

This is a significant improvement over the previous best limit from the Brookhaven National Laboratory, tightening the net by a factor of 1.5. While this result doesn't reveal the "secret ingredient" that explains the matter-antimatter imbalance, it does rule out a wide range of theories that predicted a larger tilt. The authors note that this result is limited by systematic uncertainties—specifically, how perfectly the tracking detectors were aligned. They expect that with more data from future runs, they will be able to align the detectors even better and push this limit even lower, continuing the search for that tiny, universe-defining wobble.

Technical Summary: An Improved Direct Limit on the Muon Electric Dipole Moment

Problem and Motivation
The observed matter-antimatter asymmetry of the universe cannot be explained by the known sources of charge-parity (CP) violation within the Standard Model (SM) [1, 2]. Electric dipole moments (EDMs) violate both parity (P) and time-reversal (T) symmetries; under the assumption of CPT conservation, a non-zero EDM implies CP violation. While no fundamental particle or bound state (such as the neutron) has yet been observed to possess an EDM [3–5], the SM prediction for the muon EDM is negligible ( $O(10^{-38})$ e·cm) [6]. Indirect limits derived from electron EDM measurements or muon-loop interactions in nuclei rely on assumptions (such as minimal flavor violation) that may not hold in Beyond the Standard Model (BSM) physics [7–10]. Consequently, a direct measurement of the muon EDM is critical. A result inconsistent with zero near current experimental limits would contradict the SM and constrain BSM theories [13, 14].

Methodology
This analysis utilizes data from the Fermilab Muon $g-2$ Experiment collected between 2019 and 2020 (Run-2, Run-3a, and Run-3b). The experiment employs a beam of highly polarized positive muons injected into a 1.45 T superferric storage ring with a "magic momentum" of 3.094 GeV/c, where the electric field contribution to spin precession vanishes.

Measurement Principle: In the presence of a non-zero EDM ( $d_\mu$ ), a torque is exerted on the muon spin, tilting the spin precession plane out of the horizontal plane. This tilt ( $\delta$ ) induces an oscillation in the average vertical decay angle ( $\langle \theta_y \rangle$ ) of positrons from muon decays. This oscillation occurs at the anomalous precession frequency ( $\omega_a$ ) but is $\pi/2$ out of phase with the standard spin precession oscillation.
Detection: The analysis relies on in-vacuum straw tracker stations (S12 and S18) to measure the trajectories of decay positrons. The dataset comprises $2.34 \times 10^9$ positrons detected within a specific time window (26.2 to 602.4 $\mu$ s after injection).
Analysis Strategy: The vertical decay angle $\langle \theta_y \rangle$ is binned modulo the precession period. The data is fitted to a function containing in-phase ( $C_a$ ) and out-of-phase ( $S_a$ ) components relative to the anomalous precession. The amplitude $S_a$ is directly proportional to the EDM.
Corrections and Systematics:
- R-factors: The measured amplitude is corrected for Lorentz boost ( $R_\gamma$ ), beam polarization ( $R_P$ ), momentum-dependent decay angle spread ( $R_{e^+}$ ), and detector acceptance ( $R_{acc}$ ).
- Blinding: The analysis was blinded by injecting an unknown oscillation signal. An initial "soft unblinding" check revealed a discrepancy, prompting an internal review that identified a vertical misalignment of the trackers and uncertainties in the longitudinal magnetic field.
- EDM-like Signals: Corrections were applied for false signals arising from vertical tracker misalignment (which alters the mean vertical position) and radial magnetic field components (which induce a rest-frame tilt). A longitudinal magnetic field measurement was also used to assign an uncertainty.

Key Contributions and Results
The paper presents a new direct limit on the muon EDM based on the combined analysis of 48 independent measurements (across three runs, two stations, and eight momentum bins).

Final Result: The combined measurement yields a muon EDM of:
$d_\mu = (-0.35 \pm 0.19_{\text{stat}} \pm 0.34_{\text{sys}}) \times 10^{-19} \text{ e}\cdot\text{cm}$
This result is consistent with zero.
Limits: Based on the Feldman-Cousins procedure, the paper sets a one-sided upper limit of:
$|d_\mu| < 1.10 \times 10^{-19} \text{ e}\cdot\text{cm} \quad \text{at 95\% CL}$
$|d_\mu| < 0.98 \times 10^{-19} \text{ e}\cdot\text{cm} \quad \text{at 90\% CL}$
Uncertainty Breakdown: The result is systematics-limited. The dominant source of systematic uncertainty (3.12 $\times 10^{-20}$ e·cm) arises from the correction for the vertical alignment of the trackers. Other significant contributions include track reconstruction alignment and beam dynamics coupling to acceptance. The statistical uncertainty is 1.87 $\times 10^{-20}$ e·cm.
Comparison: The total uncertainty of this result is a factor of 2.3 smaller than the previous best direct limit from the Brookhaven National Laboratory (BNL E821) experiment ( $|d_\mu| < 1.8 \times 10^{-19}$ e·cm).

Significance
The paper claims that this result sets a new direct limit on the muon EDM, improving upon the previous 95% confidence level limit by a factor of 1.5. The authors note that the current result is limited by systematic uncertainties, specifically the determination of vertical alignment. They state that this uncertainty is statistically limited and is expected to improve significantly when the full dataset from future runs (Runs 4, 5, and 6) is included, which will provide 2.5 times the statistics presented in this analysis. The measurement remains consistent with the Standard Model prediction and provides a stringent constraint for BSM theories.

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