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The Anomalous Magnetic Moment of the Muon The anomalous magnetic moment of the muon Vladimir Tishchenko Brookhaven National Laboratory ISU Colloquium 18 April, 2016 Outline ● Magnetic moment ● History of the magnetic moments ● Future muon g-2 experiment at Fermilab V. Tishchenko Idaho State University, Colloquium 18 April, 2016 2 Magnetic Moment ● … is a vector quantity characterizing magnetic interaction of an object with a magnetic field spinning ball of charge the torque orbiting charged particle current loop S – spin angular momentum (depends on mass distribution) γ - gyromagnetic ratio if charge distribution is not the same as the mass distribution, L – orbital angular momentum introduce g factor, V. Tishchenko Idaho State University, Colloquium 18 April, 2016 3 Some History ● 1896 Zeeman effect – splitting of spectral lines into several components in presence of a magnetic field ● 1922 Stern-Gerlach experiment ● 1924 Pauli postulated a fourth quantum number to explain the anomalous Zeeman effect ● 1925 R. Kronig (20): concept of spinning electron. Unpublished. ● 1925 G. E. Uhlenbeck (25) and S. A. Goudsmit (23): hypothesis of electron spin, with possible quantum numbers of either + ½ or -½. Sent for publication by Ehrenfest: "Well, that is a nice idea, though it may be wrong. But you don't yet have a reputation, so you have nothing to lose". V. Tishchenko Idaho State University, Colloquium 18 April, 2016 4 Solution of the electron g problem ● 1928 P. Dirac (25) ● 1933 O. Stern and I. Estermann: g-factor of the proton Pauli: “Don't you know the Dirac theory? It is obvious that gp=2.” measured value: gp≈5.6 μ turned out to be a harbinger of new physics! p Was finally explained, along with the g value of the BNL neutron, g =-3.8 om the 1960 by the quark model. proton substructure! n V. Tishchenko Idaho State University, Colloquium 18 April, 2016 5 Nature abhors a vacuum ● At least for the electron, things finally in good shape with Dirac's new theory until... ● 1930s Oppenheimer and others tried to calculate correction to ge=2. Result: infinity. ● 1947 P. Kusch and H.M. Foley: ● 1948 J. Schwinger ● QED ● Feynman diagrams... ● 1970s weak interactions unified with QED V. Tishchenko Idaho State University, Colloquium 18 April, 2016 6 anomalous magnetic moment V. Tishchenko Idaho State University, Colloquium 18 April, 2016 7 Present status: electron ● 2008 G. Gabrielse, Harvard PRL 100 (2008) 120801 ● Take α from external measurements to test QED PRA 73 (2006) 032504 PRL 106 (2011) 080801 ● Or, assume ge and calculate α PRL 100 (2008) 120801 μ gives the most precise determination of the fine structure constant! e V. Tishchenko Idaho State University, Colloquium 18 April, 2016 8 Theory ● th QED now calculated ae to 5 order in (12672 diagrams). Kinoshita & collaborator., 2008, 2012 Schwinger 1948 Karplus & Kroll 1950; Petermann, Sommerfield 1957 Elend 1966 Fujikawa, Lee, Sanda 1972; Czarnecki, Krause, Marciano 1996; Knecht, Peris, Perrottet, Rafael, 2002; Czarnecki, Marciano, Vainshtein, 2003; Nomura & Teubner, 2012; Lautrup, Peterman, de Rafael 1974; Laporta, Remiddi 1996; Kinoshita 1995 Prades, Rafael, Vainshtein, 2009 Samuel & Li, 1991 Samuel & Li, 1991 Samuel & Li, 1991 Kinoshita & collaborator., 1983, 2002, 2005, 2007, 2012 Sensitivity of ae to “new physics” at a mass scale Λ Berestetskii, 1956 V. Tishchenko Idaho State University, Colloquium 18 April, 2016 9 choice of heavy particles to probe NP Only exist as complicated multi-body objects Too fleeting or no electric charge Neutral (and too light) V. Tishchenko Idaho State University, Colloquium 18 April, 2016 10 tauon ● mτ = 1777 MeV ● 7 (mτ/me)2 ≈ 1.2x10 ● τ meson has heightened sensitivity to higher-mass exchanges ● ττ ~ 0.29 ps ● Limits current precision to - 0.052 < aτ <0.013 V. Tishchenko Idaho State University, Colloquium 18 April, 2016 11 muon ● mμ = 106 MeV ● 4 (mμ/me)2 ≈ 4x10 ● ττ ~ 2.2 μs → convenient for exp. study V. Tishchenko Idaho State University, Colloquium 18 April, 2016 12 muon ● 1933 First observed in cosmic rays. “Particle of uncertain nature”, Paul Kunze, Z. Phys. 83 (1933) 1. ● 1935 Hideki Yukawa: meson theory, Proc. Phys.-Math. Soc. Jap. 17 (1985), 48 ● 1936 Seth Neddermeyer and Carl Anderson: particle in cosmic rays with a mass “greater than an electron but smaller than a proton”. I. I. Rabi: "Who ordered that?" ● … -1957 V.B. Berestetskii, R.P. Feynman, J.S Schwinger: The muon (g − 2) experiment was recognized as a very sensitive test of the existence new fields, and potentially a crucial signpost to the μ–e problem. ● 1956-1957 T.D. Lee, C.N. Yang, C.S. Wu: parity violation ● 1957 R.L. Garwin, L. Lederman, M. Weinrich - antecedent of the (g-2) measurements V. Tishchenko Idaho State University, Colloquium 18 April, 2016 13 muon – “self analyzing polarimeter” q e+ V. Tishchenko Idaho State University, Colloquium 18 April, 2016 14 R.L. Garwin, L. Lederman, M. Weinrich, 1957 The magnetizing coil was close wound directly on the graphite to provide a uniform vertical field of 79 gauss per ampere. The various counters defined the event by use of a coincidence-anticoincidence analyzer V. Tishchenko Idaho State University, Colloquium 18 April, 2016 15 Muon g-2 experiment in a nutshell 1) Take polarized muons (come naturally from pion decay) 2) Inject muons into a uniform magnetic field – Momentum precession (cyclotron frequency) – Spin precession momentum spin V. Tishchenko Idaho State University, Colloquium 18 April, 2016 16 1st CERN muon g-2 experiment 1958-1962 6-m-long 52-cm-wide 14-cm-gap bending magnet, B=1.5 T. 440 turns during τ=2.2 μs. Muon step size from 0.4cm to 11 cm. Time t spent inside the magnet was determined by by coincidence in counters 123 at input, and counters 466'57 at the output. t=2-8 μs depending on the location of the orbit center on the varying gradient field. 150 MeV/c muons V. Tishchenko Idaho State University, Colloquium 18 April, 2016 17 1st CERN muon g-2 experiment 1958-1962 The first CERN g-2 team: Sens, Charpak, Muller, Farley, Zichichi (CERN/1959) → muon behaved so precisely as a structureless point-like QED particle; a heavy twin for the electron V. Tishchenko Idaho State University, Colloquium 18 April, 2016 18 1st muon storage ring at CERN, 1962-1968 features: ● weak focusing ring, n=0.13 ● B=1,.711 T ● orbit diameter: 5m ● aperture: 4cm x 8 cm ● beam: 10.5 GeV protons ● injection time: 10 ns ● rotation time: 50 ns ● stored muons: p=1.28 GeV/c ● γ = 12, t=27 μs problems: ● high background ● low muon polarization V. Tishchenko Idaho State University, Colloquium 18 April, 2016 19 1st muon storage ring at CERN, 1962-1968 … after an error in QED LBL calculations was corrected J. Aldins et al., PRD 1 (1970) 2378 V. Tishchenko Idaho State University, Colloquium 18 April, 2016 20 2nd muon storage ring at CERN, 1969-1976 Motivation ● to look for departures from standard QED ● to detect contributions of strong interactions to aμ through hadron loops in the vacuum polarization ● to search for new interactions of the muon V. Tishchenko Idaho State University, Colloquium 18 April, 2016 21 2nd muon storage ring at CERN, 1969-1976 features: ● 40 C-shaped bending magnets ● pole: 38-cm x 14 cm (width x gap) ● field in each magnet stabilized with NMR probes ● electric quadrupoles for vertical focusing ● pion injection! V. Tishchenko Idaho State University, Colloquium 18 April, 2016 22 2nd muon storage ring at CERN, 1969-1976 ● Excellent agreement with theory ● QED calculations verified up to the sixth order ● Confirmation of the existence of hadronic vacuum polarization at the level of 5σ. ● No evidence of special coupling to the muon V. Tishchenko Idaho State University, Colloquium 18 April, 2016 23 Final stop on the history tour...Brookhaven Motivation ● to measure electroweak contributions to aμ which arise from single loop diagrams with vitural W and Z bosons ● to search for new interactions of the muon A picture from 1984 showing the attendees of the first collaboration meeting to develop the BNL g-2 experiment. Standing from left: Gordon Danby, John Field, Francis Farley, Emilio Picasso, and Frank Krienen. Kneeling from left: John Bailey, Vernon Hughes and Fred Combley V. Tishchenko Idaho State University, Colloquium 18 April, 2016 24 SM prediction for aμ QED Weak Hadronic QED: photonic and leptonic (e,τ,μ) loops, Weak: loops involving W±, Z or Higgs suppressed by at least a factor of , Hadronic: quark and gluon loops. at present not calculable from first principles relies on a dispersion relation approach Total: -- PDG-2013 V. Tishchenko Idaho State University, Colloquium 18 April, 2016 25 Brookhaven storage ring ● Long list of innovations beyond CERN III – Flux in 12 bunches from the AGS – Long enough beamline to operate with pion or muon injection – Inflector to get muons through the back yoke...allowed muon injection – High voltage, fast, non-ferric kickers to shift muon onto orbit in first cycle – Thin quadrupoles and scalloped vacuum vessels minimize preshower – In situ, field measurements with NMR trolley – Continuous NMR monitoring and <0.1 ppm absolute calibration – Pb/Scifi calorimeters, hodoscopes, and a traceback wire chambers V. Tishchenko Idaho State University, Colloquium 18 April, 2016 26 BNL g-2 experiment in a nutshell V. Tishchenko Idaho State University, Colloquium 18 April, 2016 27 BNL g-2 experiment in a nutshell Determining the anomalous magnetic moment requires measuring 2001 data from E821 ● The spin precession frequency muon decay is self-analyzing: higher energy positrons are emitted preferen- tially in direction of muon spin wrapped around modulo 100 μs ● The magnetic field B ( ) 375 fixed NMR probes 17 NMR trolley probes V. Tishchenko Idaho State University, Colloquium 18 April, 2016 28 Electric quads to contain the beam vertically +HV -HV -HV +HV E-field contribution vanishes V.
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