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4/26/2007 The Fine Structure Constant and Electron (g‐2) Factor Nick Hutzler Physics 135c Spring 2007 Theory Review • A (spin) magnetic moment μ quantifies how a particle interacts with magnetic fields particle interacts with magnetic fields • The electron has μ proportional to spin μ=g eh S S = gμ B 2m h h • The fine structure constant α characterizes the strength of the EM interaction α= e2 1 ≈ 4πε0 hc 137 Nick Hutzler // Ph 135c // Spring 2007 2 1 4/26/2007 Theory Review • The (spin) factor g is dimensionless and varies b by particle type ti l t – Classical charged sphere: g = 1 – Dirac point particle: g = 2 – Neutron: g = ‐3.826 085 45(90) – Proton: g Proton: g = 5.585 5.585 694 713(46) • The anomalous magnetic moment is defined as a = (g‐2)/2 Nick Hutzler // Ph 135c // Spring 2007 3 Theory Review • Why measure g? – Probe of possible internal structure – One of best tests of QFT/QED, new physics – Fine structure constant α determined by g+QED Nick Hutzler // Ph 135c // Spring 2007 4 2 4/26/2007 Theory Review • Why isn’t g = 2? – TTree level Feynman l lF diagram gives g = 2 – Higher order corrections from quantum fluctuations add ~.001 Nick Hutzler // Ph 135c // Spring 2007 5 Theory Review • g and α are closely related – a has a series expansion in α (remember that α is commonly expanded in perturbation series) a = C1 ( απ ) + C2 ( απ ) + C3 ( απ ) + L + aμτ + ahadronic + aweak 2 3 – The Ci are calculated from QED – The aμτ,hadronic,weak μτ hadronic weak terms are the QED muon/tau contribution, and non‐QED hadronic and weak contributions (respectively) Nick Hutzler // Ph 135c // Spring 2007 6 3 4/26/2007 Theory Review Nick Hutzler // Ph 135c // Spring 2007 7 History • Earlier α measurements – Quantum Hall effect RK = μ 0c 2α – Atomic spectra R∞ = α 2 me c 2h – Josephson effect U= h ∂φ 2e ∂t – Recoil measurements, numerology, others Nick Hutzler // Ph 135c // Spring 2007 8 4 4/26/2007 Philosophy • Why does α have this value? – Anthropic Principle: small changes in the value of α Principle: small changes in the value of α would dramatically change the universe – Numerology: Arthur Eddington calculated α=1/136 using numerology and gave the Eddington Number: N = 2256/ α – Feynman: “one of the greatest damn mysteries of physics: a magic number that comes to us with no physics: a magic number that comes to us with no understanding by man” – James Gilson: α has a formula: α= cos(π / 137 ) tan(π / (137 ⋅ 29 )) ≈ 1 / 137.0359997867 137 π / (137 ⋅ 29 ) Nick Hutzler // Ph 135c // Spring 2007 9 The Experiment • We shall discuss a recent measurement of g and resulting calculation of α d lti l l ti f • New Measurement of the Electron Magnetic Moment Using a One‐Electron Quantum Cyclotron – Odom, Hanneke, D Odom, Hanneke, D’Urso, Urso, Gabrielse Gabrielse – Harvard Physics Department – PRL 2006 Nick Hutzler // Ph 135c // Spring 2007 10 5 4/26/2007 The Experiment • Overview: – Put an electron in cyclotron motion – Measure jumps between lowest quantum states – Calculate g – Calculate α Nick Hutzler // Ph 135c // Spring 2007 11 Penning Traps • Static fields used to trap charged particles charged particles – Uniform axial B field – Quadrupole E field • Earnshaw’s Theorem: static electric fields alone cannot confine a alone cannot confine a charged particle Nick Hutzler // Ph 135c // Spring 2007 12 6 4/26/2007 Penning Traps • Four motions: – – – – Spin (ν Spin (νs) Cyclotron (νc = 2 νs/g) Axial (νz) Magnetron (νm) • In the present experiment: – – – – νs ≈ νcc’ ≈ 149 GHz νz’ ≈ 200 MHz νm’ ≈ 134 kHz Prime denotes “actual” Nick Hutzler // Ph 135c // Spring 2007 13 Particle Motion • Spin motion is essentially free • Cyclotron motion is damped by synchrotron radiation (~0.1 s in free space) – However, in this trap the fields are tuned so that cyclotron motion is far from a cavity mode – Lifetime extended to several seconds Nick Hutzler // Ph 135c // Spring 2007 14 7 4/26/2007 Energy Levels • Measure jumps between lowest spin (ms) and cyclotron (n) levels E (n , ms ) = 1 g 2 hν m + (n + 1 / 2 )hν c' − hδ(n + 1 / 2 + ms ) 2 c s 2 • νa’ and fc’ are anomaly and spin‐up frequencies (respectively) • νc is classical cyclotron frequency eB/2πm Nick Hutzler // Ph 135c // Spring 2007 15 Energy Levels • νc is obtained using the Brown Gabrielse Brown‐Gabrielse Invariance Theorem: (ν c )2 = (ν c' )2 + (ν z' )2 + (ν m' )2 • This allows us to calculate g/2: l l /2 g ν a' + ν c' ν a' − ν 2z' / (2 f c' ) = ≅ 1+ 2 νc f c' + 3δ / 2 + ν 2z' / (2 f c' ) Nick Hutzler // Ph 135c // Spring 2007 16 8 4/26/2007 What is Measured? • Spin and cyclotron jumps induce a change jumps induce a change in νz’ • A resonant circuit drives the axial motion at νz’ (SEO) • Quantum Jump Quantum Jump Spectroscopy Nick Hutzler // Ph 135c // Spring 2007 17 What is Measured? • Anomaly transitions are created by inducing created by inducing spin‐flips with a perpendicular B field • Cyclotron transitions are induced by microwaves • Both drives are always B hd i l on, but tuned so that only one affects the electron Nick Hutzler // Ph 135c // Spring 2007 18 9 4/26/2007 Results • g/2 = 1.001 159 652 180 85(76) • That’s 76 parts per trillion • Certainly of the most accurate measurements ever made Nick Hutzler // Ph 135c // Spring 2007 19 Sources of Error • Magnetic field instabilities – After After settling for several months, the superconducting settling for several months the superconducting solenoid is constant to 10‐9/hours – Maintain in 0.3K environment – Perform measurements at night • Fitting/statistics – ~50 measurements/night • Cavity radiation modes Cavity radiation modes • Blackbody Photon Excitation – Cool sample to <100mK Nick Hutzler // Ph 135c // Spring 2007 20 10 4/26/2007 Fine Structure Constant • This g‐value translates to α‐1 = 137.035 999 710(90)(33)[0.66][0.24] = 137.035 999 710(96)[0.70] • The top line errors are experimental, QED respectively (second line gives total error) • Square brackets give error in ppb Nick Hutzler // Ph 135c // Spring 2007 21 Fine Structure Constant • C4,C6,C8,C10 require the evaluation of 7 72 891 12 672 F 7,72,891,12 672 Feynman diagrams di respectively • C8 is known fairly well, C10 is still being calculated Nick Hutzler // Ph 135c // Spring 2007 22 11 4/26/2007 Important Conclusions • QED continues to be a highly accurate d description of the physical world i ti f th h i l ld • The electron can still be viewed as having no internal structure Nick Hutzler // Ph 135c // Spring 2007 23 Electron Internal Structure • Internal constituents must have m > 130 GeV – Calculations made assume no internal structure – Thus corrections must come from very high energy/short distance scales – i.e. constituents must be very tightly bound • No QED error: m No QED error: m > 600 GeV 600 GeV Nick Hutzler // Ph 135c // Spring 2007 24 12 4/26/2007 References • New Measurement of the Electron Magnetic Moment Using a One‐Electron Using a One Electron Quantum Cyclotron Quantum Cyclotron Odom, Hanneke, D’Urso, Gabrielse. PRL 97, 030801 • New Determination of the Fine Structure Constant from the Electron g Value and QED Gabrielse, Hanneke, Kinoshita, Hio, Odom. PRL 91 030802 • Fully Quantum Measurement of the Electron Magnetic Moment Magnetic Moment Brian Odom, Thesis, Harvard University, 2004 • A Finer Constant, Czarnecki, Nature 443 p. 516 • James Gilson, fine‐structure‐constant.org Nick Hutzler // Ph 135c // Spring 2007 25 13