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1 Test of fundamental symmetries Sumerian, 2600 B.C. (British Museum) With thanks to Antoine Weis from an atomic physics perspective Mike Tarbutt

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2 CPT theorem Charge conjugation C Parity P Time-reversal T CPT Combine All local, Lorentz-invariant quantum field theories are invariant under CPT

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3 CP & T violation CP violationT violation 1964 – CP violation observed in decays of neutral K-mesons 1998 – T violation observed in decays of neutral K-mesons 2001 – CP violation observed in decays of neutral B-mesons Consistent with Standard Model CPT theorem Our solar system – 2 billion billion billion tonnes of matter Our galaxy – 200 billion stars Observable universe – 80 billion galaxies

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4 How to measure T-violation + + - - E B + + - - E B T E.B is T-odd AND P-odd + + - - E B P + + E B Gives us an apparatus to measure T-odd (and P-odd) properties

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5 + - Spin Edm + - Spin Edm T TCP implies Insufficient CP Either d e = 0, or T 10 -24 10 -22 10 -26 10 -28 10 -30 10 -32 10 -34 10 -36 Multi Higgs Left - Right MSSM ~ 1 MSSM ~ Standard Model Predicted values for the electron edm d e (e.cm) Experimental upper bound Particle EDM’s, the Standard Model & beyond

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Measuring the EDM – spin precession Gyroscope precessing in a gravitational field Electron precessing in a magnetic field Electron precessing in parallel magnetic and electric fields Electron precessing in anti-parallel magnetic and electric fields Measure change in precession rate when electric field direction is reversed – this is proportional to the EDM To measure the electron EDM, use an electron inside an atom or molecule

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7 Using atoms & molecules to measure e-edm Atom / Molecule Electric Field E Interaction energy = - d e.E eff = - d e.( E) N.B. Analogous to interaction of magnetic dipole moment with a magnetic field, - B Enhancement factor E eff = F P Structure dependent, ~ 10 (Z/80) 3 GV/cm Polarization factor For more details, see E. A. Hinds, Physica Scripta T70, 34 (1997)

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8 2 Tl atomic beams hf = B polarise analyse ± d E E ± B The solution: add 2 more Tl beams going down 4 analyse polarise The solution: Add 4 Na beams for magnetometry 1st huge problem: motional interaction v E The Tl edm experiment 2 nd huge problem: stray static magnetic fields B.C. Regan, E.D. Commins, C.J. Schmidt and D. DeMille, PRL 88, 071805 (2002) Tl – enhancement factor = 585 Final result (2002) |d e | < 1.6 x 10 -27 e.cm (90% CL)

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9 Molecules are even more sensitive than atoms “Huge” edm interaction energy (10aeV, 2mHz, 80f cm -1, 100 fK) Less demanding magnetic field control (d false = 3x10 -27 e.cm/pT) Insensitive to B perpendicular to E (suppressed by 10 10 ) Thus, insensitive to motional-B (B mot = v E / c 2 = 10 4 pT) Enhancement factor for YbF For more details, see PRL 89, 023003 (2003) E eff = F P Structure dependent, ~ 10 (Z/80) 3 GV/cm Polarization factor For atoms, P ~ 10 -3 For molecules, P ~ 1

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Result of the YbF EDM experiment d e = (-2.4 ± 5.7 stat ± 1.5 syst ) × 10 -28 e.cm | d e | < 10.5 × 10 -28 e.cm (90% confidence level) For details, see Nature 473, 493 (2011)

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10 -24 10 -22 10 -26 10 -28 10 -30 10 -32 10 -34 10 -36 Multi Higgs Left - Right MSSM ~ 1 MSSM ~ Standard Model Predicted values for the electron edm d e (e.cm) Our result: | d e | < 10.5 × 10 -28 e.cm Measurement & theory Excluded region (5 × 10 -19 Debye)

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12 CPT – precision spectroscopy of antihydrogen All local, Lorentz-invariant quantum field theories are invariant under CPT CPT theorem Should be tested Magnetic moments (g-2) of e - and e + Completed Equal – 1 part in 10 12 PRL 59, 26 (1987) Precision spectroscopy of H and anti-H Being developed Claimed potential – 1 part in 10 18 !! N.B g/2(e - ) = 1.00115965218085(76) PRL 97, 030801 (2006) For Hydrogen, f(1s-2s) already measured to 1 part in 10 14

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Quantum Electrodynamics Dirac Equation : spin 1/2.

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