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

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

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

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

5 + - Spin Edm + - Spin Edm T TCP implies Insufficient CP Either d e = 0, or T 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

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

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)

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, (2002) Tl – enhancement factor  = 585 Final result (2002) |d e | < 1.6 x e.cm (90% CL)

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 = 3x e.cm/pT)  Insensitive to B perpendicular to E (suppressed by )  Thus, insensitive to motional-B (B mot = v  E / c 2 = 10 4 pT) Enhancement factor for YbF For more details, see PRL 89, (2003) E eff = F P Structure dependent, ~ 10 (Z/80) 3 GV/cm Polarization factor For atoms, P ~ For molecules, P ~ 1

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

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 × e.cm Measurement & theory Excluded region (5 × Debye)

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 PRL 59, 26 (1987) Precision spectroscopy of H and anti-H Being developed Claimed potential – 1 part in !! N.B g/2(e - ) = (76) PRL 97, (2006) For Hydrogen, f(1s-2s) already measured to 1 part in 10 14