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 conjugationC

ParityP

Time-reversalT

CPT

Combine

All local, Lorentz-invariant quantum field theories are invariant under CPT

3

CP & T violation

CP violation T violation

1964 – CP violation observed in decays of neutral K-mesons1998 – T violation observed in decays of neutral K-mesons2001 – 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

T CPimplies

Insufficient CP

Either de = 0, or T

10-24

10-22

10-26

10-28

10-30

10-32

10-34

10-36

Multi Higgs Left -

Right

MSSM f ~ 1

MSSM f ~ a/p

Standard ModelPred

icte

d va

lues

for t

he e

lect

ron

edm

de (

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 / MoleculeElectricField

E Interaction energy = - de .Eeff = - de .(hE)

N.B. Analogous to interaction of magnetic dipole moment with a magnetic field, -m . B

Enhancement factor

Eeff = 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 = mB

polarise

analyse

± dhEE±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 m v E

The Tl edm experiment

2nd 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 h = 585

Final result (2002)|de| < 1.6 x 10-27 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 (dfalse= 3x10-27 e.cm/pT)

Insensitive to B perpendicular to E (suppressed by 1010)

Thus, insensitive to motional-B (Bmot = v E / c2 = 104 pT)

Enhancement factor for YbF

For more details, see PRL 89, 023003 (2003)

Eeff = F P

Structure dependent, ~ 10 (Z/80)3 GV/cm

Polarization factor

For atoms, P ~ 10-3

For molecules, P ~ 1

Result of the YbF EDM experiment

de = (-2.4 ± 5.7stat ± 1.5syst) × 10-28 e.cm

| de | < 10.5 × 10-28 e.cm (90% confidence level) For details, see Nature 473, 493 (2011)

10-24

10-22

10-26

10-28

10-30

10-32

10-34

10-36

Multi Higgs Left -

Right

MSSM f ~ 1

MSSM f ~ a/p

Standard Model

Pred

icte

d va

lues

for t

he e

lect

ron

edm

de (

e.cm

)

Our result: | de | < 10.5 × 10-28 e.cm

Measurement & theory

Excluded region

(5 × 10-19 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 1012

PRL 59, 26 (1987)

Precision spectroscopy of H and anti-H

Being developed

Claimed potential – 1 part in 1018 !!

N.B g/2(e-) = 1.00115965218085(76)PRL 97, 030801 (2006) For Hydrogen, f(1s-2s) already measured to 1 part in 1014