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Gabrielse
The Electron and Its Moments:
The Most Precise Tests of the Standard Model
Gerald Gabrielse
Leverett Professor of Physics, Harvard University
1. The Electron Magnetic Moment
 Most precisely measured property of an elementary particle
 Most precise prediction of the Standard Model
 Incredible agreement
2. The Electron Electric Dipole Moment
 Standard Model predicts unmeasurable small moment
 Extensions to Standard Mode predict measureable moments
 None detected so far (will this change this fall?)
Supported by NSF
Download papers: http://gabrielse.physics.harvard.edu
Gabrielse
The Amazing Electron
Electron orbits give atoms their size, but the electron itself
may actually have no size
R  2 10
20
m
m*  10.3 TeV / c
2
20000 electron masses
of binding energy for
“ingredients”
Electron has angular momentum (spin) even though it has no
size and nothing is rotating:
S m R2 
Magnetic moment:
S
  
/2
(exists and well-measured)
Electric dipole Moment:
S
d  d
/2
(d is extremely small)
Gabrielse
Electron Spin Magnetic Moment
magnetic    g  S
B
2
/2
moment
angular momentum
Bohr magneton e
2m
 / B   g / 2
magnetic moment in Bohr magnetons for spin 1/2
 /  B   g / 2  1/ 2 mechanical model with identical charge
and mass distribution
 /  B   g / 2  1
spin for simple Dirac point particle
 /  B   g / 2  1.001 159 ...
simplest Dirac spin, plus QED
(if electron g/2 is different  electron has substructure)
Gabrielse
Quantum Measurement of the Magnetic Moment
Spin flip energy:
Cyclotron energy:
s    B
eB
c 
m
s


c
B
Bohr magneton e
2m
Need to resolve the quantum states of the cyclotron motion
 Relativistic shift is 1 part in 109 per quantum level
Gabrielse
Need Good Students and Stable Funding
20 years
8 theses
Elise Novitski
Joshua Dorr
Shannon Fogwell Hogerheide
David Hanneke
Brian Odom,
Brian D’Urso,
Steve Peil,
Dafna Enzer,
Kamal Abdullah
Ching-hua Tseng
Joseph Tan
N$F
Gabrielse
David Hanneke G.G.
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Need New Ideas Needed  quantum homemade atom
Van Dyck, Schwinberg, Dehemelt did a good job in 1987
Phys. Rev. Lett. 59, 26 (1987)
(spent some years trying to improve but …)
first measurement with
these methods
Takes time to develop new ideas and methods
needed to measure with 2.8 parts in 1013 uncertainty
• One-electron quantum cyclotron
• Resolve lowest cyclotron states as well as spin
• Quantum jump spectroscopy of spin and cyclotron motions
• Cavity-controlled spontaneous emission
• Radiation field controlled by cylindrical trap cavity
• Cooling away of blackbody photons
• Synchronized electrons identify cavity radiation modes
• Trap without nuclear paramagnetism
• One-particle self-excited oscillator
Gabrielse
Cylindrical Penning Trap
V ~ 2 z 2  x2  y 2
• Electrostatic quadrupole potential  good near trap center
• Control the radiation field  inhibit spontaneous emission by 200x
(Invented for this purpose: G.G. and F. C. MacKintosh; Int. J. Mass Spec. Ion Proc. 57, 1 (1984)
Gabrielse
Quantum Jump Spectroscopy
• one electron in a Penning trap
• lowest cyclotron and spin states
“In the dark” excitation
 turn off all detection
and cooling drives
during excitation
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Inhibited Spontaneous Emission
excite,
measure time in excited state
t = 16 s
20
10
0
0
10
20
30
40
decay time (s)
50
60
15
12
9
Y Axis 2
30
axial frequency shift (Hz)
number of n=1 to n=0 decays
Application of Cavity QED
6
3
0
-3
0
100
200
time (s)
300
Most precisely measured property of an elementary particle
Electron Magnetic Moment Measured
to 3 x 10-13
2.8  10 13
(improved measurement is underway)
Gabrielse
Gabrielse
The Standard Model Predicts
the Electron Magnetic Moment
in terms of the
fine structure
constant
e2
1


4 0 c 137
1
Gabrielse
Standard Model of Particle Physics
Prediction
essentially
exact
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Probing 10th Order and Hadronic Terms
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Most Precise Determination
of the Fine Structure Constant (g/2 + QED)
exp`t
Determinations
of the fine
structure constant
theory
before 2012
Gabrielse
Next Most Accurate Way to Determine  (use Cs example)
Combination of measured Rydberg, mass ratios, and atom recoil
e2
 
4 0 hc
1
2 
2 R h
c me
2 R h M Cs M p

c M Cs M p me
 2  4 R c
Biraben, …

f recoil M Cs M 12C
( f D1 )2 M 12C me
e4 me c
R 
(4 0 ) 2 2h3c 2
1
Pritchard, …

h
2 f recoil
 2c
M Cs
( f D1 ) 2
Haensch, …
Chu, …
Haensch, …
Tanner, …
Werthe, Quint, Blaum, …
• Now this method is 3 times less precise
• We hope that it will also improve in the future  test QED
(Rb measurement is similar except get h/M[Rb] a bit differently)
Gabrielse
(Greatest?) Triumph of the Standard Model
Measured:
“Calculated”:
 /  B   g / 2  1.000 159 652 180 73 (28) [0.28 ppt ]
 /  B   g / 2  1.000 159 652 181 88 (78) [0.77 ppt ]
(Uncertainty from measured fine structure constant)
From Freeman Dyson – One Inventor of QED
Gabrielse
Dear Jerry,
... I love your way of doing experiments, and I am happy to congratulate you for
this latest triumph. Thank you for sending the two papers.
Your statement, that QED is tested far more stringently than its inventors could
ever have envisioned, is correct. As one of the inventors, I remember that we
thought of QED in 1949 as a temporary and jerry-built structure, with
mathematical inconsistencies and renormalized infinities swept under the rug. We
did not expect it to last more than ten years before some more solidly built theory
would replace it. We expected and hoped that some new experiments would
reveal discrepancies that would point the way to a better theory. And now, 57 years
have gone by and that ramshackle structure still stands. The theorists … have kept
pace with your experiments, pushing their calculations to higher accuracy than we
ever imagined. And you still did not find the discrepancy that we hoped for. To
me it remains perpetually amazing that Nature dances to the tune that we scribbled
so carelessly 57 years ago. And it is amazing that you can measure her dance to
one part per trillion and find her still following our beat.
With congratulations and good wishes for more such beautiful experiments, yours
ever, Freeman.
Gabrielse
Test for Physics Beyond the Standard Model
 g

  1  aQED ( )   aSM :Hadronic Weak   aNew Physics
B 2
measure
to a very high
precision
calculate these
to a very high
precision
look for a
disagreement
expected to be 40000 times
larger for a muon
compared to an electron
 m 


 me 
2
Measure electron moment  test predictions of the standard model
Measure muon moment  look for physics beyond the Standard Model
Gabrielse
Test for Physics Beyond the Standard Model
 g

  1  aQED ( )   aSM :Hadronic Weak   aNew Physics
B 2
Does the electron have internal structure?
m*  total mass of particles bound together to form electron
R  5 10
19
m
R  2 1019 m
m
 360 GeV / c 2
a
m
m* 
 1 TeV / c 2
a
m* 
limited by the uncertainty in
independent  value
if our uncertainty
was the only limit
Not bad for an experiment done at 100 mK, but LEP does better
R  2 1020 m
m*  10.3 TeV / c 2
LEP contact interaction limit
> 20000 electron masses of binding energy
Gabrielse
Emboldened by the Great Signal-to-Noise
Make a one proton (antiproton) self-excited oscillator
 detect proton (and antiproton) spin flips
Gabrielse
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Does the Electron Also Have an Electric Dipole Moment?
Magnetic moment:
S
  
/2
S
Electric dipole moment: d  d
/2
(exists and well-measured)
(d is extremely small)
No Electron EDM Detected so Far
Commins limit (2002)
Tl
q = 10-9 e
Regan, Commins, Schmidt, DeMille,
Phys. Rev. Lett. 88, 071805 (2002)
r = 2 x 10-20 m
q = -10-9 e
Imperial College (2011)
YbF
Hudson, Kara, Smallman, Sauer, Tarbutt, Hinds,
Nature 473, 493 (2011)
Gabrielse
Advanced Cold-Molecule Electron EDM
Harvard University
Yale University
John Doyle Group
David DeMille Group
Gerald Gabrielse Group
Nearing publication of a new result
for the electron EDM
Funding from NSF
Gabrielse
Particle EDM Requires Both P and T Violation
Magnetic moment:
S
  
/2
(exists and well-measured)
P
T
Electric dipole Moment:
S
d  d
/2
(d is extremely small)
If reality is invariant under parity
transformations P
 d=0
If reality is invariant under time reversal
transformations T
 d=0
Gabrielse
Standard Model of Particle Physics
 Currently Predicts a Non-zero Electron EDM
Standard model: d ~
10-38
e-cm
Too small to measure by orders of magnitude
best measurement: d ~ 2 x 10-27 e-cm
Weak interaction couples quark pairs (generations)
CKM matrix relates to d, s, b quarks
(Cabibbo-Kabayashi-Maskawa matrix)
almost the unit matrix
four-loop
level in
perturbatio
theory
Extensions to the Standard Model
 Measureable Electron EDM
Gabrielse
An example
Low order contribution
 larger moment
Low order contribution
 vanishes
From Fortson, Sandars and Barr, Physics Today, 33 (June 2003)
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EDM Predictions
Cannot Use Electric Field Directly
on an Electron or Proton
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Simple E and B can be used for neutron EDM measurement
(neutron has magnetic moment but no net charge)
Electric field would accelerate an electron out of the apparatus
Electron EDM are done within atoms and molecules
(first molecular ion measurement is now being attempted)
Gabrielse
Schiff Theorem – for Electron in an Atom or Molecule
Schiff (1963) – no atomic or molecular EDM (i.e. linear Stark effect)
• from electron edm
• nonrelativistic quantum mechanics limit
Sandars (1965) – can get atomic or molecular EDM (i.e. linear Stark
effect)
• from electron edm
• relativistic quantum mechanics
• get significant enhancement (D >> d) for large Z
Commins, Jackson, DeMille (2007) – intuitive explanation for escape
from Schiff
 Lorentz contraction of the electron EDM viewed in
lab frame Schiff, Phys. Rev. Lett. 132, 2194 (1963);
Sandars, Phys. Rev. Lett. 14, 194 (1965); ibid 22, 290 (1966).
Commins, Jackson, DeMille, Am. J. Phys. 75, 532 (2007).
Gabrielse
No Particle EDM Has Yet Been Detected
Electron EDM limit
Commins, …
PRL 88, 071805 (2002)
1.0
Hinds, 2011
Neutron EDM limit
IIL Grenoble,
PRL 97, 131801 (2006)
Proton EDM limit
Heckel, Fortson, …
PRL 102, 101601 (2009)
from
also sets
199Hg
electronneutron
10-
10-
29
28
101027e∙cm 26
proton
10-
10-
25
24
Gabrielse
Why Use a Molecule?
 To Make Largest Possible Electric Field on Electron
Tl atom (best EDM limit till YbF)
Elab  123 kV/cm

E eff  72 MV/cm
ThO molecule
Elab  100 V/cm

Eeff  100 GV/cm
Molecule can be more easily polarized using nearby energy levels with
opposite parity (not generally available in atoms)
Gabrielse
Promising Molecules
Molecular calc.
project on
atomic basis
Imperial
Oklahoma
Yale
JILA
Harvard - Yale
Thallium atom
Experiment used
used 120 kV/cm
GV/cm
89
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Why ThO?
Omega doublets in excited H state
 closely spaced levels with opposite parity
(i.e. easily polarized with small lab electric field)
 high internal electric field with weak lab field
Molecule is “easier to understand” than some, Hunds case c
 leads to rigid rotor “rotation” states
(despite the inclusion of electronic ang. mom. J)
Excited H state is triplet, with ground state singlet  long-lived as
needed for a beam
Excited H state has small magnetic moment (0.01 Bohr magnetons)
 not very vulnerable to magnetic field noise
Th has high Z  escape the Schiff theorem (and get enhancement)
Excitation laser tuning tuning changes the direction of mol. polarization
(i.e. the direction of the internal E with respect to the laboratory E)
All transitions accessible with diode lasers
Old spectroscopy papers made it easier to find the states
Gabrielse
Measure Magnetic Moment of the H State
NdFeB permanent magnets: 2 kG
Rotate polarization to empty (to E state)
the M=0 state (red)
or the M=+/-1 states (green)
Small enough that magnetic noise should
not be a big problem
Gabrielse
B E
Conceptual EDM Measurement
B E
ThO
B E
ThO
detect phase of evolved state
make superposition of the
polarized edm states
look for changes as E is reversed
time evolution 
Gabrielse
Detect the Energy Difference
S
 g
/2
S
de  de
/2
two states evolve differently in time
e
 i E t / hbar
Gabrielse
Detecting an EDM
ground state superposition evolve: E +
edm
cold
ThO
source
combine
emit
E B
electric field plates
magnetic field
light
detector
apparatus control
and data acquisition
Gabrielse
Apparatus in Lab 1
Molecu
lar
Beam
Source
Pulse Tube Cooler
“Interacti
on
Region”:
E-field
plates
inside, Bfield
shields
and coils
outside
Pulsed
YAG
Prep
Lasers Probe
Lasers
laser fiber docks
Lasers
100m
away
39
Gabrielse
Magnetic Field Coils and Shielding
mu metal
endplates
5 shields
(no shown)
~ 10-5
shielding
ThO beam
Cos(theta)
coils to
provide
transverse
B field
Interaction
chamber
inside
200 mG with uniformity of 10-3 over 26 cm
Gabrielse
Using ThO Itself to Measure the Electric Field
20
cm
𝐸𝑙𝑎𝑏
Pum
p
Measurement of
Transpar
ent Field
Plates
Prob
e
Ram
an
𝑥
𝐸𝑙𝑎𝑏 measured
at position of
Raman beam
(𝑥)
Δ𝑠𝑡 = 2 𝐷𝐻 ⋅ 𝐸𝑙𝑎𝑏 𝑥
C
Δ
Ram
an
PMT
𝑁 = −1
𝑁 = +1
Δ𝑠𝑡
𝛿
X
H
(Ground
(ED
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Estimates of Statistical Precision
Parameter
Symbol
Estimate
Beam yield: molecules/state/pulse (Neon)
Nbeam
2.6 x 1011
Beam forward velocity (Neon)
vf
180 m/s
Beam divergence (Neon)
Ωb
0.36 sr
Solid angle of beam detected
Ωd
8 x 10-5 sr
Beam length before interaction region
L0
70 cm
Beam length in interaction region
L
22 cm
Coherence time = L/vf
tc
1.22 ms
H state lifetime
tH
≥ 1.8 ms
Surviving H state fraction = Exp[-tc/tH]
f
0.50
State preparation efficiency
ep
6%
Geometric collection efficiency
eg
25%
Quantum efficiency of detector: PMT
eq
10%
Pulse repetition rate
R
100 Hz
Photon counts/sec =
Nbeam(Ωd/Ωb)fepegeqR
S0
4.3 x 106
d ~ 5 x 10-30 e-cm
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Superblock Switches
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Outside of a Block:
•C state omega doublet (2 blocks)
•[Interweaved Systematic of the day, if applicable]
•E field lead switch (4 blocks)
Alternative Method
of E field Switch
•Change relative pump-probe waveplate by 45 degrees (8
blocks)
•Rotate pump and probe waveplates in phase (16 blocks)
Total superblock length ~(32-128 blocks or .5 hr-2hrs)
These are switches that we do not expect to change any of the
measurements that we perform as systematic checks
Gabrielse
Statistical Comparison of ACME and Imperial
7 x 1.7 x 2 = 24
ACME ThO
Effective E field
100 GV/cm
Coherence time
1.1 ms
Photons/second*
1000 x 50
=50,000
Precision in same time:
Time for same precision
1
1
Imperial YbF
14 GV/cm
7
0.65 ms
1.7
500 x 25
=12,500
41/2
24
(24)2 ~ 600
*Our molecule source is more intense, allowing us to use a
Gabrielse
Total Phase Equation:
𝜙 𝑁, 𝐸, 𝐵
= 𝑔 + Δ𝑔 𝑁 𝐵0 + 𝐵𝑛𝑟 𝐵 + 𝐵𝑙𝑒𝑎𝑘 𝐸 𝜇𝐻 𝜏 + 𝑑𝑒 𝐸𝑒𝑓𝑓 𝐸 𝑁
++-
B0 g  t
+-+
Bleak g  t
+--
0
-++
Bnr g  t
-+-
B0 g  t
--+
de Eeff t
B0 η Enr  t
phase (rad)
Bnr g  t + θnr
3±5
x 10-5 rad
block (~1 min)
phase (rad)
+++
---
single block
10 blocks averaged
Derived quantities
392 ± 5
x 10-5 rad
block (~1 min)
phase (rad)
Parity sum (NEB)
??? ± 5
x 10-5 rad
block (~1 min)
phase (rad)
single block
10 blocks averaged
block (~1 min)
B0 g  t
+-+
Bleak g  t
+--
0
-++
Bnr g  t
-+-
B0 g  t
--+
de Eeff t
---
B0 η Enr  t
phase (rad)
++-
-3590 ± 5
x 10-5 rad
-2 ± 5
x 10-5 rad
block (~1 min)
phase (rad)
Bnr g  t + θnr
phase (rad)
Derived quantities
+++
-1530 ± 5
x 10-5 rad
4±5
x 10-5 rad
block (~1 min)
phase (rad)
Parity sum (NEB)
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-1 ± 5
x 10-5 rad
block (~1 min)
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New Electron EDM Measurement Close
Gabrielse
Relationship to LHC Physics
The LHC is exciting and important but EDMs also play a role
• should get an improved electron EDM on the LHC time scale
• If the LHC sees new particles, is CP violation involved?
• If the LHC sees nothing, EDM game is the only one in town
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Planned Improvements
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e.g. Stimulated Raman Adiabatic Passage
Current state
preparation
STIRAP
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ULE cavity for laser stabilization
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Some Lensing and Pumping
May Increase Our Signal (demos done)
2100 V
4 rods, 6 mm
Perhaps get a factor of 4 in solid angle
 Perhaps another factor of 4 from
pumping the X state into one rotational level
Also STIRAP
6 - 14
Gabrielse
Summary
Electron Magnetic Dipole Moment
Most precisely measured property of an elementary particle
Most precise prediction of the Standard Model
Most precise and successful confrontation of theory and experiment
Electron Electric Dipole Moment
New result is close at hand. Stay tuned
Substantial improvement in precision seems possible