Download Tests of fundamental symmetries - lecture 1

Test of fundamental symmetries
from an atomic physics perspective
With thanks to
Antoine Weis
Mike Tarbutt
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Sumerian, 2600 B.C. (British Museum)
The plan…
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Introduction to symmetry
Mirror symmetry – parity – P
Puzzles
Time-reversal symmetry – T
CPT
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What is symmetry?
Take a ‘thing’
Thing, T
Do something to it
Symmetry operation, O
Does the thing remain the same?
New thing, T’
Examples of a ‘thing’:
 Macroscopic object
 Particle \ atom \ molecule
 Process
 Elementary force \ interaction
Property, P
Property, P’
If P’ = P
We say “T is invariant under
the symmetry operation O”
We say “O is a symmetry of T”
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Symmetry operations
Continuous symmetries
 Space translation
 Time translation
 Orientation
 Boosts (Lorentz transformation)
Discrete symmetries
 Space reflection (parity)
 Time reversal
 Charge conjugation
 Interchange of identical particles
The laws of nature (or in some cases, a subset of them) are
invariant under these operations (as far as we can tell).
Note – this is an experimental matter!
“In all physics nothing has shown up indicating an intrinsic difference
of left and right. The same problem of equivalence arises with respect
to past and future, and with respect to positive and negative electricity.
A priori evidence is not sufficient to settle the question; the empirical
facts have to be consulted.”
Hermann Weyl (1951)
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Some counter-examples
• You can tell when a system is rotating, without
looking from the outside (e.g. the earth)
• No invariance under a change of scale
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No scale invariance – why giants don’t exist
From Galileo’s “Two New Sciences”
“To illustrate briefly, I have sketched a bone whose natural length has been increased three times and whose
thickness has been multiplied until, for a correspondingly large animal, it would perform the same function
which the small bone performs for its small animal.”
“From the figures here shown you can see how out of proportion the enlarged bone appears….the smaller the
body the greater its relative strength. Thus a small dog could probably carry on his back two or three dogs of
his own size; but I believe that a horse could not carry even one of his own size. “
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Noether’s theorem
For every continuous symmetry of the laws of
physics, there must exist a conservation law.
For every conservation law there must exist a
continuous symmetry.
Symmetry
Conserved quantity
Emmy Noether, 1882-1935
Space translations
Rotations
Time translations
Momentum
Angular momentum
Energy
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Parity and mirror symmetry
Mirror reflection
Parity operation
P
{x,y,z}
r
{x,y,z}
{-x,-y,-z}
y
Reflect
{x,y,-z}
y
z
x
x
y
-z
z
-r
x
Parity operation
=
mirror reflection
+
rotation by p around the z-axis
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Parity conservation and violation
When a thing looks the same after
reflection in a mirror we say:
“this thing conserves parity”
When the mirror image of a thing is not
the same as the thing itself we say:
“this thing is chiral”
“it has handedness”
“it has helicity”
“it violates parity”
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Rotations, axial vectors, polar vectors & handedness
-V
V
A
Polar vector:
rank 1 spherical tensor, odd under parity
Rotation
Axial vector
A
+
Axis
=
A
Axial vector:
rank 1 spherical tensor, even under parity
Handedness
Polar vector
Helicity
V
V. A
|V||A|
Pseudoscalar:
odd under parity
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1957: weak interactions violate parity
1956 - Lee & Yang - no experimental evidence for parity
conservation in weak interactions; suggest possible experiments.
T.D. Lee & C.N. Yang, Physical Review 104, 254 (June 22 1956)
January 1957 - 3 papers appear in Physical Review proving that
weak interactions violate parity.
C.S. Wu, E. Ambler, R.W. Hayward, D.D. Hoppes and R.P.
Hudson, Physical Review 105, 1413 (15 January 1957)
R.L. Garwin, L.M. Lederman and M. Weinrich, Physical Review
105, 1415 (15 January 1957)
J.I. Friedman and V.L. Telegdi,
Physical Review 105, 1681 (17 January 1957)
C.S. Wu, in the lab
Lee and Yang awarded the 1957 Nobel prize in Physics
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Weak interactions violate parity
Beta-decay
n
p
e
e
60%
udd
40%
60Co
d
u
Neutrino helicity
d
100%
uud
u
W
e
e
e
e
e
e
0%
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Is parity violation possible in atoms?
 In b-decay, parity violation is mediated by the weak charged currents, W+/-
 Identity of interacting particles changes at the vertex (they carry charge)
 Cannot occur for stable atoms
 No atomic parity violation mediated by weak charged currents
 Atomic parity violation CAN be mediated by weak neutral currents
Two types of neutral-current interaction between a nucleon and an electron in an atom:
N
e
N
N
e
N
 Electromagnetic
 Mediated by exchange of photons
 Conserves parity
Z
0
e
e
 Weak
 Mediated by exchange of Z0
 Violates parity
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How to search for parity violation in atoms
Circular dichroism
Optical rotation
IL
IR
Measure absorption of left-handed and
right-handed circularly polarized light.
Measure plane of polarization of incident
and transmitted plane-polarized light.
Is there a difference?
Is there a difference?
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The parity violating potential
What is the form of the potential responsible for parity violation in atoms?
Interaction is mediated by a massive particle
Yukawa potential
r0 is the “range” of the potential
The coupling of a Z0 to an e is proportional to the e helicity
Electromagnetic potential
Z – electric charge
e – coupling constant
Parity-violating potential
Qw – weak nuclear charge
g – coupling constant (~e, unification)
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What is QW?
QW
Weak nuclear charge
Additive – just add together the weak charges for all the quarks in the nucleus
Neutron – ddu
Proton – uud
Number of protons
Number of neutrons
Weak charge
of up-quark
Weak charge
of down-quark
Standard model gives us
Primary aim of atomic parity violation experiments – measure QW
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How to search for Atomic Parity Violation I
N
e
N
N
e
N
Electromagnetic process:
Assign an amplitude Aem
Z
0
e
e
Weak process:
Assign an amplitude AW
First idea: The brute force approach
Look directly at a “pure” parity-violating signal
e.g. drive a transition that is otherwise completely forbidden
Rate is proportional to | AW |2.
Relative to an allowed E1 transition, suppressed by 20-30 orders of magnitude!
Completely impossible.
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How to search for Atomic Parity Violation II
N
e
N
N
e
N
Electromagnetic process:
Assign an amplitude Aem
Z
0
e
e
Weak process:
Assign an amplitude AW
These two processes have identical initial and final states.
The probability for the process is given by:
Sign depends on handedness of
experiment
Since AW <<Aem
Try to measure this interference term
N.B. Linear in Aw
A good measure of the degree of Left-Right asymmetry is
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How big is it?
For both types of interaction, the amplitude is
g1, g2 - coupling constants at the vertices,
q - momentum transfer
M – mass of the mediating gauge boson
Consider the hydrogen atom
For the electromagnetic interaction,
g1= g2= e
M = Mg = 0
q= electron momentum= ma c
For the weak interaction,
g1=g2 = g
M = MZ
q << M c
Electroweak unification: g = e
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All is not lost
Enhance AW by using heavier atoms – turns out that AW ~ Z3
Suppress Aem by using forbidden transitions (i.e. not E1)
An example – 6S1/2 – 7S1/2 in Cs:
E1 – strictly forbidden by parity (in absence of parity violation!)
M1 –approximately forbidden by Dn=0 selection rule
E2 – J=1/2 – J=1/2 transitions are strictly forbidden
M2, E3 – parity forbidden…
Excite
7S
6P
6S
Enhancements can result in
Beware – forbidden transitions allow for much larger Left-Right
asymmetry, but result in very small signals.
Is it better to measure 10-8 of something, or 10-4 of nothing?
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Stark-induced E1 transition
Search for the parity-violating 6S – 7S E1 transition
In presence of electric field, there is a Stark-induced component to the 6S-7S rate
This allows the transition rate to be controlled
Stronger signal
Smaller asymmetry
Trade-off between size of signal and size of
asymmetry can be controlled using an electric field
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Colorado Cs experiment I
7S
Excite
6P
6S
Excite 6S-7S transition
Observe resulting fluorescence
Does excitation rate change when
apparatus handedness is reversed?
Reversals
Coordinate system defined by electric field,
magnetic field and photon angular momentum
vectors – defines the handedness.
E
-E
B
-B
s
-s
m
-m
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Colorado Cs experiment II
Electric field plates
divided into 5 segments
Build-up cavity,
F=30000
Intensity stabilizer
Optical isolator
Half-wave plate
Pockels cell
4 lasers – Df/f=10-14, DI/I=10-6
31 servo-loops
23 magnetic field coils
32 switch states
7 years of development
5 years on systematic effects
8 months of data-taking
1 result, 0 Nobel prizes!
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Colorado Cs experiment - results
The absorption coefficient of Cs depends on the handedness of the apparatus
Difference is about 6 parts per million, measured to 0.35% precision
Experimental
result
Atomic physics
calculations
Combine
Compare to Standard Model:
Agree within 1s
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What does a parity violating atom look like?
Example – the 2p1/2 state of hydrogen
Calculate the current density:
e ~ 10-11 – too small to visualize.
Artificially increase it by 10 orders of magnitude
N.B. You could solve this problem yourselves,
with the help of Am. J. Phys. 56, 1086 (1988)
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Shoes
More left shoes are washed up on
Dutch beaches, more right shoes
on Scottish beaches!
Results of a 1997 study:
Texel, Holland: 68 left, 39 right
Shetland islands: 63 left, 93 right
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Chiral molecules
Limonene
Smells of oranges
Carvone
Tastes of spearmint
Smells of lemons
(or turpentine!)
Tastes of caraway
Thalidomide
(R)
Sedative. Treatment of morning sickness
(S)
Malformations in over 10,000 children
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Biological homochirality
Chiral molecules synthesized in the lab
Equal mixture of left and right handed enantiomers
Not so in life…
Racemic mixture
All amino acids found in life are left-handed
Biologically relevant sugars are right-handed
Maximal parity violation
How did it happen?
Is the weak interaction involved?
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