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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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The plan…

• Introduction to symmetry• Mirror symmetry – parity – P• Puzzles• Time-reversal symmetry – T• CPT

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What is symmetry?

If P’ = P

We say “T is invariant under the symmetry operation O”

We say “O is a symmetry of T”

Take a ‘thing’

Do something to it

Does the thing remain the same?

Thing, T Property, P

Symmetry operation, O

New thing, T’ Property, P’

Examples of a ‘thing’: Macroscopic object Particle \ atom \ molecule Process Elementary force \ interaction

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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

“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. “

From Galileo’s “Two New Sciences”

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Noether’s theorem

Emmy Noether, 1882-1935

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

Space translations

Rotations

Time translations

Conserved quantity

Momentum

Angular momentum

Energy

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Parity and mirror symmetry

{x,y,z} {-x,-y,-z}P

zy

x

r

-r

Parity operation

zy

x

-z

y

x

{x,y,z} {x,y,-z}Reflect

Mirror reflection

Parity operation = mirror reflection + rotation by p around the z-axis

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Parity conservation and violation

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”

When a thing looks the same after reflection in a mirror we say:

“this thing conserves parity”

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Rotations, axial vectors, polar vectors & handedness

A A

Axial vector:rank 1 spherical tensor, even under parity

Polar vector:rank 1 spherical tensor, odd under parity

V-V

Rotation + Axis = Handedness

Axial vector

A

Polar vector

V

Helicity.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)

Lee and Yang awarded the 1957 Nobel prize in Physics

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

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Weak interactions violate parity

60Co 60Ni e e

n p e e

udd uud e e

d u e e

u

d

e

e

W

60%

40%

Neutrino helicity

100% 0%

Beta-decay

60Co

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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:

e

N

N

e

Electromagnetic Mediated by exchange of photons Conserves parity

e

N

N

eZ 0

Weak Mediated by exchange of Z0

Violates parity

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How to search for parity violation in atoms

IL

IR

Circular dichroism

Measure absorption of left-handed and right-handed circularly polarized light.

Is there a difference?

Optical rotation

Measure plane of polarization of incident and transmitted plane-polarized light.

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 Vr err0r

r0 is the “range” of the potential r0 M c

The coupling of a Z0 to an e is proportional to the e helicity Vr he e.vecVemr Z e2

r errr because M 0

Electromagnetic potential

Z – electric chargee – coupling constant Qw – weak nuclear charge

g – coupling constant (~e, unification)

Parity-violating potential

VPVr 12

Qw g2

r errZ e.vecrZ

Mz c

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What is QW?

Neutron – dduProton – uud

QW 2Z NQWuZ 2NQWdNumber of protons

Number of neutrons Weak charge of up-quark

Weak charge of down-quark

Weak nuclear chargeAdditive – just add together the weak charges for all the quarks in the nucleus

QW

QWu 1 83 Sin

2W

QWd 1 43 Sin

2W

Standard model gives us QW 1 4Sin2WZ N

Primary aim of atomic parity violation experiments – measure QW

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How to search for Atomic Parity Violation I

First idea: The brute force approachLook 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.

e

N

N

e

Electromagnetic process:Assign an amplitude Aem

e

N

N

eZ 0

Weak process:Assign an amplitude AW

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How to search for Atomic Parity Violation II

e

N

N

e

Electromagnetic process:Assign an amplitude Aem

e

N

N

eZ 0

Weak process:Assign an amplitude AW

These two processes have identical initial and final states.The probability for the process is given by:

PLR Aem AW2 Sign depends on handedness of experiment

A good measure of the degree of Left-Right asymmetry is

ALR PL PRPL PR

2AemAWAem2 2AWAem

PLR Aem2 2AWAemSince AW<<Aem

Try to measure this interference termN.B. Linear in Aw

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How big is it?

For both types of interaction, the amplitude isg1g2

q2 M 2c2

g1, g2 - coupling constants at the vertices, q - momentum transferM – mass of the mediating gauge boson

ALR2me2

MZ2 1015

Consider the hydrogen atom

For the electromagnetic interaction,g1= g2= eM = Mg = 0q= electron momentum= ma c

For the weak interaction,g1=g2 = gM = 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)

ALR105Enhancements 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?

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 ruleE2 – J=1/2 – J=1/2 transitions are strictly forbiddenM2, E3 – parity forbidden…

Exci

te

Detect

6S

7S

6P

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Stark-induced E1 transition

Search for the parity-violating 6S – 7S E1 transitionIn presence of electric field, there is a Stark-induced component to the 6S-7S rate

This allows the transition rate to be controlled

Trade-off between size of signal and size of asymmetry can be controlled using an electric field

ALR 2AWAem

Aem AStark E

Stronger signal

SignalAem2 E2

Smaller asymmetry

Asymmetry ALR 1E

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Colorado Cs experiment I

Exci

te

Detect

6S

7S

6P

Excite 6S-7S transitionObserve resulting fluorescence

Does excitation rate change when apparatus handedness is reversed?

Coordinate system defined by electric field, magnetic field and photon angular momentum

vectors – defines the handedness.

Reversals

E -E

B -B

s -s

m -m

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Build-up cavity, F=30000

Intensity stabilizerOptical isolatorHalf-wave plate

Pockels cell

Electric field plates divided into 5 segments

Colorado Cs experiment II

4 lasers – Df/f=10-14, DI/I=10-6

31 servo-loops23 magnetic field coils32 switch states7 years of development5 years on systematic effects8 months of data-taking1 result, 0 Nobel prizes!

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Colorado Cs experiment - results

The absorption coefficient of Cs depends on the handedness of the apparatusDifference is about 6 parts per million, measured to 0.35% precision

Experimental result

Atomic physics calculations

QWexp 72.71 0.29exp 0.39th

Combine

Compare to Standard Model:

QWSM 73.19 0.13

Agree within 1s

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What does a parity violating atom look like?

Example – the 2p1/2 state of hydrogen2p122p12 2s122s12HPV2p12E2s12 E2p12

Calculate the current density:

J P ;P electron momentum operator

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

Smells of oranges Smells of lemons(or turpentine!)

Limonene Carvone

Tastes of spearmint Tastes of caraway

Sedative. Treatment of morning sickness

(R) (S)

Malformations in over 10,000 children

Thalidomide

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Biological homochirality

All amino acids found in life are left-handedBiologically relevant sugars are right-handed

Not so in life…

Maximal parity violation

Chiral molecules synthesized in the lab

Equal mixture of left and right handed enantiomers Racemic mixture

How did it happen?Is the weak interaction involved?