INTRODUCTION TO PARTICLE PHYSICS

PART II

Physics 129, Fall 2010; Prof. D. Budker

Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

Intrinsic parity of particlesA brief history of parity:

• Concept found (no parity in everyday life): O. Laporte, 1924• Concept understood: Wigner, 1927• Concept becomes dogma• Dogma fails: Lee, Yang, Wu, 1956-1957

3

Parity of atomic states

• Spatial inversion (P) : , ,x x y y z z • Or, in polar coordinates :

, ,r r

xy

z

xy

z

4

Parity of atomic states• It might seem that P is an operation that may be reduced to

rotations• This is NOT the case• Let’s see what happens if we invert a coordinate frame :

xy

z

'x

'y

• Now apply a rotation around z’

'z

"x"y

''zRight-handed frame left

handed• P does NOT reduce to

rotations !

5

Parity of atomic states

• An amazing fact : atomic Hamiltonian is rotationally invariant but is NOT P-invariant

• We will discuss parity nonconservation effects in detail later on in the course…

6

Parity of atomic states

Wavefunctions in this formare automatically of certain

parity : 1 lP

nlm nlm

• In hydrogen, the electron is in centro-symmetric nuclear potential• In more complex atoms, an electron sees a more complicated

potential• If we approximate the potential from nucleus and other electrons

as centro-symmetric (and not parity violating) , then :

• Since multi-electron wavefunction is a (properly antisymmetrized) product of wavefunctions for each electron, parity of a multi-electron state is a product of parities for each electron:

1 ii

l

This is because:

7

Comments on multi-electron atoms

• Potential for individual electrons is NOT centrosymmetric

• Angular momenta and parity of individual electrons are not exact

notions (configuration mixing, etc.)

• But for the system of all electrons, total angular momentum and parity are good !

• Parity of a multi-electron state:

1 21 1 ... 1 nl l l

W A R N I N G

1 L

8

Parity of atomic statesA bit of formal treatment…

• Hamiltonian is P-invariant (ignoring PNC) : P-1HP=H

• spatial-inversion operator commutes with Hamiltonian :

[P,H]=0

• stationary states are simultaneous eigenstates of H and P

• What about eigenvalues (p; Pψ=pψ) ?

• Note that doing spatial inversion twice brings us back to where

we started

• P2 ψ=P(P ψ)=P(pψ)=p(Pψ)=p2 ψ. This has to equal ψ p2=1 p=1

• p=1 – even parity; p=-1 – odd parity

Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

Intrinsic parity of particles

Consider a reaction:

a + b c + d

Initial wavefunction:

Initial parity:

motion relativeba

lba 1)(p)(p

motion relativedc

'1)(p)(p ldc

Final wavefunction:

Final parity:

Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

Intrinsic parity of particles Parity of proton is defined: p(p) = +1 Parity of other particles is found from processes

like a + b c + d and parity conservation

Example: d + π - n + n d : J=1; relative ang. moment. of p and n (mostly) 0

The π – is captured from an l=0 orbit, so we have:

lba 1)(p)(p '1)(p)(p ldc

)(p)(p)(p npd

'1)(p)(p)(p)(p)(p)(p)(p lnnnpd

Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

Intrinsic parity of particles

What can we say about l’ ? Total angular momentum of the two neutrons: 1 (because

the d spin is 1, and the π - spin is 0) Total wavefunction is antisymmetric (fermions) If spin singlet l’ = 0, 2, … cannot be! (because the

total angular momentum is 1) If spin triplet l’ = 1

Neutron parity is chosen positive Gauge bosons, , Z, W+, W-, g negative parity Leptons: not much to talk about: disrespect of parity

'1)(p)(p)(p)(p)(p)(p)(p lnnnpd

)(p)(p n

1)(p

Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

Intrinsic parity of antiparticles Not arbitrary! Must be related to that of particles 0 is its own antiparticle all pions have odd parity All antibosons have the same parity as their bosons For fermions it is the opposite: opposite parity for

particles and antiparticles How do we know? Dirac and Experiment

Consider para-Ps decay: e+e-(1S0) Possible amplitudes:

1 2 scalar not observed

1 2(k 1 - k 2) pseudoscalar observed!

Only possible if p(e+) p(e-) = -1

Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

Charge conjugation (C)

A misnomer; better way to think about this:All particles antiparticles

If a particle is an eigenstate of C (most are not),c=1 (because c2 = 1)

c() = -1 (this is e/m field, after all)0 + allowed0 + + forbidden

Week interactions do not respect C

Parity-Violation:ParticlesNucleiAtoms

Molecules

Outline

1. What is parity? Parity violation2. Atomic parity violation (APV=PNC)

a. Optical-rotation exptsb. APV-Stark interferencec. Brief (personal) history of APV

3. APV in Yb4. APV in Dy5. Conclusions

What is parity?

x

yz

P

x’

y’ z’

x’’

z’’

y’’=y’

Rotation around y’

Left hand cannot be rotated into right hand !

Normal vs. axial vectors

Under Spatial Inversion (P):

• V -V r, p, E, d = er, …• A A L = rp, S, B

Similarly for scalars (pseudo-scalars)

Under Spatial Inversion (P):

• S S Energy, any VV’, AA’ …

• PS -PS any A V, …

Discrete vs. Continuous Transformations and Symmetries

• Continuous:

• Translation → momentum conservation

• Translation in time → energy conservation

• Rotation → angular momentum conservation

• Discrete:

• Spatial Inversion (P) → P-invariance (parity)

• Charge Conjugation (C) → C-invariance

• Time reversal (T) → T-invariance

• CP

• CPT

• Permutation of identical particles → PSP, spin-statistics

The (broken) law of parity

Because the laws of Nature should be the same in the “real” world and its mirror image, no pseudo-scalar correlation should be observed in experiments, for example

Does not apply to cork-screws !

pI

Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

The - paradox (the demise of parity)

Two particles with same mass and same lifetime… But opposite parity ??? In modern terminology: + = + = K+ ( ) Resolution of the paradox: parity violation in weak interactions

su

The theorists who said: check it !

Prof. T. D. LeeProf. C. N. Yang            

Prof. C. S. Wu (1913-1997)

The shatterer of the parity illusion (1956)…

The Co-60 experiment

Parity and Quantum Mechanics

PHHPPHPPHPHPHP ˆˆˆˆˆˆ 11

• If Hamiltonian is P-invariant nondegenerate sate is eigenfunction of P

11

)(

Now,

2

2

pp

ppPpPPP

IPP

pP

• Atomic states are even or odd

• If parity is violated eigenstates are of mixed parity

Z

e

e

g

Weak interaction

(violates parity)

Electromagnetic interaction

(conserves parity)

Atomic Parity Violation (APV)

• APV = PNC = Parity Non-Conservation

M1E1

PNC

M1-E1PNC interference

Atomic PNC: optical rotation

Optical Rotation

Medium

Linear Polarization

Circular Components

28

PNC optical rotation: TlVetter, Meekhov, Lamoreaux, Fortson, PRL 74, 2658 (1995)

Result: PNC to 1 % (exp); 3 % (theo)

• 500 data hrs averaged

• Many absorp. length → line wings

• Polarimetric sensitivity: ~10-8 rad

• No reversals

New approaches needed for progressProf. E. N. Fortson

M1E1

PNC+EDC

E1Stark -E1PNC interference

• Reversals !

Atomic PNC: Stark interference

Atomic parity violation: the parents

Profs. Marie-Anne and Claude Bouchiat

Atomic PV landmarks• 1959 Ya. B. Zel’dovich:

PNC (Neutr. Current) Opt. Rotation in atoms

• 1974 M.-A. & C. Bouchiat

Z3 enhancement PV observable in heavy atoms

• 1978-9 Novosibirsk, Berkeley

discovery of PV in OR(Bi) and Stark-interf.(Tl)

•…1995 Boulder, Oxford, Seattle, Paris

PV measured to 1-2% in Cs, Tl, Bi, Pb

• 1997 Boulder

0.35% measurement, discovery of anapole moment

Why the French?

ATOM

ATOM

ATOME

ATOM

E

The Boulder Cs PNC Experiment

• P-odd, T-even correlation: • [E B]

• 5 reversals to distinguish PNC from systematics

1982-1999

The Champions of Parity violation

Prof. Carl E. Wieman

Atomic PV landmarks• 1959 Ya. B. Zel’dovich:

PNC (Neutr. Current) Opt. Rotation in atoms

• 1974 M.-A. & C. Bouchiat

Z3 enhancement PV observable in heavy atoms

• 1978-9 Novosibirsk, Berkeley

discovery of PV in OR(Bi) and Stark-interf.(Tl)

•…1995 Boulder, Oxford, Seattle, Paris

PV measured to 1-2% in Cs, Tl, Bi, Pb

• 1997 Boulder

0.35% measurement, discovery of anapole moment

• 2009 Berkeley Large APV in Yb (personal landmark)

26 y

ears

What were we doing all this time?• 1983-1988 Bi, diatomic molecules, Sm

(Novosibirsk) with L. M. Barkov and M. Zolotorev

• 1989-1994 Tl(Berkeley) with E. D. Commins, D. DeMille, and M. Zolotorev

• 1989- Dy M. Zolotorev, D. DeMille, E. D. Commins, A.-T.Nguyen,

A. Cingoz, N. Leefer

• 1995-1997 SmS. M. Rochester

• 1995- YbS. J. Freedman, C. J. Bowers, G. Gwinner, J. E. Stalnaker, D. F. Kimball, V. V. Yashchuk, K. Tsigutkin, A. Family, D. Dounas-Frazer,…

Why did it take so long to detectPNC?

Dr. A.-T. Nguyen says: it was deposited

38

Parity Violation in Yb: motivationAtomic Physics:

Verification of large predicted atomic PV effect (x100 Cs; DeMille, Kozlov et al, Das

et al)

Nuclear Physics:Nuclear spin-dependent PV – anapole moments

(valence neutrons)

Isotopic ratios and neutron distributions (6 stable isotopes; N=8)

Anapole Momentof a current distribution (e.g., a nucleus)

rdrjraRaRA

rdrjrc

mR

RmRA

rdrjcR

RA

rrR

rRRrR

rdrR

rj

cRA

kklkkk

32)2(

33

)1(

3)0(

3

)();(

)(2

1;

0)(1

...1

2

111

||

1

||

)(1

T-conserving; P-violating

Ya. B. Zel’dovich

40

• 1959 Ya . B. Zel’dovich, V. G. Vaks

AM first introduced

• 1980-84 V.V. Flambaum, I.B. Khriplovich &O.P. Sushkov

Nuclear AM detectable in atoms

Anapole Moments

PNC within nucleus !

probe of weak meson couplings

• 1997 C. E. Wieman and co-workers

Cs AM detected !

• 1995 E.N.Fortson and co-workers

Tl AM – small…

41

Atomic Yb: energy levels and transitions

PV amplitude: 10-9e·a0

DeMille (1995)

+5d6p

|M1|10-4 μB

J.E. Stalnaker, et al, PRA 66(3), 31403 (2002)

β2·10-8 ea0/(V/cm)C.J. Bowers et al, PRA 59(5), 3513 (1999); J.E. Stalnaker et al, PRA 73,

043416 (2006)

Stark-PV-interference technique (invented by the Bouchiats in 1970s)

43

Electric and magnetic fields define handedness

The Yb PV Experiment

Rotational Invariant: B E B

tEEE cos0dc

m = -1

m = +1

m = 0

R0

R-1

R+1

1S0

3D1

sincoscos2

1

sincos2sin

2221

2220

EER

EER

011 RRRr

Transition rates

interference

Compute ratio for 1st and 2nd harm. signal

Ratio difference yields PV asymmetry: dcndst 2)2()1( Err

PV effects on rates

E-field modulation

45

Typical Stark-induced signal

-60 -40 -20 0 20 40 600.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

-60 -40 -20 0 20 40 60-0.002

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

2d harmonic signal fit

Sig

nal A

mpl

itud

e [V

]

1st harmonic signal fit PNC line shape (x100)

f [MHz]

Sig

nal A

mpl

itud

e [V

]

• 174Yb resonance split by B70 G; E=3 kV/cm

• PV asymmetry:

~ 2·10-4/ E/(kV/cm)

• Asymmetric lineshape ←

AC Stark effect

DC bias 43 V/cm

46

Atoms in electric field: the Stark effect

or LoSurdo phenomenon

Johannes Stark (1874-1957)

Nazi Fascist

47

Reversals and pseudo-reversals• E-field reversal (14 ms: 70-Hz modulation)

• Lineshape scan (200 ms/point x 100 pts/lineshape = 40 s)

• B-field reversal (every few minutes)

• Polarization angle (occasionally)

• E-field magnitude

• B-field magnitude

• Angle magnitude

For θ=/4→

48

Systematics control strategy• APV is mimicked by combinations of two or more imperfections

• Enhance one imperfection; measure the other

• Adapted from the Berkeley eEDM expt. of Prof. Commins et al

Yb PV Amplitude: Results

Accuracy is affected by HV-amplifier noise, fluctuations of stray fields, and laser drifts → to be improved

/z b=39(4)stat.(5)syst. mV/cm |z|=8.7±1.4×10-10 ea0

68% confidence band

0 2 4 6 8 10 12 14 16 18 20-50

0

50

100

150

Mean value

/ (

mV

/cm

)

Run number

Theoretical prediction

Near Future… Verification of expected isotopic dependence PV in odd isotopes: NSD PV, Anapole Moment PV in a string of isotopes; neutron distributions, …

Further Ahead (?) Testing the Standard Model [Brown et al PHYSICAL REVIEW C 79, 035501 (2009)]

Completed Work Lifetime Measurements General Spectroscopy (hyperfine shifts, isotope shifts) dc Stark Shift Measurements Stark-Induced Amplitude (β): 2 independent measurements M1 Measurement (Stark-M1 interference) ac Stark Shift Measurements Verification of APV enhancement

Progress in Yb APV

51

K. Tsigutkin A. Family D. Dounas-Frazer post-doc undergrad grad.student

V. V. Yashchuk S. J. Freedman J. E. Stalnaker

Another atom: DyIdeal APV amplifier?

Fully degenerate opposite-parity levels Large Z3 (Z=66)

Also Many stable isotopes: A=164-156 Large Z3 (Z=66) Two I=5/2 isotopes (anapole)

52

53

The parity violation experiment in Dyevolved into…

Search for temporal variation ofα

in radio-frequency transitions of Dy

Support:

Search for temporal variation of the fine-structure "constant" in radio-frequency transitions of Dy

A B

Ground State0

20,000

En

erg

y (c

m-1)

For a/a ~ 10-15 /yr dD/dt ~ 2 Hz/yr !!

l

AB

D

D ~ (3-2000) MHz

dD/dt ~ 21015 Hz a/al

Dzuba, Flambaum, Kozlov, et al

Next steps... Succeeded in laser cooling of atomic beam Operate new apparatus optimized for the a-dot experiment Measure frequency to ~1 mHz

18~ 10 / yr

Dy APV will be back!

Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html