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:
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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
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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 observed1 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
Outline1. 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
IPPpP
• Atomic states are even or odd
• If parity is violated eigenstates are of mixed parity
Ze
e
g
Weak interaction
(violates parity)
Electromagnetic interaction
(conserves parity)
Atomic Parity Violation (APV)
• APV = PNC = Parity Non-Conservation
M1 E1
PNC
M1-E1PNC interference
Atomic PNC: optical rotation
Optical Rotation
Medium
Linear Polarization
Circular Components
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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
M1 E1
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
rjc
RA
kklkkk
32)2(
33
)1(
3)0(
3
)();(
)(21;
0)(1
...12111
||1
||)(1
T-conserving; P-violating
Ya. B. Zel’dovich
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• 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-workersCs AM detected !
• 1995 E.N.Fortson and co-workersTl 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 handednessThe Yb PV Experiment
Rotational Invariant: B E B
tEEE cos0dc
m = -1
m = +1m = 0
R0
R-1
R+1
1S0
3D1
sincoscos21
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 40 600.000.050.100.150.200.250.300.350.40
-60 -40 -20 0 20 40 60-0.0020.0000.0020.0040.0060.0080.0100.0120.014
2d harmonic signal fit
Sign
al A
mpl
itude
[V]
1st harmonic signal fit PNC line shape (x100)
f [MHz]
Sign
al A
mpl
itude
[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/=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
z/ (m
V/c
m)
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
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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
Ener
gy (c
m-1)
For a/a ~ 10-15 /yr d/dt ~ 2 Hz/yr !!
l
AB
~ (3-2000) MHz
d/dt ~ 21015 Hz a/al
Dzuba, Flambaum, Kozlov, et ala
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 / yraa
Dy APV will be back!
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html