Parity Conservation in the weak (beta decay)...
Transcript of Parity Conservation in the weak (beta decay)...
Parity Conservation inthe weak (beta decay) interaction
The parity operationThe parity operation involves the transformation
†
x Æ -x y Æ -y z Æ -z
r Æ r q Æ p -q( ) f Æ f + p( )
In rectangular coordinates --
In spherical polar coordinates --
In quantum mechanics
†
ˆ P y x,y,z( ) = ±1y -x,-y,-z( )For states of definite (unique & constant) parity -
If the parity operator commutes with hamiltonian -
†
ˆ P , ˆ H [ ] = 0 fi The parity is a“constant of the motion”
Stationary states must be states of constant parity
e.g., ground state of 2H is s (l=0) + small d (l=2)
In quantum mechanicsTo test parity conservation - - Devise an experiment that could be done: (a) In one configuration (b) In a parity “reflected” configuration- If both experiments give the “same” results, parity is conserved -- it is a good symmetry.
Parity operations --
†
ˆ P E = E ˆ P r r ⋅ r r ( ) =
r r ⋅ r r ( )Parity operation on a scaler quantity -
Parity operation on a polar vector quantity -
†
ˆ P r r = -
r r ˆ P r p = -
r p Parity operation on a axial vector quantity -
†
ˆ P r L = ˆ P
r r ¥ r p ( ) = -r r ¥ -
r p ( ) = -r L
Parity operation on a pseudoscaler quantity -
†
ˆ P r p ⋅
r L ( ) = -
r p ⋅r L ( )
If parity is a good symmetry…• The decay should be the same whether the process
is parity-reflected or not.
• In the hamiltonian, V must not contain terms thatare pseudoscaler.
• If a pseudoscaler dependence is observed - paritysymmetry is violated in that process - parity istherefore not conserved.
T.D. Lee and C. N. Yang, Phys. Rev. 104, 254 (1956).
http://publish.aps.org/ tq puzzle
Parity experiments (Lee & Yang)
†
r p ⋅r I = 0
Parity reflectedOriginal
Look at the angular distribution of decay particle(e.g., red particle). If this is symmetricabove/below the mid-plane, then --
†
r p
†
r I
†
r p
†
r I
If parity is a good symmetry…• The the decay intensity should not
depend on .
• If there is a dependence onand parity is not conserved in beta decay.
†
r p ⋅r I = 0
†
r p ⋅r I ( )
†
r p ⋅r I ≠ 0
†
r p ⋅r I ( )
Discovery of parity non-conservation (Wu, et al.)
Consider the decay of 60Co
Conclusion: G-T, allowed
C. S. Wu, et al., Phys. Rev 105, 1413 (1957)
http://publish.aps.org/
†
Hb- = -
vc
†
n
†
Hn =1
†
b-
†
n
†
Hb- = -
vc
†
b-
†
Hn =1
†
n
†
Hn = -1
†
n
†
Hn = -1
NotobservedMeasure
Trecoil
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GT : DI =1
A :1-13
vc
cosq
†
F : I = 0 Æ I = 0
V :1+vc
cosq
†
Hn =1
†
Hb- = -
vc
†
GT : DI =1
A :1-13
vc
cosq
†
F : I = 0 Æ I = 0
V :1+vc
cosq
Conclusions
GT is an axial-vector F is a vector
Violates parity Conserves parity
†
VN -N = Vs + Vw
ImplicationsInside the nucleus, the N-N interaction is
Conservesparity
Can violateparity
†
y =ys + Fyw ; F ª10-7The nuclear state functions are a superposition
\ Nuclear spectroscopy not affected by Vw
Generalized b-decay
†
H = g y p* gmyn( ) y e
*gmyn( ) + h.c. = gV
H = g y p* gmg 5yn( ) y e
*gmg5yn( ) + h.c. = gA
The hamiltonian for the vector and axial-vector weakinteraction is formulated in Dirac notation as --
†
H ª g CVV + CA A( )
Or a linear combination of these two --
Generalized b-decay
†
H = g Ci y p* Oiyn( ) ye
*Oi 1+ g5( )yn[ ]i=A,V
 + h.c.
OV = gm ; OV = gmg5
The generalized hamiltonian for the weak interactionthat includes parity violation and a two-componentneutrino theory is --
†
g CA CVEmpirically, we need to find -- and
Study: n Æ p (mixed F and GT), and: 14O Æ 14N* (I=0 Æ I=0; pure F)
Generalized b-decay14O Æ 14N* (pure F)
†
ft =2p 3h7 log2
m5c4 M F2
g2CV2( )
g2CV2( ) = 1.4029 ± 0.0022 ¥10-49 erg cm3
n Æ p (mixed F and GT)
†
ft =2p 3h7 log2
g2m5c4 CV2( ) M F
2+ CA
2( ) MGT2È
Î Í ˘ ˚ ˙
Generalized b-decay
†
2CV2
CV2 + 3CA
2 = 0.3566 Æ CV2
CA2 =1.53
Assuming simple (reasonable) values for thesquare of the matrix elements, we can get (bytaking the ratio of the two ft values --
Experiment shows that CV and CA have opposite signs.
Universal Fermi InteractionIn general, the fundamental weak interaction is ofthe form --
†
H µ g V - A( )
†
n Æ p + b- + n e
m- Æ e- + n e + nm
p - Æ m- + n m
Lo Æ p - + p
semi-leptonic weak decay
pure-leptonic weak decay
semi-leptonic weak decay
Pure hadronic weak decay
All follow the (V-A) weak decay. (c.f. Feynman’s CVC)
Universal Fermi InteractionIn general, the fundamental weak interaction is ofthe form --
†
H µ g V - A( )
†
m- Æ e- + n e + nm pure-leptonic weak decay
The Triumf Weak Interaction Symmetry Test - TWIST
BUT -- is it really that way - absolutely?
How would you proceed to test it?
Other symmetriesCharge symmetry - C
†
n Æ p + b- + n e fi n Æ p + b+ + ne C
All vectors unchanged
Time symmetry - T
†
n Æ p + b- + n e fi n ¨ p + b- + n e
ne + n Æ p + b-
T
All time-vectors changed (opposite)
(Inverse b-decay)
Symmetries in weak decayp+ at rest Note helicities
of neutrinos
†
r s p = 0
†
m-
†
nm
†
m+†
p +
†
fi
†
‹CP
†
p -
†
n m
†
m-
†
n m†
p -
Symmetries in weak decayp+ at rest Note helicities
of neutrinos
†
r s p = 0
†
p +
†
nm
†
fiCP
†
p -
†
m-
†
n m
†
m+
†
fi
†
n m†
p -†
m-
Conclusions1. Parity is not a good symmetry in the weak
interaction. (P)
2. Charge conjugation is not a good symmetry in theweak interaction. (C)
3. The product operation is a good symmetry in theweak interaction. (CP) - except in the kaon system!
4. Time symmetry is a good symmetry in the weakinteraction. (T)
5. The triple product operation is also a goodsymmetry in the weak interaction. (CPT)