1. Parity Conservation in the weak (beta decay) interaction

2. The parity operation The parity operation involves the transformation
In rectangular coordinates --
In spherical polar coordinates --

3. The parity is a “constant of the motion”
In quantum mechanics
For states of definite (unique & constant) parity -
If the parity operator commutes with hamiltonian -
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)

4. In quantum mechanics
To 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.

5. Parity operations -- Parity operation on a scaler quantity -
Parity operation on a polar vector quantity -
Parity operation on a axial vector quantity -
Parity operation on a pseudoscaler quantity -

6. 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 that are pseudoscaler.
If a pseudoscaler dependence is observed - parity symmetry is violated in that process - parity is therefore not conserved.
T.D. Lee and C. N. Yang, Phys. Rev. 104, 254 (1956).
 puzzle

7. Parity experiments (Lee & Yang)
Original
Parity reflected
Look at the angular distribution of decay particle (e.g., red particle). If this is symmetric above/below the mid-plane, then --

8. If parity is a good symmetry…
The the decay intensity should not depend on
If there is a dependence on and parity is not conserved in beta decay.

9. 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)

10. Not observed
Measure Trecoil

11. Conclusions GT is an axial-vector F is a vector
Violates parity Conserves parity

12.  Nuclear spectroscopy not affected by Vw
Implications
Inside the nucleus, the N-N interaction is
Conserves parity
Can violate parity
The nuclear state functions are a superposition
 Nuclear spectroscopy not affected by Vw

13. Generalized -decay
The hamiltonian for the vector and axial-vector weak interaction is formulated in Dirac notation as --
Or a linear combination of these two --

14. Generalized -decay
The generalized hamiltonian for the weak interaction that includes parity violation and a two-component neutrino theory is --
Empirically, we need to find and
Study: n  p (mixed F and GT), and: 14O  14N* (I=0  I=0; pure F)

15. Generalized -decay
14O  14N* (pure F)
n  p (mixed F and GT)

16. Experiment shows that CV and CA have opposite signs.
Generalized -decay
Assuming simple (reasonable) values for the square of the matrix elements, we can get (by taking the ratio of the two ft values --
Experiment shows that CV and CA have opposite signs.

17. Universal Fermi Interaction
In general, the fundamental weak interaction is of the form --
semi-leptonic weak decay
pure-leptonic weak decay
Pure hadronic weak decay
All follow the (V-A) weak decay. (c.f. Feynman’s CVC)

18. Universal Fermi Interaction
In general, the fundamental weak interaction is of the form --
BUT -- is it really that way - absolutely?
How would you proceed to test it?
pure-leptonic weak decay
The Triumf Weak Interaction Symmetry Test - TWIST

19. All time-vectors changed (opposite)
Other symmetries
Charge symmetry - C C
All vectors unchanged
Time symmetry - T T
All time-vectors changed (opposite)
(Inverse -decay)

20. Symmetries in weak decay
 at rest
Note helicities of neutrinos P C

21. Symmetries in weak decay
 at rest
Note helicities of neutrinos P C

22. Conclusions Parity is not a good symmetry in the weak interaction. (P)
Charge conjugation is not a good symmetry in the weak interaction. (C)
The product operation is a good symmetry in the weak interaction. (CP) - except in the kaon system!
Time symmetry is a good symmetry in the weak interaction. (T)
The triple product operation is also a good symmetry in the weak interaction. (CPT)