Parity Conservation in the weak (beta decay) interaction

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

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

3. 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) In quantum mechanics

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 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 - Parity operations --

6. If parity is a good symmetry… • The decay should be the same whether the process is parity-reflected or not. • In the hamiltonian, Vmust 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). http://publish.aps.org/  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) http://publish.aps.org/

10. Not observed Measure Trecoil

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

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

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

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

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

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

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

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