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Transcript
Parity Conservation in the weak (beta decay) interaction The parity operation The parity operation involves the transformation In rectangular coordinates -- x x y y z z In spherical polar coordinates -- r r In quantum mechanics For states of definite (unique & constant) parity - ˆ x, y,z 1 x,y,z If the parity operator commutes with hamiltonian - ˆ , Hˆ 0 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 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. Parity operations -Parity operation on a scaler quantity - ˆ E ˆ r r r r E Parity operation on a polar vector quantity - ˆ r r ˆ p p Parity operation on a axial vector quantity - ˆ ˆ r p r p L L Parity operation on a pseudoscaler quantity - ˆ p L p 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 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 Parity experiments (Lee & Yang) Original I Parity reflected p I p Look at the angular distribution of decay particle (e.g., red particle). If this is symmetric above/below the mid-plane, then -- p I 0 If parity is a good symmetry… • The p I 0 the decay intensity should not depend on p I . p I 0 there is a dependence on p I • If and parity is not conserved in beta decay. Discovery of parity nonconservation (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/ GT : I 1 F:I 0I 0 1v A :1 cos 3c v V :1 cos c v H c H 1 v H c Measure Trecoil H 1 H 1 Not observed H 1 Conclusions GT : I 1 F:I 0I 0 1v A :1 cos 3c v V :1 cos c GT is an axial-vector Violates parity v H c F is a vector Conserves parity H 1 Implications Inside the nucleus, the N-N interaction is VNN Vs Vw Conserves parity Can violate parity The nuclear state functions are a superposition s Fw ; F 107 Nuclear spectroscopy not affected by Vw Generalized -decay The hamiltonian for the vector and axial-vector weak interaction is formulated in Dirac notation as -- H g H g h.c. gV h.c. gA * p n * p 5 * e n * e 5 Or a linear combination of these two -- H gCV V C A A Generalized -decay The generalized hamiltonian for the weak interaction that includes parity violation and a two-component neutrino theory is -- * H g Ci p Oi n iA,V * e Oi 1 5 h.c. OV ; OV 5 Empirically, we need to find -- g and C A CV Study: n p (mixed F and GT), and: 14O 14N* (I=0 I=0; pure F) Generalized -decay 14O 14N* (pure F) 2 3 ft 7 5 4 m c MF log 2 2 g 2 CV2 g 2 CV2 1.4029 0.0022 10 49 erg cm 3 n p (mixed F and GT) 2 3 ft 2 5 4 g m c 7 MF 2 C V log 2 2 M GT C A2 2 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 -2CV2 CV2 3C A2 0.3566 CV2 C A2 1.53 Experiment shows that CV and CA have opposite signs. Universal Fermi Interaction In general, the fundamental weak interaction is of the form -- H gV A n p e e e o 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 Interaction In general, the fundamental weak interaction is of the form -- H gV A BUT -- is it really that way - absolutely? How would you proceed to test it? e e pure-leptonic weak decay The Triumf Weak Interaction Symmetry Test - TWIST Other symmetries Charge symmetry - C n p e C n p e All vectors unchanged Time symmetry - T n p e e n p T n p e (Inverse -decay) All time-vectors changed (opposite) Symmetries in weak decay s 0 Note helicities of neutrinos at rest P C Symmetries in weak decay s 0 at rest P Note helicities of neutrinos C Conclusions 1. Parity is not a good symmetry in the weak interaction. (P) 2. Charge conjugation is not a good symmetry in the weak interaction. (C) 3. The product operation is a good symmetry in the weak interaction. (CP) - except in the kaon system! 4. Time symmetry is a good symmetry in the weak interaction. (T) 5. The triple product operation is also a good symmetry in the weak interaction. (CPT)