Parity Conservation in the weak (beta decay) interaction

Transcription

1 Paity Consevation in the weak (beta decay) inteaction

2 The paity opeation The paity opeation involves the tansfomation In ectangula coodinates -- x Æ -x y Æ -y z Æ -z In spheical pola coodinates -- Æ q Æ p -q ( ) f Æ f + p ( )

3 In quantum mechanics Fo states of definite (unique & constant) paity - P ˆ y( x,y,z) = ±1y (-x,-y,-z) If the paity opeato commutes with hamiltonian - [ P ˆ, H ˆ ] = 0 fi The paity is a constant of the motion Stationay states must be states of constant paity e.g., gound state of 2 H is s (l=0) + small d (l=2)

4 In quantum mechanics To test paity consevation - - Devise an expeiment that could be done: (a) In one configuation (b) In a paity eflected configuation - If both expeiments give the same esults, paity is conseved -- it is a good symmety.

5 P ˆ E = E Paity opeations -- Paity opeation on a scale quantity - P ˆ ( ) = ( ) Paity opeation on a pola vecto quantity - P ˆ = - P ˆ p = -p Paity opeation on a axial vecto quantity - P ˆ L = ˆ ( p ) = (- -p ) = -L P Paity opeation on a pseudoscale quantity - ( ) = -( ) P ˆ p L p L

6 If paity is a good symmety The decay should be the same whethe the pocess is paity-eflected o not. In the hamiltonian, V must not contain tems that ae pseudoscale. If a pseudoscale dependence is obseved - paity symmety is violated in that pocess - paity is theefoe not conseved. T.D. Lee and C. N. Yang, Phys. Rev. 104, 254 (1956). tq puzzle

7 Paity expeiments (Lee & Yang) I Oiginal p Paity eflected I p Look at the angula distibution of decay paticle (e.g., ed paticle). If this is symmetic above/below the mid-plane, then -- p I = 0

8 If paity is a good symmety The p I = 0 the decay intensity should not depend on ( p I ). If p I 0 thee is a dependence on p I and paity is not conseved in beta decay. ( )

9 Discovey of paity nonconsevation (Wu, et al.) Conside the decay of 60 Co Conclusion: G-T, allowed C. S. Wu, et al., Phys. Rev 105, 1413 (1957)

10 GT : DI =1 A :1-1 3 v c cosq F : I = 0 Æ I = 0 V :1+ v c cosq H b - = - v c H n = -1 H b - = - v c b - n b - n Measue T ecoil n Not obseved H n =1 n H n =1 H n = -1

11 Conclusions GT : DI =1 A :1-1 3 v c cosq F : I = 0 Æ I = 0 V :1+ v c cosq GT is an axial-vecto Violates paity F is a vecto Conseves paity H b - = - v c H n =1

12 Implications Inside the nucleus, the N-N inteaction is V N -N = V s + V w Conseves paity Can violate paity The nuclea state functions ae a supeposition y =y s + Fy w ; F ª10-7 \ Nuclea spectoscopy not affected by V w

13 Genealized b-decay The hamiltonian fo the vecto and axial-vecto weak inteaction is fomulated in Diac notation as -- ( )( y * ) e g m y n + h.c. = gv H = g y p * g m y n ( )( y * ) e g m g 5 y n + h.c. = ga H = g y p * g m g 5 y n O a linea combination of these two -- H ª g C V V + C A A ( )

14 Genealized b-decay The genealized hamiltonian fo the weak inteaction that includes paity violation and a two-component neutino theoy is -- H = g  i=a,v ( )[ y * e O i ( 1+ g 5 )y n ] C i y p * Oi y n O V = g m ; O V = g m g 5 + h.c. Empiically, we need to find -- g and C A C V Study: n Æ p (mixed F and GT), and: 14 O Æ 14 N* (I=0 Æ I=0; pue F)

15 Genealized b-decay 14 O Æ 14 N* (pue F) ft = 2p 3 h 7 log2 m 5 c 4 2 M ( F g 2 2 C ) V ( g 2 2 C ) V = ± eg cm 3 n Æ p (mixed F and GT) ft = 2p 3 h 7 log2 g 2 m 5 c 4 È 2 C Î Í V ( ) 2 M F + ( 2 CA ) 2 M GT

16 Genealized b-decay Assuming simple (easonable) values fo the squae of the matix elements, we can get (by taking the atio of the two ft values -- 2C V 2 2 C V + 2 = Æ C V 2 3CA C =1.53 A 2 Expeiment shows that C V and C A have opposite signs.

17 Univesal Femi Inteaction In geneal, the fundamental weak inteaction is of the fom -- H µ g V - A ( ) n Æ p + b - + n e m - Æ e - + n e + n m p - Æ m - + n m L o Æ p - + p semi-leptonic weak decay pue-leptonic weak decay semi-leptonic weak decay Pue hadonic weak decay All follow the (V-A) weak decay. (c.f. Feynman s CVC)

18 Univesal Femi Inteaction In geneal, the fundamental weak inteaction is of the fom -- H µ g V - A ( ) BUT -- is it eally that way - absolutely? How would you poceed to test it? m - Æ e - + n e + n m pue-leptonic weak decay The Tiumf Weak Inteaction Symmety Test - TWIST

19 Othe symmeties Chage symmety - C n Æ p + b - + n e C fi n Æ p + b + + n e All vectos unchanged Time symmety - T n Æ p + b - + n e n e + n Æ p + b - T fi n p + b - + n e (Invese b-decay) All time-vectos changed (opposite)

20 Symmeties in weak decay s p = 0 m - p + at est n m Note helicities of neutinos n m p - P p - C fi p + n m m - m +

21 Symmeties in weak decay s p = 0 p + at est Note helicities of neutinos n m m - m + p - P fi p - fi C p + m - n m n m

22 Conclusions 1. Paity is not a good symmety in the weak inteaction. (P) 2. Chage conjugation is not a good symmety in the weak inteaction. (C) 3. The poduct opeation is a good symmety in the weak inteaction. (CP) - except in the kaon system! 4. Time symmety is a good symmety in the weak inteaction. (T) 5. The tiple poduct opeation is also a good symmety in the weak inteaction. (CPT)