Transcript Parity Conservation in the weak (beta decay) interaction

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 L  
ˆ r  p  r  p  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
1v
A :1
cos
3c
v
H   
c



Measure
Trecoil

v
H   
c
H  1




F:I 0I 0
v
V :1 cos
c


H  1


H  1
Not
observed





H  1
Conclusions
GT : I 1
1v
A :1
cos
3c

GT is an axial-vector
Violates parity
v
H   
c
F:I 0I 0
v
V :1 cos
c

F is a vector
Conserves parity
H  1
Implications
Inside the nucleus, the N-N interaction is
VN N  Vs  Vw

Conserves
parity
Can violate
parity
The nuclear state functions are a superposition
  s  Fw ; F 107
 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  gCV V  C A A
Generalized -decay
The generalized hamiltonian for the weak interaction
that includes parity violation and a two-component
neutrino theory is --

*
Ci  p Oi n
Hg 
iA,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
 CV
log 2
2

 M GT
2
CA
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  gV  A

n  p    e


  e  e   

      

   p
o
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  gV  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





Note helicities
of neutrinos
P


 



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)