introduction-weak-interaction-volume-one

We find that any wave function 14r(x) satisfies both the free Dirac equatio n
( r (Zxr) + m)q( x ) = o , (3 .6 .18 )
and also the 'chirality' relation
+ ( 1 + Y 5 ) 5(x) = X ( x ) . (3 .6 .19 )
We now postulate that all spin - particles may be described by two-componen t
spinors of the form x(x), and from our definition (3 .6 .16), (3 .6 .17), we
may immediately deduce that l
e
1 (1 + Y 5) (3 .6 .20 )
This now implies a V - A structure for beta decay in the same manner a s
did the Marshak-Sudarshan formulation (46) .
The third theoretical justification for a V - A interaction wa s
proposed by Sakurai in 1958 (49) . He noticed that the Dirac equation
was invariant under the two transformations
9 Y 5 (3 .6 .21a )
m >,- m (3 .6 .21b )
applied simultaneously, where
2
= 1 . (3 .6 .21c )
This is known as 'mass-reversal' invariance . We now observe that th e
relativistic requiremen t
m2 = p0 2 -
1 2 1 2 (3 .6 .22 )
involves only m2 and not m, and hence does not determine its sign . Thus
we are forced to conclude that the relation
(fr (a/axr ) - m) r 5 " V(x) = 0 (3 .6 .23 )
is exactly equivalent to the usual Dirac equation (3 .6 .18) . Using the
argument outlined above, we see that the Sakurai formulation also
predicts a V - A form for the beta decay interaction Hamiltonian . We
note, however, that sofar, we have produced no theoretical or experimental
evidence concerning the relative signs of the V and A couplings .
1 . Assuming 'chirality invariance' .