introduction-weak-interaction-volume-one

of iron whose direction of magnetization was reversed every 200 a . The
scattered photons were detected by an Nal (Ti) scintillator, and th e
results obtained (38) were consistent with h e . - v .
3 .8 The Two-Component Neutrino Hypothesis .
With our knowledge of the type and strength of interaction s
occuring in neutron decay, we may now rewrite our original Hamiltonia n
(3 .3 .6) : (68 )
H 1 = (Cv/1-2) J 1p Yryn re Yr (1 + Y 5 ) V v
- ( CA/ 2)
J p Y r Y5 1-n ljre V 1 r (1 + Y 5 ) V- v +
t Heim . conj . (3 .8 .1 )
We observe that, in this expression, a factor (1 + '( 5 ) always
preceeds the neutrino field operator . Sinc e
( 1 + Y S ) _ ( 1 ± Y 5 ) Y 5 , (3 .8 .2 )
the neutrino wave function must always be invariant under the 'chirality '
transformation
(3 .8 .3 )
As we saw in 3 .6, this is only the case for massless particles, and henc e
the neutrino mass must be precisely zero . On this assumption, we
analyse the neutrino spin along its direction of motion, and thus th e
Dirac equation yieldsl :
(1 + Y5) uv(+)(r)(n„)
_
1-
1 -1 (r) 1 (1 - 6z ) (r) 1
j -1 1 d 1 ( r ) 47f =
L 1 -z
- ( 1 - 6Z) y( r )
We see that all components of the neutrino spinor vanish for r
henc e
. 1, and
( l /[2) (1 + 1 5 )yv = ( 1 t y5) ;57 n
(u(+)(2)(a)ejgx 8 (2) (n )
u(-)(1)(-n)e jqx bt(1) (n) . (3 .8 .5 )
1 . Using the gamma-matrix representation in which Ye is not diagonal .