introduction-weak-interaction-volume-one

((Jg - E) w
j )r qr u =
= 0 , (3 .8 .10 )
-(6 g - E) v
which may be resolved into two uncoupled relations :
(E + 6g) v = 0 , (3 .8 .11a )
(E - (_ g) w 0 . (3 .8.11b)
Thus the projection of the spin along the direction of motion i s
-E/1gj for v, and E/Igl for w . Hence, massless particles with positive
energy must have negative helicity if they correspond to the solutio n
v, and positive helicity if to w . Since w is the antiparticle solution
in (3 .8 .10), we now inferr that all neutrinos have negative helicity whil e
all antineutrinos have positive helicity . The equations (3 .8 .11) were
first proposed by Weyl (71), but they were condemned by Pauli because the y
implied parity noninvariance (72) . However, after the experiment of Wu et
al ., they were revived by Salam (73), Lee and Yang (74), and Landau (75) .
Finally, we examine a number of useful predictionsmade by the
two-component neutrino theory. We assume that in a Fermi decay (A J = 0) ,
the recoiling nucleus takes up no momentum . We consider the case in which electron
and antineutrino emerge in opposite directions with equal momenta . Since
the antineutrino has positive helicity, so also must the electron . However,
if we assume that the electron has enough energy to be satisfactoril y
described by a two-component wave function, then we predict that i t
should have negative helicity, and hence that its spin should be paralle l
to that of the antineutrino . This would imply nonconservation of angular
momentum, and consequently we are forced to conclude that the situation
described is impossible . From this we may inferr that the e-v angula r
correlation factor should vanish for 0 = r[ , which is consistent wit h
experiment and with (3 .5 .13) .
The two-component neutrino theory may be used (76) to derive th e
correct V - A structure of beta decay . Since the antineutrino has positiv e
helicity, it follows that, in the m e
0 approximation, the electron
must have negative helicity . By angular momentum conservation,
this implie s
that the nucleon spins must both be parallel to the antineutrino spin .