introduction-weak-interaction-volume-one

neutrinos is 10 22 .5 * 2 .5 (22) . The latter agrees better with experimenta l
evidence than the former, but since it is impossible to observe the two
electrons in (4 .5 .4)
experimentally, this experiment does not rule out lepto n
number violation . However, the figures quoted above set an upper limit on
the lepton number violating amplitude in double beta decay of 3 x 1 0-3 .
More direct evidence for lepton conservation comes from a study o f
antineutrino capture . The antineutrino in beta decay has a lepton number of -1 ,
and hence the proces s
ve + (z, A) >(z+1, A) + e (4 .5 .5 )
cannot occur . However ,
ve + (Z, A) (Z - 1, A) + e t (4 .5 .6 )
does not violate lepton number conservation . Antineutrinos from atomic pile s
have been observed to produce positrons according to (4 .5 .6) (23), and
no electrons have been found due to the interaction of antineutrinos an d
01 37 .
We now consider a possible alternative assignment of lepton numbe r
than that discussed above . The electron, positron, e-neutrino and anti-e-neutrin o
retain the same lepton number as before, but the lepton number of the muon
and associated particles change sign, according to the suggestion o f
Konopinski and Mahmoud (24) . Thus the t~
is now a lepton, while the
e -
becomes an antilepton . The four types of neutrinos still remain, but, sinc e
both the v e
and the ve are left-handed (i .e . they have a helicity of -1), th e
ve is now a left-handed lepton state, while the y r is a left-handed antilepton .
Thus we have dispensed with the need for an electron and muon number . Thi s
means that we may use a single 4-component field to describe the neutrino s
instead of the usual two 2-component ones . The latter are separated purel y
because of the existence of muon and electron number . Let (x) and (1)y, (x )
r
be the field operators for the muon and electron neutrinos respectively .
Since we know the helicity or chirality of the states yr and ve , we may write
(1),,r, (x) _ '-( l - Y5)Jv1 ( x ) (4 .5 .7 )
and
q,, (x) +(l + 1 5 )-t (x ) . (4 .5 .8)
Since the only distinction between 1 J,~~(x) and 2~f, ,r (x) now lies in their