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20.3. Lepton number and lepton flavours
20.3 Lepton number and lepton flavours
In section 1.2.1 of volume 1 we gave a brief discussion of leptonic quantum
numbers (‘lepton flavours’), adopting a traditional approach in which the data
is interpreted in terms of conserved quantum numbers carried by neutrinos,
which serve to distinguish neutrinos from antineutrinos. We must now examine the matter more closely, in the light of what we have learned about the
helicity properties of the V-A interaction.
In 1995, Davis (1955) – following a suggestion made by Pontecorvo (1946) –
−
−
argued as follows. Consider the e capture reaction e +p → ν +n, which was
−
of course well established. Then in principle the inverse reaction ν+n → e +p
should also exist. Of course, the cross section is extremely small, but by using
a large enough target volume this might perhaps be compensated. Specifically,
− +
37
the reaction ν +
37 Cl → e
Ar was proposed, the argon being detected
17
18
through its radioactive decay. Suppose, however, that the ‘neutrinos’ actually
used are those which accompany electrons in β
− -decay. If (as was supposed
in section 1.2.1) these are to be regarded as antineutrinos, ‘¯ ν’, carrying a
conserved lepton number, then the reaction
−
37
‘¯ ν’ +
37
e +
(20.34)
17 Cl →
18 Ar
should not be observed. If, on the other hand, the ‘ν’ in the capture process
and the ‘¯ ν’ in β-decay are not distinguished by the weak interaction, the
reaction (20.34) should be observed. Davis found no evidence for reaction
(20.34), at the expected level of cross section, a result which could clearly be
interpreted as confirming the ‘conserved electron number hypothesis’.
However, another interpretation is possible. The e
− in β-decay has predominately negative helicity, and its accompanying ‘¯ ν’ has predominately positive helicity. The fraction of the other helicity present is of the order m/E,
where E ∼ few Mev, and the neutrino mass is less than 1eV; this is, therefore,
an almost undetectable ‘contamination’ of negative helicity component in the
‘¯ ν’. Now the property of the V-A interaction is that it conserves helicity in
the zero mass limit (in which chirality is the same as helicity). Hence the
positive helicity ‘¯ ν’ from β
− -decay will (predominately) produce a positive
helicity lepton, which must be the e
+ not the e
− . Thus the property of the
V-A interaction, together with the very small value of the neutrino mass, conspire effectively to forbid (20.34), independently of any considerations about
‘lepton number’.
Indeed, the ‘helicity-allowed’ reaction
+
‘¯ ν’ + p → e + n
(20.35)
was observed by Reines and Cowan (1956) (see also Cowan et al. 1956). Reaction (20.35) too, of course, can be interpreted in terms of ‘¯ ν’ carrying a lepton
number of -1, equal to that of the e
+ . It was also established that only ‘ν’
20.3. Lepton number and lepton flavours
20.3 Lepton number and lepton flavours
In section 1.2.1 of volume 1 we gave a brief discussion of leptonic quantum
numbers (‘lepton flavours’), adopting a traditional approach in which the data
is interpreted in terms of conserved quantum numbers carried by neutrinos,
which serve to distinguish neutrinos from antineutrinos. We must now examine the matter more closely, in the light of what we have learned about the
helicity properties of the V-A interaction.
In 1995, Davis (1955) – following a suggestion made by Pontecorvo (1946) –
−
−
argued as follows. Consider the e capture reaction e +p → ν +n, which was
−
of course well established. Then in principle the inverse reaction ν+n → e +p
should also exist. Of course, the cross section is extremely small, but by using
a large enough target volume this might perhaps be compensated. Specifically,
− +
37
the reaction ν +
37 Cl → e
Ar was proposed, the argon being detected
17
18
through its radioactive decay. Suppose, however, that the ‘neutrinos’ actually
used are those which accompany electrons in β
− -decay. If (as was supposed
in section 1.2.1) these are to be regarded as antineutrinos, ‘¯ ν’, carrying a
conserved lepton number, then the reaction
−
37
‘¯ ν’ +
37
e +
(20.34)
17 Cl →
18 Ar
should not be observed. If, on the other hand, the ‘ν’ in the capture process
and the ‘¯ ν’ in β-decay are not distinguished by the weak interaction, the
reaction (20.34) should be observed. Davis found no evidence for reaction
(20.34), at the expected level of cross section, a result which could clearly be
interpreted as confirming the ‘conserved electron number hypothesis’.
However, another interpretation is possible. The e
− in β-decay has predominately negative helicity, and its accompanying ‘¯ ν’ has predominately positive helicity. The fraction of the other helicity present is of the order m/E,
where E ∼ few Mev, and the neutrino mass is less than 1eV; this is, therefore,
an almost undetectable ‘contamination’ of negative helicity component in the
‘¯ ν’. Now the property of the V-A interaction is that it conserves helicity in
the zero mass limit (in which chirality is the same as helicity). Hence the
positive helicity ‘¯ ν’ from β
− -decay will (predominately) produce a positive
helicity lepton, which must be the e
+ not the e
− . Thus the property of the
V-A interaction, together with the very small value of the neutrino mass, conspire effectively to forbid (20.34), independently of any considerations about
‘lepton number’.
Indeed, the ‘helicity-allowed’ reaction
+
‘¯ ν’ + p → e + n
(20.35)
was observed by Reines and Cowan (1956) (see also Cowan et al. 1956). Reaction (20.35) too, of course, can be interpreted in terms of ‘¯ ν’ carrying a lepton
number of -1, equal to that of the e
+ . It was also established that only ‘ν’