6
1. The Particles and Forces of the Standard Model
forbidden, the left-hand side having L e = 0 and L μ = 1, while the right-hand
side has L e = 1 and L μ = 0.
The electromagnetic interactions of the mu and the tau leptons are the
same as for the electron. In weak interactions, each charged lepton (e, μ, τ) is
accompanied by its ‘own’ neutral partner, a neutrino. The one emitted with
the e
− in β-decay was originally introduced by Pauli in 1930, as a ‘desperate
remedy’ to save the conservation laws of four-momentum and angular momentum. In the Standard Model, the three neutrinos are assigned lepton flavour
quantum numbers in such a way as to conserve each lepton flavour separately.
Thus we assign L e = −1, L μ = 0, L τ = 0 to the neutrino emitted in neutron
β-decay
n → p + e
− + ¯
ν e ,
(1.2)
since L e = 0 in the initial state and L e (e
− ) = +1; so the neutrino in (1.2) is an
antineutrino ‘of electron type’ (or ‘of electron flavour’). The physical reality
of the antineutrinos emitted in nuclear β-decay was established by Reines and
collaborators in 1956 (Cowan et al. 1956), by observing that the antineutrinos
from a nuclear reactor produced positrons via the inverse β-process
¯
ν e + p → n + e
+ .
(1.3)
The neutrino partnering the μ
− appears in the decay of the π
− :
π
−
→ μ
− + ¯
ν μ
(1.4)
where the ¯
ν μ is an antineutrino of muon type (L μ (¯ ν μ ) = −1, L e (¯ ν μ ) = 0 =
L τ (¯ ν μ )). How do we know that ¯
ν μ and ¯
ν e are not the same? An important
experiment by Danby et al. (1962) provided evidence that they are not. They
found that the neutrinos accompanying muons from π-decay always produced
muons on interacting with matter, never electrons. Thus, for example, the
lepton flavour conserving reaction
ν ¯ μ + p → μ
+ + n
(1.5)
was observed, but the lepton flavour violating reaction
+
ν ¯ μ + p → e + n
(not observed)
(1.6)
was not. As with (1.1), ‘non-observation’ of course means, in practice, an
upper limit on the cross section. Both types of neutrino occur in the β-decay
of the muon itself:
μ
−
→ ν μ + e
− + ¯
ν e ,
(1.7)
in which L μ = 1 is initially carried by the μ
− and finally by the ν μ , and the
L e ’s of the e
− and ¯
ν e cancel each other out.
In the same way, the ν τ is associated with the τ
− , and we have arrived at
three generations of charged and neutral lepton doublets:
(ν e , e
− )
(ν μ , μ
− )
and
(ν τ , τ
− )
(1.8)
together with their antiparticles.
1. The Particles and Forces of the Standard Model
forbidden, the left-hand side having L e = 0 and L μ = 1, while the right-hand
side has L e = 1 and L μ = 0.
The electromagnetic interactions of the mu and the tau leptons are the
same as for the electron. In weak interactions, each charged lepton (e, μ, τ) is
accompanied by its ‘own’ neutral partner, a neutrino. The one emitted with
the e
− in β-decay was originally introduced by Pauli in 1930, as a ‘desperate
remedy’ to save the conservation laws of four-momentum and angular momentum. In the Standard Model, the three neutrinos are assigned lepton flavour
quantum numbers in such a way as to conserve each lepton flavour separately.
Thus we assign L e = −1, L μ = 0, L τ = 0 to the neutrino emitted in neutron
β-decay
n → p + e
− + ¯
ν e ,
(1.2)
since L e = 0 in the initial state and L e (e
− ) = +1; so the neutrino in (1.2) is an
antineutrino ‘of electron type’ (or ‘of electron flavour’). The physical reality
of the antineutrinos emitted in nuclear β-decay was established by Reines and
collaborators in 1956 (Cowan et al. 1956), by observing that the antineutrinos
from a nuclear reactor produced positrons via the inverse β-process
¯
ν e + p → n + e
+ .
(1.3)
The neutrino partnering the μ
− appears in the decay of the π
− :
π
−
→ μ
− + ¯
ν μ
(1.4)
where the ¯
ν μ is an antineutrino of muon type (L μ (¯ ν μ ) = −1, L e (¯ ν μ ) = 0 =
L τ (¯ ν μ )). How do we know that ¯
ν μ and ¯
ν e are not the same? An important
experiment by Danby et al. (1962) provided evidence that they are not. They
found that the neutrinos accompanying muons from π-decay always produced
muons on interacting with matter, never electrons. Thus, for example, the
lepton flavour conserving reaction
ν ¯ μ + p → μ
+ + n
(1.5)
was observed, but the lepton flavour violating reaction
+
ν ¯ μ + p → e + n
(not observed)
(1.6)
was not. As with (1.1), ‘non-observation’ of course means, in practice, an
upper limit on the cross section. Both types of neutrino occur in the β-decay
of the muon itself:
μ
−
→ ν μ + e
− + ¯
ν e ,
(1.7)
in which L μ = 1 is initially carried by the μ
− and finally by the ν μ , and the
L e ’s of the e
− and ¯
ν e cancel each other out.
In the same way, the ν τ is associated with the τ
− , and we have arrived at
three generations of charged and neutral lepton doublets:
(ν e , e
− )
(ν μ , μ
− )
and
(ν τ , τ
− )
(1.8)
together with their antiparticles.