7
1.2. The fermions of the Standard Model
TABLE 1.1
Properties of SM leptons.
Generation Particle Mass (MeV) Q/e L e L μ L τ
1
ν e
e
−
< 2 × 10
−6
0.511
0
- 1
1
1
0
0
0
0
2
ν μ
μ
−
< 0.19
105.658
0
- 1
0
0
1
1
0
0
3
ν τ
τ
−
< 18.2
1777
0
- 1
0
0
0
0
1
1
We should at this point note that another type of weak interaction is
known, in which – for example – the ¯
ν μ in (1.5) scatters elastically from the
proton, instead of changing into a μ
+ :
ν ¯ μ + p → ν ¯ μ + p.
(1.9)
This is an example of what is called a ‘neutral current’ process, (1.5) being a
‘charged current’ one. In terms of the Yukawa-like exchange mechanism for
particle interactions, to be described in the next section, (1.5) proceeds via
the exchange of charged quanta (W
± ), while in (1.9) a neutral quantum (Z
0 )
is exchanged.
As well as their flavour, one other property of neutrinos is of great interest,
namely their mass. As originally postulated by Pauli, the neutrino emitted in
β-decay had to have very small mass, because the maximum energy carried
off by the e
− in (1.2) was closely equal to the difference in rest energies of
the neutron and proton. It was subsequently widely assumed (perhaps largely
for simplicity) that all neutrinos were strictly massless, and it is fair to say
that the original Standard Model made this assumption. Yet there is, in fact,
no convincing reason for this (as there is for the masslessness of the photon
– see chapter 6), and there is now clear evidence that neutrinos do indeed
have very small, but non-zero, masses. It turns out that the question of
neutrino masslessness is directly connected to another one: whether neutrino
flavour is, in fact, conserved. If neutrinos are massless, as in the original
Standard Model, neutrinos of different flavour cannot ‘mix’, in the sense of
quantum-mechanical states; but mixing can occur if neutrinos have mass. The
phenomenon of neutrino flavour mixing (or ‘neutrino oscillations’) is now well
established, and is a subject of intense research. In this book we shall simply
regard non-zero neutrino masses as part of the (updated) Standard Model.
The SM leptons are listed in table 1.1, along with some relevant properties.
Note that the limits on the neutrino masses, which are taken from Nakamura
1.2. The fermions of the Standard Model
TABLE 1.1
Properties of SM leptons.
Generation Particle Mass (MeV) Q/e L e L μ L τ
1
ν e
e
−
< 2 × 10
−6
0.511
0
- 1
1
1
0
0
0
0
2
ν μ
μ
−
< 0.19
105.658
0
- 1
0
0
1
1
0
0
3
ν τ
τ
−
< 18.2
1777
0
- 1
0
0
0
0
1
1
We should at this point note that another type of weak interaction is
known, in which – for example – the ¯
ν μ in (1.5) scatters elastically from the
proton, instead of changing into a μ
+ :
ν ¯ μ + p → ν ¯ μ + p.
(1.9)
This is an example of what is called a ‘neutral current’ process, (1.5) being a
‘charged current’ one. In terms of the Yukawa-like exchange mechanism for
particle interactions, to be described in the next section, (1.5) proceeds via
the exchange of charged quanta (W
± ), while in (1.9) a neutral quantum (Z
0 )
is exchanged.
As well as their flavour, one other property of neutrinos is of great interest,
namely their mass. As originally postulated by Pauli, the neutrino emitted in
β-decay had to have very small mass, because the maximum energy carried
off by the e
− in (1.2) was closely equal to the difference in rest energies of
the neutron and proton. It was subsequently widely assumed (perhaps largely
for simplicity) that all neutrinos were strictly massless, and it is fair to say
that the original Standard Model made this assumption. Yet there is, in fact,
no convincing reason for this (as there is for the masslessness of the photon
– see chapter 6), and there is now clear evidence that neutrinos do indeed
have very small, but non-zero, masses. It turns out that the question of
neutrino masslessness is directly connected to another one: whether neutrino
flavour is, in fact, conserved. If neutrinos are massless, as in the original
Standard Model, neutrinos of different flavour cannot ‘mix’, in the sense of
quantum-mechanical states; but mixing can occur if neutrinos have mass. The
phenomenon of neutrino flavour mixing (or ‘neutrino oscillations’) is now well
established, and is a subject of intense research. In this book we shall simply
regard non-zero neutrino masses as part of the (updated) Standard Model.
The SM leptons are listed in table 1.1, along with some relevant properties.
Note that the limits on the neutrino masses, which are taken from Nakamura