29
1.3. Particle interactions in the Standard Model
the charges becomes greater than about 1 fm. In the second volume, we shall
see that numerical simulations of QCD, in which the space–time continuum is
represented as a discrete lattice of points, indicate that such a linear potential
does arise when QCD is treated non-perturbatively. It remains a challenge
for theory to demonstrate that confinement follows from QCD.
It is believed that gluons too are confined by QCD, so that – like quarks
– they are not seen as isolated free particles. But they too ‘hadronize’ after
being produced in a primitive short-distance collision process, as happens in
the case of q’s and ¯
q’s. Such ‘gluon jets’ provide indirect evidence for the
existence and properties of gluons, as we shall see in volume 2.
This is an appropriate moment at which to emphasize what appears to
be a crucial distinction between the three ‘charges’ (electromagnetic, weak
and strong) on the one hand, and the various flavour quantum numbers on
the other. The former have a dynamical significance, whereas the latter do
not. In the case of electric charge, for example, this means simply that a
particle carrying this property responds in a definite way to the presence of
an electromagnetic field and itself creates such a field. No such force fields are
known for any of the flavour numbers, which are (at present) purely empirical
classification devices, without dynamical significance.
1.3.7 The gauge bosons of the Standard Model
We can now gather together the mediators of the SM forces. They are all gauge
bosons, meaning that they are the quanta of various 4-vector gauge fields. For
example, the photon is the quantum of the electromagnetic (Maxwell) 4-vector
potential A
μ (x) (see chapter 2 and section 6.3.1), which is the simplest gauge
field. The gluon is the quantum of the QCD potential A
μ (x), where the colour
a
index a runs from 1 to 8. The reason there are 8 of them may be guessed
from figure 1.9: each gluon can be thought of as carrying one colour-anticolour
combination, such as ¯ bg, and so on; the symmetric combination rr + ¯
rb, ¯
¯
bb
+¯ gg is totally colourless and is discarded (see section 12.2 in volume 2). In
μ
the GSW electroweak theory, there are four gauge fields, W (x) where i runs
i
from 1 to 3, and B
μ (x) which is analogous to A
μ (x). One linear combination
μ
of W (x) and B
μ (x) is associated with the photon field A
μ (x); the orthogonal
3
combination is associated with the Z
μ (x) field whose quantum is the Z
0 . The
μ
μ
charged carriers W
± are associated with the W (x) and W (x) components
1
2
of the W
μ (x) field.
i
We shall assume that the mass of the photon and of the gluon is exactly
zero. This can never be established experimentally, of course: the current
experimental limit on the photon mass is that it is less than 1 × 10
−18 (Nakamura et al. 2010). All gauge fields have spin 1 (in units of ħ). Ordinarily, a
spin-1 particle would be expected to have three polarization states, according
to quantum mechanics. However it is a general result that in the massless
case the quanta have only two polarization states, both transverse to the direction of motion; the longitudinally polarized state is absent (this property,
1.3. Particle interactions in the Standard Model
the charges becomes greater than about 1 fm. In the second volume, we shall
see that numerical simulations of QCD, in which the space–time continuum is
represented as a discrete lattice of points, indicate that such a linear potential
does arise when QCD is treated non-perturbatively. It remains a challenge
for theory to demonstrate that confinement follows from QCD.
It is believed that gluons too are confined by QCD, so that – like quarks
– they are not seen as isolated free particles. But they too ‘hadronize’ after
being produced in a primitive short-distance collision process, as happens in
the case of q’s and ¯
q’s. Such ‘gluon jets’ provide indirect evidence for the
existence and properties of gluons, as we shall see in volume 2.
This is an appropriate moment at which to emphasize what appears to
be a crucial distinction between the three ‘charges’ (electromagnetic, weak
and strong) on the one hand, and the various flavour quantum numbers on
the other. The former have a dynamical significance, whereas the latter do
not. In the case of electric charge, for example, this means simply that a
particle carrying this property responds in a definite way to the presence of
an electromagnetic field and itself creates such a field. No such force fields are
known for any of the flavour numbers, which are (at present) purely empirical
classification devices, without dynamical significance.
1.3.7 The gauge bosons of the Standard Model
We can now gather together the mediators of the SM forces. They are all gauge
bosons, meaning that they are the quanta of various 4-vector gauge fields. For
example, the photon is the quantum of the electromagnetic (Maxwell) 4-vector
potential A
μ (x) (see chapter 2 and section 6.3.1), which is the simplest gauge
field. The gluon is the quantum of the QCD potential A
μ (x), where the colour
a
index a runs from 1 to 8. The reason there are 8 of them may be guessed
from figure 1.9: each gluon can be thought of as carrying one colour-anticolour
combination, such as ¯ bg, and so on; the symmetric combination rr + ¯
rb, ¯
¯
bb
+¯ gg is totally colourless and is discarded (see section 12.2 in volume 2). In
μ
the GSW electroweak theory, there are four gauge fields, W (x) where i runs
i
from 1 to 3, and B
μ (x) which is analogous to A
μ (x). One linear combination
μ
of W (x) and B
μ (x) is associated with the photon field A
μ (x); the orthogonal
3
combination is associated with the Z
μ (x) field whose quantum is the Z
0 . The
μ
μ
charged carriers W
± are associated with the W (x) and W (x) components
1
2
of the W
μ (x) field.
i
We shall assume that the mass of the photon and of the gluon is exactly
zero. This can never be established experimentally, of course: the current
experimental limit on the photon mass is that it is less than 1 × 10
−18 (Nakamura et al. 2010). All gauge fields have spin 1 (in units of ħ). Ordinarily, a
spin-1 particle would be expected to have three polarization states, according
to quantum mechanics. However it is a general result that in the massless
case the quanta have only two polarization states, both transverse to the direction of motion; the longitudinally polarized state is absent (this property,