26
1. The Particles and Forces of the Standard Model
gauge symmetry being ‘spontaneously broken’ in the case of weak interactions. This is a central feature of the GSW electroweak theory. An indication
of how gauge quanta might acquire mass will be given in section 11.4 but a
fuller explanation, with application to the electroweak theory, is reserved for
volume 2. We will have a few more words to say about it in section 1.4.1.
1.3.6 Strong interactions
We turn to the contemporary version of Yukawa’s theory of strong interactions, now viewed as occurring between quarks rather than nucleons. Evidence
that the strong interquark force is in some way similar to QED comes from
nucleon-nucleon (or nucleon-antinucleon) collisions. Regarding the nucleons
as composites of point-like quarks, we would expect to see prominent events at
large scattering angles corresponding to ‘hard’ q–q collisions (recall Rutherford’s discovery of the nucleus). Now the result of such a hard collision would
normally be to scatter the quarks to wide angles, ‘breaking up’ the nucleons
in the process. However, quarks (except for the t quark) are not observed
as free particles. Instead, what appears to happen is that, as the two quarks
separate from each other, their mutual potential energy increases – so much so
that, at a certain stage in the evolution of the scattering process, the energy
stored in the potential converts into a new q¯ q pair. This process continues,
with in general many pairs being produced as the original and subsequent
pairs pull apart. By a mechanism which is still not quantitatively understood
in detail, the produced quarks and antiquarks (and the original quarks in the
nucleons) bind themselves into hadrons within an interaction volume of order
1 fm
3 , so that no free quarks are finally observed, consistent with ‘confinement’. Very strikingly, these hadrons emerge in quite well-collimated ‘jets’,
suggesting rather vividly their ancestry in the original separating qq pair.
Suppose, then, that we plot the angular distribution of such ‘two jet events’:
it should tell us about the dynamics of the original interaction at the quark
level.
Figure 1.8 shows such an angular distribution from proton–antiproton scattering, so that the fundamental interaction in this case is the elastic scattering
process ¯
¯
¯
mass
qq → qq. Here θ is the scattering angle in the qq centre of
system
(CMS). Amazingly, the θ-distribution follows almost exactly the ‘Rutherford’
form sin
−4 θ/2.
We saw how, in the Coulomb case, this distribution could be understood
as arising from the propagator factor 1/q
2 , which itself comes from the 1/r
potential associated with the massless quantum involved, namely the photon.
In the present case, the same
¯
1/q
2 factor is responsible: here, in the qq centre
of mass system, k and −k are the momenta of the initial q ¯ and q, while k
′ and
−k
′ are the corresponding final momenta. Once again, for elastic scattering
2
2
there is no energy transfer, and q = −q = −(k − k
′ )
2 = −4k
2 sin
2 θ/2 as
before, leading to the sin
−4 θ/2 form on squaring 1/q
2 . Once again, such a
1. The Particles and Forces of the Standard Model
gauge symmetry being ‘spontaneously broken’ in the case of weak interactions. This is a central feature of the GSW electroweak theory. An indication
of how gauge quanta might acquire mass will be given in section 11.4 but a
fuller explanation, with application to the electroweak theory, is reserved for
volume 2. We will have a few more words to say about it in section 1.4.1.
1.3.6 Strong interactions
We turn to the contemporary version of Yukawa’s theory of strong interactions, now viewed as occurring between quarks rather than nucleons. Evidence
that the strong interquark force is in some way similar to QED comes from
nucleon-nucleon (or nucleon-antinucleon) collisions. Regarding the nucleons
as composites of point-like quarks, we would expect to see prominent events at
large scattering angles corresponding to ‘hard’ q–q collisions (recall Rutherford’s discovery of the nucleus). Now the result of such a hard collision would
normally be to scatter the quarks to wide angles, ‘breaking up’ the nucleons
in the process. However, quarks (except for the t quark) are not observed
as free particles. Instead, what appears to happen is that, as the two quarks
separate from each other, their mutual potential energy increases – so much so
that, at a certain stage in the evolution of the scattering process, the energy
stored in the potential converts into a new q¯ q pair. This process continues,
with in general many pairs being produced as the original and subsequent
pairs pull apart. By a mechanism which is still not quantitatively understood
in detail, the produced quarks and antiquarks (and the original quarks in the
nucleons) bind themselves into hadrons within an interaction volume of order
1 fm
3 , so that no free quarks are finally observed, consistent with ‘confinement’. Very strikingly, these hadrons emerge in quite well-collimated ‘jets’,
suggesting rather vividly their ancestry in the original separating qq pair.
Suppose, then, that we plot the angular distribution of such ‘two jet events’:
it should tell us about the dynamics of the original interaction at the quark
level.
Figure 1.8 shows such an angular distribution from proton–antiproton scattering, so that the fundamental interaction in this case is the elastic scattering
process ¯
¯
¯
mass
qq → qq. Here θ is the scattering angle in the qq centre of
system
(CMS). Amazingly, the θ-distribution follows almost exactly the ‘Rutherford’
form sin
−4 θ/2.
We saw how, in the Coulomb case, this distribution could be understood
as arising from the propagator factor 1/q
2 , which itself comes from the 1/r
potential associated with the massless quantum involved, namely the photon.
In the present case, the same
¯
1/q
2 factor is responsible: here, in the qq centre
of mass system, k and −k are the momenta of the initial q ¯ and q, while k
′ and
−k
′ are the corresponding final momenta. Once again, for elastic scattering
2
2
there is no energy transfer, and q = −q = −(k − k
′ )
2 = −4k
2 sin
2 θ/2 as
before, leading to the sin
−4 θ/2 form on squaring 1/q
2 . Once again, such a