Abstract
Quantum chromodynamics is responsible for some of the most complex and interesting phenomena observed in nuclear physics. Two of which stand out in particular are confinement and asymptotic freedom. The structure of the colour SU(3) gauge group means that as the energy scale increases, the quark-gluon coupling vanishes. This is asymptotic freedom and it results in hadrons appearing to consist of essentially free, point-like particles at large momenta. At the other end of the scale, confinement occurs. The quark-gluon coupling grows with decreasing energy—equivalent to large distances—causing the potential between quarks to increase. At large separation, the energy required to break the bond between quarks is sufficient to create a \(q \bar{q}\) pair out of the vacuum. Consequently, quarks and gluons cannot be observed in isolation, but only in the form of bound, ‘colour-singlet’ states. Figure 4.1 illustrates the behaviour of the strong coupling constant, \(\alpha _s\), as a function of momentum transfer.
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Notes
- 1.
The boundary between the perturbative and nonperturbative regions is somewhat loosely defined and later discussions in Chap. 8 on the moments of structure function will touch on this issue.
- 2.
Although there appears to be a \(1/Q^2\) dependence in the second term of Eq. (4.25), by expanding out the logarithm one can check that the cross section vanishes as \(Q^2 \rightarrow 0\).
- 3.
In their analysis, GHRM take the background uncertainty from the model which gives the largest error i.e., Model II.
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Hall, N.L. (2016). Structure Functions. In: Hadron Structure in Electroweak Precision Measurements. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-20221-1_4
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