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The Proton-Proton Cross Section

Let us consider the energy dependence of the proton-proton cross section data (see [1], p. 11; [2], p. 9). The data show clearly the following properties of this cross section:

  1. At high energy, the total cross section begins to rise in parallel with the increase of the collision energy.
  2. At high energy, the elastic cross section begins to rise in parallel with the increase of the collision energy.
  3. At high energy, the ratio between the elastic and the total cross section remains (nearly) constant with the increase of the collision energy.

The behavior of the electron-proton cross section is completely different (see [3], chapter 6; [4], chapters 7, 8).

1′. At high energy, the total cross section decreases with the increase of the collision energy.

2′. At high energy, the elastic cross section decreases with the increase of the collision energy (see the next item).

3′. At high energy, the ratio between the elastic and the total cross section decreases and tends to zero (see [4], pp. 160, 161).

According to the interpretation of deep inelastic electron-proton scattering,  the process begins as an elastic electron-quark process and this heavily struck quark produces an inelastic event (see [4], pp. 160, 161).

Research topic #1: Why the number of elastic events of a quark that was heavily struck by an electron become relatively negligible, whereas in proton-proton scattering, a quark that was heavily struck by another quark, produces a non-negligible number of elastic events?

Research topic #2: Why the electron-proton cross section decreases with the increase of the collision energy, whereas the proton-proton cross section increases with the collision energy?

Research topic #3: The increase of the projectile’s energy  is manifested as a decrease of its wavelength. In this case the scattered projectile is affected by smaller spatial details of the target. By contrast, according to the quark-quark asymptotic freedom attribute, the intensity of the quark-quark interaction should decrease as the distance becomes smaller (see [4], p. 259; [5]). Textbooks do not discuss the consistency of QCD’s asymptotic freedom with the data presented above, according to which the electromagnetic electron-quark cross section decreases with the increase of the collision energy, whereas the quark-quark cross section increases with the collision energy. This problem awaits an explanation.

References

[1] http://pdg.lbl.gov/2012/reviews/rpp2012-rev-cross-section-plots.pdf

[2] http://pdg.lbl.gov/2018/reviews/rpp2018-rev-cross-section-plots.pdf

[3] D. H. Perkins, Introduction to High Energy Physics (Addison-Wesley, Menlo Park CA, 1987).

[4] M. Thomson, Modern Particle Physics (Cambridge University Press, Cambridge UK, 2013).

[5] https://en.wikipedia.org/wiki/Asymptotic_freedom