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Correct me if I am wrong: If we collide protons with protons then we can have elastic scattering, inelastic scattering (large momentum transfer between partons), and diffractive dissociation. I am assuming that these three processes occur with a significant dependence on the impact parameter. I understand the first two processes (elastic, inelastic). However, the concept of diffractive dissociation is somewhat confusing. Is it just a process in which after the interaction one or both of the protons dissociate into a spray of partons (which eventually hadronize). If so, how are those processes interesting (except maybe to understand the pdf of the proton slightly better). Are all such diffractive dissociation processes discarded in a physics analysis. Any insight is appreciated. Thanks.

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Just some terminology: Elastic scattering refers to processes in which both the projectile and the target stay intact, and no extra particles are produced. Inelastic scattering is everything else.

"Diffractive" scattering is not a completely precise term. It refers to high energy, small angle scattering, which can be treated using the semiclassical approximation, in analogy with geometric optics (hence the name). Diffraction can be elastic or inelastic. Indeed, in the black disk limit the two cross sections are equal.

Diffractive dissociation is a diffractive process in which the projectile is disintegrated, but the target stays intact (or vice versa). The text book example, originally studied by Glauber and others, is the diffractive dissociation of the deuteron (a very weakly bound nucleus) in scattering on a heavy nucleus. This calculation is described in standard text books on quantum mechanics, for example in Landau and Lifschitz.

So why do we care about diffractive dissociation in QCD? Historically, it was important to ignore "soft" processes, and focus on hard scattering (reactions like DIS, jet production, etc.). Hard scattering revealed partons inside the proton, scaling, and asymptotic freedom. It established QCD as the correct theory of the strong interaction.

However, small angle scattering dominates the total cross section, and the total multiplicity. Surely, if we are interested in QCD we would like to understand the total cross section, and the total multiplicity. In some ways diffractive dissociation is a special class of soft events that we may be able to understand in QCD, as a stepping stone to understanding the total cross section.

Furthermore, soft or semi-hard reactions at high energy may reveal a new regime semi-classical regime of QCD in which the density of gluons is very large, but the effective coupling is weak.

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It is better to think of the colliding protons as perturbations in a wavefunction in this case as assuming they are discrete particles leads to confusion due to the insufficiency of human laguage as you have realized.

Although of course mathematical derivations of colliding tides in oceans and other kinds of waves are far from the energy and time scales in question they may be of some use to understand how glancing waves merge, diffract, and ‘disassociate’. Their behaviour is somewhat illustrative of how protons undergo diffractive disassociation.

I haven’t come across a good formulation or diagram of this process for protons specifically yet.

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