Colour confinement

The term confinement indicates that coloured free particles do not exist in Nature.

Besides valence quarks, a hadron contains a population of more quarks and gluons. From the (b) side of the Figure in the previous post (*) it is possible to infer that the strong interaction between two quarks enhances with the increasing of their distances.
The corresponding colour field lines of force between the quark and the antiquark become packed into a tube-like region, as shown in the (a) side of the following Figure.

Differences between lines of force of electric field and colour field (a). Formation of new q q-bar pair at the increasing of the separation energy (b). [Picture from F. Halzen and D.H. Martin (see References)]
This constitutes a significant difference with the Coulomb field where there is no self-coupling of the photons to contain lines of force and then nothing prevents them from spreading out.
If the colour tube is supposed to have a constant energy density per unit length, the potential energy between a quark and an antiquark in a hadron grows with separation and its form can be assumed V \sim \lambda r.
The separation can go on until the potential energy becomes high enough to create anotherq\bar q pair, the (b) side of the Figure.
The process also works backwards i.e. the annihilation of two quarks produces a gluon. Such new quarks – and gluons – are said of the sea.

Why quarks and gluons cannot escape from hadrons results now explained.

One should infer that the origin of the hadron mass is the strong interaction since light quark masses only represent less than 10% of the total hadron mass.
In this respect, the Higgs boson only explains about 1% of the total mass of the proton and neutron which are the main massive constituents of ordinary matter , so the question is still open.

Although the phenomenon of confinement has been clearly observed, it is not supported by accurate predictions within the Standard Model, and in general, unlike the electroweak interactions, it is not possible to handle the QCD with the perturbative approach (*).
However, lattice non-perturbative approaches have confirmed quark confinement as an intrinsic property of QCD.
While, as remarked, in normal conditions quarks and gluons are confined in their parent hadrons, at the QGP condition they are expected to be free to move through protons and neutrons that constitute the nucleus, as depicted in the left side of the following Figure. Such phase is known as deconfined.

A state in which quarks and gluons from originary nucleons are free to move through the matter, i.e. deconfinement, is expected to happen at extreme conditions of temperature and density, as those expected for the first few instants (10^{-6}\ s) after the Big Bang.


References and further readings:
G. M. Garcìa, Advances in Quark Gluon Plasma, [arXiv:nucl-ex/1304.1452v1], 2013
J. Letessier and J. Rafelski, Hadrons and Quark–Gluon Plasma, (Cambridge monographs on Particle Physics, nuclear Physics and Cosmology), 2002.
C. Quigg, Gauge Theories of the Strong, Weak and Electromagnetic Interactions, (Addison-Wesley Publishing Company), 1997.
F.Halzen and A.D. Martin, Quarks and Leptons: an Introductory Course in Modern Particle Physics, (John Wiley & Sons), 1984.

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