Why Aren't Atomic Nuclei Quark Gluon Plasmas?

Question:

The standard picture of the nucleus of atom is that is several distinct nucleons, which themselves are composed of quarks. However, it seems like a much simpler picture is that the nucleus is directly made out of quarks, without having nucleons as substructures. That is, that the nucleus is the ground state of a quark-gluon plasma. Why do atomic nuclei (other than hydrogen-1 which is just a single proton) have nucleons as substructures?

(This is an abridged and reformatted cross-post version of an answer I posted at the Physics Stack Exchange).

Answer:

This is a consequence of the part of the Standard Model of Particle Physics called quantum chromodynamics (QCD), which governs how quarks and gluons interact.

Confinement and its exceptions

One of the core principles of QCD is confinement which means that the strong force between quarks that is mediated by gluons is so pervasive that none of the five kinds of quarks that are not top quarks (top quarks decay so quickly they don't have time to form composite structures which is called hadronizing before they decay) are ever observed in nature outside of a hadron (a composite particle made of quarks bound by gluons) - generally either three quarks (one of each of the three QCD color charges) in a baryon or a quark and an antiquark bound in a meson. Baryons are fermions of spin 1/2+N (an integer), which means that they behave like ordinary matter (i.e. to oversimplify, you can't have two of them in the same place at the same time), while mesons are bosons with integer spin N (i.e. to oversimplify, more than one can be in the same space at the same time).

In principle, QCD allows four or more quark composite particles (tetraquarks, pentaquarks, etc.) and a handful have been observed, but in practice, the four or more quark composite particles are extremely unstable and hard to create in the first place, so even in the rarified environment of a particle collider you see almost entirely mesons and baryons.

A quark-gluon plasma can "fudge" the otherwise rather automatic and complete sorting of quarks into confined hadrons only at extremely high energies because the strong force powerfully constrains them to stay within a particular hadron. So, in the "infrared" environment that we encounter in daily life or even in quite high energy applications, the temperature isn't enough to overcome the strong force's tendency to bind quarks into hadrons.

How hot does it have to be?

The cross-over temperature is about 2⋅10¹² K which corresponds to an energy density of a little less than 1 GeV/fm³ (i.e. the temperature has to contribute kinetic energy density comparable in amount to the energy density of the gluons in a proton or neutron to overcome their clutches). This is more than one hundred times as hot as the hottest it gets anywhere inside the Sun (which is about 1.5⋅10¹⁰ K).

How hard is it to get something that energetic?

The first time humans were able to artificially create those energy densities was in 2015 at the Large Hadron Collider (although non-definitive hints that we might have done it were seen at other colliders as early as 2005). Nothing in the solar system had ever been that hot previously at any time in the four or five billion years since it came into existence.

What does this imply?

Now, it also turns out that of the hundreds of possible baryons and mesons, no meson has a mean lifetime of more than about a ten millionth of a second, and only two kinds of baryons have mean lifetimes of more than about ten billionths of a second. The proton (which is made up of two up quarks and one down quark bound by gluons) does not decay, and the neutron (which is made up of one up quark and two down quarks) has a mean lifetime of about 15 minutes if free (and can potentially be stable in the right kind of atomic nucleus mostly due to conservation of mass-energy considerations in a bound nucleus).

So, the theoretical reason that atomic nuclei are not quark-gluon plasmas is because: (1)(a) at cool enough temperatures and (1)(b) given the tiny fraction of a second necessary for an unstable hadrons to decay, (2) their constituent quarks are forced into hadrons and (3) the hadrons decay until they consist only of stable protons and neutrons (collectively nucleons).

A residual effect of the strong force (which is mediated mostly by a kind of meson called a pion which is exchanged between nucleons) binds the nucleons together into an atomic nucleus, but far less tightly to each other than the quarks within the nucleons are bound by the strong force.

Now that binding force itself is nothing to sniff at - that is the source of all energy created by nuclear fusion in an H bomb or a star like the Sun, and the nuclear fission in an A bomb or nuclear reactor. But, the strong force binding quarks inside protons and neutrons is much stronger which is why it takes such extreme conditions to overcome.

Caveat

There are multiple, progressively more complex ways to describe what is going on in a hadron. In addition to the "valance quarks" bound exchanging gluons that I have described above, there is also a "sea" of quark-antiquark pairs that cancel out for many purposes but can't be ignored if you want to smash protons together at high speeds or you want to calculate the mass of a hadron from first principles. Thus, for example, you could smash protons only to find that strange or charm or bottom quarks fall out if the collision have enough energy, even though none of the valence quarks of a proton are of that type. But, that level of complexity isn't necessary to understand theoretically based on QCD why quarks in an atomic nuclei are subdivided into protons and neutrons.

Post script

There are a couple of things that make this question interesting.

First, it demonstrates how, for all its complexity, basic qualitative features of QCD and properties of hadrons suffice both to explain the basic internal structure of atomic nuclei and render the vast majority of QCD irrelevant in the vast majority of circumstances despite its subtle and complex edifice from just a handful of basic piece and rules. This does a good job of putting QCD in the proper context and perspective.

In particular, it demonstrates that some aspects of QCD are primarily relevant to circumstances the prevailed in Nature only immediately following the Big Bang, and hence illustrates the surprisingly close connection between QCD and cosmology.

Second, the fact that the temperature at which the quark gluon plasma overcomes the usual rule of confinement corresponds to the point at which kinetic energy exceeds the gluon field energy of a hadron is elegant. It also clarifies that somewhat misleading dogma that quarks are always confined when in fact there are top quark and quark gluon plasma exceptions to that rule.