What happens to a gluon that does not have enough energy to hadronize?

[jimi]

A real gluon created from say, some particle annihilation or decay, should hadronize when in space correct? Well what if that gluon does not suffice in energy to form quarks? Does it become a glueball? That leads me into another question, why are glueballs theorized to have specific masses, shouldn't it completely depend on how it's formed, i.e. its original energy amount should be its mass? Does negative energy that virtual gluons may hold play a role in this? Thanks.

 

[Vanadium 50]

Please ask different questions in different threads.

A gluon that cannot hadronize will combine with some other colored object in the event.,

 

[jimi]

And if there isn't some other colored object in the event?

 

[Vanadium 50]

There must be. How can there not be? The original state was color neutral.

 

[Orodruin]

That leads me into another question, why are glueballs theorized to have specific masses, shouldn't it completely depend on how it's formed

I don’t think you understand what a glueball is. It is a specific bound state for which you can compute the energy much as you would compute the energy of a hydrogen atom (well, not exactly, glueballs essentially require lattice QCD due to the nature of strong interactions).

 

[MathematicalPhysicist]

BTW if you want to dig into the ancient literature of QCD, glueball was once called gluonium.

Different names, different research themes?!

 

[ohwilleke]

A real gluon created from say, some particle annihilation or decay, should hadronize when in space correct? Well what if that gluon does not suffice in energy to form quarks? Does it become a glueball?

Disclaimer

I am working this out from sheer logic from what I have studied and read about the topic and this seems to be enough to answer this question. In physics, unlike, for example, law, you can get a long way from logical reasoning step by step from principles that you know to be true.

But I admit that I am pushing the boundaries of what I know and that there may be some salient fact or rule of quantum mechanics or the Standard Model in particular, which I wasn't aware of which throws off this analysis.

I take some comfort from the fact that this analysis produces a result that is consistent with what the end result surely should be, but take this analysis with the caveat that I am an educated layman rather than a practicing PhD QCD physicist. I humbly welcome corrections or commentary from anyone who is aware of a flaw in this analysis.

In The Rare Circumstances Where This Scenario Could Happen, The Process That Created The Gluon Would Be Reversed

This is a bit tricky, but I think the best way to work through it is to consider that any gluon came from somewhere.

In Most Scenarios, This Isn't Possible

As Vanadium 50 notes in comment #2, generally, in processes that can give rise to gluons, there are color charged particles out there, either quarks or other gluons, which can emit or absorb a gluon, effectively undoing the process that produced the gluon if no other possibilities exist.

But, there are isolated circumstances when this isn't the case, however, the most notable of which that I can think of is the decay of a Standard Model Higgs boson to a pair of gluons which should make up about 8% of Higgs boson decays. See, e.g., here. But, in that circumstance, the gluons have ample energy with which to form hadrons, since a decaying Higgs boson has approximately 125 GeV of rest mass to convert to gluons. So that doesn't present the problem in the question.

The Only Way This Could Happen Could Basically Reverse Itself

The only scenario that I can come up with, in which gluons are formed in an environment with no other color charged particles in the initial state of the process, would be photoproduction of a gluon pair. This would be a process with two photons as inputs and a gluon and its corresponding anti-gluon with the opposite color charge as outputs, in which the photons have a combined energy of less than about 5 MeV (i.e. the mass-energy of an up quark and an up antiquark at rest, the least massive possible pair of quarks and also much less mass-energy than is necessary to form the least massive possible glueball).

As best I can tell, photoproduction of gluon-antigluon pairs is a thing, even though photons themselves don't interact via the strong force. See, e.g., here.

In that situation, the only possible end state that could result that I can think of, would be for the gluon and the antigluon formed by photoproduction to annihilate back into a pair of photons again. Since there are no other possible end states for the interaction that preserve mass-energy conservation in real particles, this would happen 100% of the time, because there are no other possibilities that conserve the relevant conserved quantities of the Standard Model.

In this situation, the low energy gluon-antigluon pair created by photonproduction are strictly speaking, "on shell" and "real" gluons, and this distinction might matter for some technical reason, but for most practical purposes, gluon pairs created in this way would look very much like virtual particles, in that the photon pair output, matching the photon pair input are virtually impossible (except possibly on a statistical basis or based upon time elapsed perhaps), to distinguish from a process with two photon inputs and two photon outputs that didn't have the intermediate gluon pair state.

Footnote On The Domain Of Applicability Of The Concept Of Confinement

I'd also note that the rule of confinement is not absolute. It is a "gross" rule (I hesitate to use the word macroscopic since it applies at still tiny scales, but perhaps "systems level" would be a better choice of words) that applies at all normal energies in all observable circumstances, but is not true in absolutely all circumstances and does not mean that real isolated gluons don't come into being briefly within hadrons.

One exception to the rule of confinement is that at high enough energies you can have a quark-gluon plasma within which gluons are not confined to a single hadron. But this exception involves high energy gluons that by definition have sufficient mass-energy to hadronize by giving rise to a quark-antiquark pair even if no other color charged particles are available (which, not quite by definition, would always be available in any real world quark-gluon plasma).

Likewise, while the process of hadronization is very, very fast, which means as a practical matter, that it can't be observed by physicists, it also isn't instantaneous. It is at least roughly an order of magnitude longer than the mean lifetime of a top quark (which almost never hadronizes because it generally decays before it can do so). The mean lifetime of a top quark is approximately 5×10⁻²⁵ seconds. For most practical purposes, hadronization in 5×10⁻²⁴ seconds or so is effectively equivalent to instantaneous, but there are qualitative differences between an instantaneous process and one that is very short in duration indeed. Likewise, within hadrons, gluons routinely travel at the speed of light (roughly 3*10^8 meters per second) from one quark to another at a distance on the order of 10^-15 meters. So, that trip characteristically takes something on the order of 3*10^-7 seconds, which is almost as long as the mean lifetime of a muon.

So, while hadronization is generally a very fast process, and happens in a domain where we can't see it, which is basically what "confinement" really means in the context of QCD, "confinement" is a concept that only makes sense at a non-instantaneous level and the principle that a quark or gluon is always confined can't be applied to arbitrarily small units of time and space, or to a completely unlimited range of energies.

Glueballs a.k.a. Gluonium

That leads me into another question, why are glueballs theorized to have specific masses, shouldn't it completely depend on how it's formed, i.e. its original energy amount should be its mass? Does negative energy that virtual gluons may hold play a role in this?

A good analogy to this question is the question of "why can't a planet in orbit around a star have an arbitrary amount of angular momentum?"

The real work in answering this question is done by the definition of the word "orbit", which means a bound state of motion around the barycenter of the system. If the system doesn't have that much energy, it isn't an orbit, it is just to objects passing by each other in the same general vicinity of each other and exerting gravitational forces on each other.

This kind of situation also comes up in the somewhat analogous context of the energy shells of electrons around an atom, to which @Orodruin alludes. But since that is slightly less familiar and concrete, so I won't spell out that example here.

In the case of glueballs, a.k.a. gluonium, the definition that is doing the real work that assures that particular states have particular mass-energies is that glueballs are defined to be "bound states" of more than one gluon, and not just a system in which there are multiple gluons in the same general vicinity of each other. Indeed, depending upon the color charges of the respective gluons that are close to each other, there might not even be any strong force pull potential between the two gluons.

To be a bound state, you need an equilibrium of strong force pull between the bound gluons, which for any particular set of quantum numbers that specify a particular kind of glueball, and for any number of gluons present, has several discrete solutions: a minimal ground state, and additional excited states. At tree level, these masses are a function of just one free parameter, the strong force coupling constant. A system of gluons that doesn't match any of those values is, by definition, not bound state of gluons and not a glueball. It is just a system of two or more gluons in the same general vicinity that are not in a bound state, which doesn't have a special name until you give it one, and isn't a hadron.

The characteristic tendency of these systems to produce discrete bound states is one of the reasons why we call it "quantum mechanics."

The calculation of the masses of the bound states of systems consisting only of glueballs to arbitrary precision beyond tree level necessarily involves consideration of all sorts of virtual particles (and not just virtual gluons but also the same kind of virtual sea particles that are present, for example, in ordinary mesons like the pion and ordinary baryons like the proton and neutron, the exact composition of which would be specified by the parton distribution function(s) of the glueball(s) in question).

But, this isn't anything especially made possible by negative energies or for which virtual particles are more important than they are in any other kind of hadron. Glueballs, like all other "real", "on shell" particles in the Standard Model need to have positive mass-energy in any state which can be observed.

 

[Vanadium 50]

But, there are isolated circumstances when this isn't the case, however, the most notable of which that I can think of is the decay of a Standard Model Higgs boson to a pair of gluons which should make up about 8% of Higgs boson decays

Nope.

The Higgs is a color singlet. The gluons are therefore in a color singlet as well. That means there is a matching gluon for color reconnectiuon. And indeed, you have this reconnection - at the end of the decay chain you have only colorless hadrons.

No exception.

 

[jimi]

So you can't say like hypothetically if there was a lone gluon?

 

[Orodruin]

So you can't say like hypothetically if there was a lone gluon?

No. A lone gluon would not be color neutral.