What If Glueballs Don't Exist (w/ QG relevance)?

[ohwilleke]

One of the fundamental predictions of QCD that has not yet been definitively observed is that there exist bound states of two or three gluons that are color charge neutral. In principle, every property of every excited states of every possible glueball can be determined precisely from first principles using the bare equations QCD and the strong force coupling constant. The first calculations had been completed by 1980 and have only been refined modestly since then.

Glueballs should in principle be unstable but decay in precise and predictable ways and there are a great many of them that would have masses of about 1.4 GeV to 5 GeV.

The trouble is that despite the fact that there is a very well defined target that we are looking for and we have had colliders powerful enough to generate them since at least the LEP experiment, we have yet to make a definitive sighting of a glueball after decades of looking for them.

There are all sorts of plausible reasons why glueballs should be hard to see. While pseudo-scalar mesons (other than the neutral pion and neutral kaon) and vector mesons are well defined entities that neatly fit into their appointed places ordained by a quark theory of hadrons, neutral pions, neutral kaons, scalar mesons and axial vector mesons appear to manifest only as mixtures of different pairs of quarks. There is good reason to think that glueballs may share this property.

On the other hand, no experimental data rules out the possibility that glueballs (or other "QCD exotics" such as hybrids of glueballs and quarks, or "true tetraquarks" as opposed to meson molecules, etc. that are permitted by naive application of the rules of QCD) don't exist in nature, even though they are well defined composite particles with well defined properties in the equations of QCD that we can calculate with some precision using lattice methods (at least to the level of precision with which we know the QCD coupling constant, of a bit less than 1%).

Give that QCD exotics have been so hard to observe, maybe they really don't exist. And, if that is the case, then some fundamental rule of QCD is missing from the Standard Model.

Quite unlike most of the rest of fundamental physics, where there is a rich literature of BSM physics possibilities, and a surprisingly thin (but critical) literature working out the implications of the SM without modification, in the literature of QCD exotics, there is a rich literature of what the SM predicts without modification and very little academic interest in the possibility that the SM must be modified in such a manner that would rule out QCD exotics, despite the fact that this seems much more interesting to me than issues like the strong CP problem (basically a question about why a QCD parameter has a value of zero) that doesn't differ much from the question of why any SM parameter takes its experimentally measured value.

But, what subtle modification to the SM would be necessary to prevent QCD exotics from arising and in particular to rule out glueballs?

I imagine that such a rule might be similar to the OZI rule which states that "any strongly occurring process will be suppressed if its Feynman diagram can be split in two by cutting only internal gluon lines. An explanation of the OZI rule can be seen from the decrease of the coupling constant in QCD with increasing energy (or momentum transfer). For the OZI suppressed channels, the gluons must have high q2 (at least as much as the rest mass energies of the quarks into which they decay) and so the coupling constant will appear small to these gluons." (per the Wikipedia article on the OZI rule).

It might be hiding in plain sight due to an unrecognized feature of the equations governing the strong force, or it might require the addition of a new principle or two.

In addition to being important for its own sake, such an obscure issue in QCD might be relevant to quantum gravity, both because gravity has a resemblance to QCD squared, and because any rule relating to glueballs must be intimately related to the fact that QCD is non-abelian and self-interacting, just like gravity.

For example, a feature of QCD that ruled out glueballs, might also rule out vacuum solutions of the equations of GR as non-physical even though they are permitted by the equations themselves. It might also provide a more principled approach than an ad hoc Killing vector to remove ghost solutions from quantum gravity equations.

Is anyone familiar with any academic literature of BSM modifications of QCD that forbid glueballs or other exotic states (or in the alternative, hypothetical interpretations of SM QCD rules that would have the same effect)? Simple searches of arXiv and Google using combinations of words that I've been able to come up with haven't pinpointed this kind of research, perhaps because I don't know the right buzzwords.

 

[tom.stoer]

I don't think that there is any principle or no-go theorem ruling out the existence of glueballs. Instead the glueballs mix with ordinary resonances such that you cannot tell apart i) the ordinary baryon or meson and ii) the glueball

 

[ohwilleke]

One problem with QCD, however, is that we seem to lack a very principled way of determining how they mix - even though empirically, only certain discrete particular mixtures with well defined properties, rather than a continuous range of mixture proportions are obsrved.

Also, while I agree that there is not any principle or no-go theorem ruling out the existence of glueballs (at least that is widely accepted and known) in QCD, I am wondering what sort of BSM modifications to the SM would be necessary to give rise to such a principle, and what other implications it would have for QCD.

 

[tom.stoer]

One problem with QCD, however, is that we seem to lack a very principled way of determining how they mix

You mix states with identical quantum numbers; I would call that a superselection rule.

rather than a continuous range of mixture proportions are obsrved.

I don't understand what you mean by "continuous range of mixtures".

I am wondering what sort of BSM modifications to the SM would be necessary to give rise to such a principle, and what other implications it would have for QCD.

Why would you like to do that? I don't think that the resulting theory should be called QCD.

 

[nikkkom]

Admittedly, I'm not a particle physicist, I am only a mathematician by my University education. So correct me where I'm wrong.

A linear combination of any number of gluons can't add up to a color singlet state. Therefore, glueball can't be "white" like baryons are.

And QCD doesn't allow colored hadrons.

 

[tom.stoer]

A linear combination of any number of gluons can't add up to a color singlet state. Therefore, glueball can't be "white" like baryons are.

A combination of two gluons (each living in the adjoint rep. "8") can add up to a color singlet:

[tex]8 \otimes 8 = 1 \oplus 8 \oplus 8 \oplus 10 \oplus \overline{10} \oplus 27[/tex]

So there is one color singlet rep "1".

 

[torquil]

Admittedly, I'm not a particle physicist, I am only a mathematician by my University education. So correct me where I'm wrong.

A linear combination of any number of gluons can't add up to a color singlet state. Therefore, glueball can't be "white" like baryons are.

And QCD doesn't allow colored hadrons.

The quantum state of a system of several particles is described by products of single particle states (and possibly linear combinations thereof). The total colour charge is an additive function of the values from each factor in such a product. So, e.g. a bound state consisting of two gluons with colour charges [itex]r\bar{g}[/itex] and [itex]g\bar{r}[/itex], respectively, would be a colour neutral state. Here, r=red, g=green, and a bar is used for the corresponding anti-colour.

 

[ohwilleke]

You mix states with identical quantum numbers; I would call that a superselection rule.

There are lots of boson states with the quantum numbers of a vacuum, since this is shared, for example, by all five of the ground states different forms of quarkonium (uu, dd, ss, cc, bb). There are also hypothetical glueball and tetraquark states with those quantum numbers.

In baryons (and other fermions) and vector mesons and heavier pseudo-scalar mesons, superselection is pretty rigorous and there aren't many opportunities for significant mixing. But, in scalar and axial vector mesons there are lots of combinations that share quantum numbers and hence lots more room for mixing, especially when lighter quarks are involved.

I don't understand what you mean by "continuous range of mixtures".

There are an infinite number of linear combinations of, for example, bound states that share the same quantum numbers with the vacuum, although if you limit the number of states that can contribute to a mixture to some number N (e.g. 3 or 6), and require a single coefficient and sign for any particular bound state incorporated in the mix, the number is finite and merely large.

The number of observed mixed bound states with these quantum numbers, however, is far smaller than the number of states that one might expect to exist even with a fairly low limit on N.

There isn't a consensus rule concerning which combinations mix, and which do not, within the constraint that only bosons with the same quantum numbers mix (which isn't to say that there aren't good faith attempts, for example, a paper today trying to reproduce the observed cc and bb spectrum http://arxiv.org/abs/1409.3205). Yet, clearly, only some of the possibilities actually happen.

Why would you like to do that? I don't think that the resulting theory should be called QCD.

If one is going to look for BSM physics, why not look in the one corner of the SM where experimental results are not infrequently discrepant with theoretical predictions that strive to produce SM results.

For example, a review of four different LHC experiments through the lens of two of the leading operational implementations of QCD revealed that both theories predict substantial polarization in heavy quarkonia production (cc and bb), but this prediction was contradicted in every case with the actual observed behavior being a total absence of polarization, contrary to the theory. http://arxiv.org/abs/1409.2601 When polarization that you expect to see based upon your theoretical calculations doesn't manifest, it is suggestive of the possibility that there is an additional symmetry in the relevant systems that are being analyzed with QCD that has not been recognized. Or, perhaps there is a source of entanglement in these systems that the cancels out the polarization that is underappreciated.

Similarly, while one would naively expect the hadronization of top quarks to be suppressed because the mean lifetime of a top quark is on the order of 10% of the mean time of hadronization, the actual lifetime of a top quark can be longer or shorter than average, and the proportion of top quarks that live longer than the mean hadronization time is great enough that we would have expected to see some of the hundreds of thousands of top quark decays that have been observed in HEP experiments to briefly hadronize, and yet, no one has ever seen that happen ever.

Another problem is how to derive from first principles in the existing QCD equations, the observed spectrum of scalar and axial vector mesons with the properties that we see, even though if the SM is correct, that ought to be possible and even straight forward to accomplish. Of the theoretical approaches to address this issue, some of the older approaches to dealing with QCD phenomena with operational equations that have been abandoned for many other purposes, like the linear sigma models, seem to work better than other models that are more popular for most purposes these days in QCD like lattice QCD and chiral perturbative QCD. Maybe the older models are implicitly including assumptions that aren't widely recognized and aren't carried over into the newer QCD calculation methods worked out from something closer to first principles instead of phenomenologically.

In general, none of the leading approaches to operationalizing QCD work in all circumstances, and worse, it isn't possible to consistently know in advance which approach will most accurately reproduce experimental results in which situations.

Now, this isn't to say that QCD doesn't do a yeoman's work. There are lots of circumstances in which theoretical QCD predictions generated with operationalized approaches to making QCD calculations nail the observed phenomena or at least come pretty close given the limited accuracy of the parameter inputs like the light quark masses and the strong force coupling constant and limited computational power to do with calculations with.

And the circumstances where QCD does work well suggests that the rules of QCD that we have in the SM, so far as they go, are correct or at least correct enough to produce the right answers the vast majority of the time. A QCD with four colors, or another flavor of quark, or materially different strong force coupling constant or strong force coupling constant beta function, for example, would destroy the functionality of QCD in the cases where it does work.

But, it wouldn't be at all surprising to me if the underwhelming performance of theoretical QCD predictions is due not just to the fact that the math is harder for QCD than electroweak physics because QCD is non-abelian and because confinement makes it impossible to do direct measurements of a kind that are available in QED. It could also be due to the fact that there may be a principle or two or three in the SM articulation of QCD that are missing or not stated precisely correctly in the SM.

Maybe there are missing rules that have the effect of prohibiting or dramatically suppressing phenomena like top quark hadrons, glueballs, tetraquarks, pentaquarks, or quarkonia polarization to extents that the SM theoretical predictions applied in a straight forward way, no matter how accurately they are done, gets wrong.

Then again, it could be that theorists making QCD predictions in some of these circumstances are skipping important considerations in their approximations.

For example, it is notable that like the decay channels suppressed by the OZI rule (which arises from first principles because the decay channels it suppresses have higher q^2 than those it does not, effectively reducing the strength of the strong force coupling constant in those channels), tetraquarks and pentaquarks have more quarks than the usual strong force interactions, which may increase the q^2 of the interaction which may lead to the running of the strong force coupling constant to surprisingly low values that conventional theorists aren't properly evaluating.

And, similarly, maybe people predicting the properties of glueballs are failing to account for the mass that gluons acquire dynamically in the infrared regime (on the order of 500-750 MeV which is about midway between the mass of a strange quark and a charm quark http://iopscience.iop.org/0954-3899/38/4/045003;jsessionid=B5DC138A8397721A1EC4A8407012A01F.c2) which may drive up q^2 and cause the strong force coupling constant to run to lower values which thereby suppress those interactions.

Top quark hadrons, similarly, would have a very high q^2 which, in addition to their short mean lifetime might also be driving down the strong force coupling constant which suppressed hadron formation in top quarks in a second and independent way from its short mean lifetime relative to the mean hadronization time.

Perhaps many of the discrepancies between theory and experiment could be resolved by more rigorously incorporating a more general version of the OZI rule, derived from QCD equation first principles, into a much wider array of scenarios for which one wants to make theoretical QCD predictions.

For that matter, maybe a generalized OZI rule could be the key to drawing the line between the hypothetically infinite number of mixing combinations of composite particles with the same quantum numbers, and the finite number actually observed, by suppressing higher N combinations which have higher q^2 and hence a lower effective strong force coupling, even though usually, you analyze QCD interactions in a manner that holds the running of the strong force coupling constant at a single value for every possible loop of the decay channels that you are trying to predict.

Similarly, maybe the lack of polarization in heavy quarkonia is because the theoretically predicted polarization arises mostly from higher q^2 loops in the calculation that are suppressed relative to lower q^2 loops that exhibit less polarization. I certainly don't have enough of a grasp of the math in those calculations to know, but heuristically, it would make sense.

The other big bonus prize to fixing the last not so few kinks in making accurate predictions with QCD, is that if you managed that, as I alluded to in the first place, this might provide some really useful insights into quantum gravity, with the reality check of experiments that can be done with the acreage and power demands of a small city on Earth, rather than requiring galactic or larger extreme environments to keep theorists on the right track. Any new insight into how the non-abelian mathematics of QCD work are very likely to also provide insight into the non-abelian mathematics of QG.

For example, in the QG context, the kind of generalized OZI rule I've pondered in this comment for QCD could provide a natural mechanism by which QG exhibits scale dependent behavior, acting one way at the Planck scale, another at a high energy atomic system scale, another at a solar system scale, another at a galactic scale, another at a galactic cluster scale, and another still at a whole universe or Big Bang scale.

 

[tom.stoer]

I still don't see how you can talk about a missing rule but still call the theory QCD.

QCD is nothing else but an SU(3) gauge theory with three quark generations which you have to quantize and to solve. So on that fundamental level I don't see how to introduce a new rule w/o making it a new theory.

I agree that there may be rules on the phenomenological level which should in principle follow from QCD on the fundamental level. And of course there could be some phenomenological rules which we have overlooked so far and which suppress glueballs. Then the approach must be to check whether the experiments tell us that there are indeed no glueballs (up to now they don't say anything like that, afaik) and to derive this suppresion theoretically (just like chiral symmetry breaking, confinement, ...).

Theoretically I don't see how glueballs could be suppressed. Afaik they do exist in pure-gluon QCD on the lattice. Now it would be interesting to go beyond the quenched approximation and study if and how the fermion determinant kills these glueballs. Afaik the determinant never produced new effects but just contributes some smaller corrections (which are of course relevant when calculating the mass spectrum etc.).

Now the question is what you are really looking for: experiments proving the existence of glueballs? experiments disproving the existence of glueballs? a no-go theorem for glueballs based on QCD? something beyond the SM?

Btw.: there are many non-trivial (and non-perturbative) results from QCD which are directly related to its non-abelian nature; but I haven't seen any hint regarding QG. Even if QG is formulated as a gauge theory (e.g. using Ashtekar variables known from LQG) besides the local SU(N) gauge invariance the mathematical structure of QG is totally different from QCD.

 

[ohwilleke]

I still don't see how you can talk about a missing rule but still call the theory QCD.

I agree that there may be rules on the phenomenological level which should in principle follow from QCD on the fundamental level. And of course there could be some phenomenological rules which we have overlooked so far and which suppress glueballs. Then the approach must be to check whether the experiments tell us that there are indeed no glueballs (up to now they don't say anything like that, afaik) and to derive this suppresion theoretically (just like chiral symmetry breaking, confinement, ...).

Theoretically I don't see how glueballs could be suppressed. Afaik they do exist in pure-gluon QCD on the lattice. Now it would be interesting to go beyond the quenched approximation and study if and how the fermion determinant kills these glueballs. Afaik the determinant never produced new effects but just contributes some smaller corrections (which are of course relevant when calculating the mass spectrum etc.).

Now the question is what you are really looking for: experiments proving the existence of glueballs? experiments disproving the existence of glueballs? a no-go theorem for glueballs based on QCD? something beyond the SM?

Btw.: there are many non-trivial (and non-perturbative) results from QCD which are directly related to its non-abelian nature; but I haven't seen any hint regarding QG. Even if QG is formulated as a gauge theory (e.g. using Ashtekar variables known from LQG) besides the local SU(N) gauge invariance the mathematical structure of QG is totally different from QCD.

First, yes, it would be a modification of QCD - i.e. BSM physics, a new theory, if you will. I am not saying that the existing SM QCD rules give rise to this conclusion and have no reason to think that they do (although, in principle, it could be that there is simply an error in how SM QCD is approximated that has this effect).

But, it is BSM physics only in the tamest of "friendly amendment" senses. More specifically, it would be a proposal that would conclude that SM QCD was not so much wrong as incomplete.

Probably 70%-80% of the HEP-phenomenology and HEP-theory papers at arXiv propose BSM physics, but surprisingly few of them address New Physics particular to the QCD sector, and of those that have any experimental motivation, most are driven by 2-3 sigma anomalies that are probably flukes in the electroweak or Higgs sector. Yet, the overwhelming majority of experimental results that are at odds with SM theory predictions and could motivate New Physics or any kind of SM modification arise in QCD experiments. So, theorists should really spend more time pondering if those many discrepancies could be resolved with BSM physics in the QCD sector, although they'd have to be subtle so as not to disturb the apple cart of QCD physics that does work.

The point is that we've had a very clear glueball target to look for in experiments for forty years and a lot of those experiments haven't found naive realizations of the quark-less hadrons that the theory predicts. Certainly, this could be because glueballs are just hard to find. It took decades to find the Higgs boson too. But, it could be because QCD fails to describe reality in some important respect (i.e. that QCD is wrong) because SM QCD fails to include some rule that Nature follows and people doing SM QCD equations do not.

A comparison to the Higgs boson case is informative. Every aspect of the Higgs boson, except its mass, was predicted precisely by the SM. Similarly, every aspect of glueballs, including their mass is predicted precisely by the SM.

But, in the case of the Higgs boson, we didn't see it until we have powerful enough experiments and then when we did see it, two years ago, it has acted in precisely the way that theorists had told us that it would 40 years earlier giving rise to an unambiguous discovery of it.

In contrast, we have had experiments that are theoretically powerful enough to unambiguously disclose the naive pure glueballs that whose properties have been known for decades for a couple of decades at least, and they haven't made an unambiguous appearance. Instead, we've seen dozens of resonances that can't be explained with the simple quark content and spin-alignment rules that complete describe all of the vector mesons and pseudo-scalar mesons (and all of their excited states) except the neutral pion and the neutral kaon, and we have no rule in SM QCD that tells us how to predict those resonances from first principles by applying the rules that we can use naively to predict the existence of the pseudo-scalar and vector mesons from possible combinations of one of five hadronizing quark flavors and one of two possible sets of spin alignments, and which can also be used naively to predict the existence of pretty much every observed baryon, whether or not it is in an excited state. Now, QCD doesn't say that any of the mesons that we see violate the rules of QCD, but it also doesn't tell us which mixings will happen and which will not, in a way that explains why we see most of the hadrons that are naively allowed by QCD, but do not definitively see lots of other "exotic hadrons" that QCD as it exists in the SM does allow. SM QCD does not provide clear guidance regarding which of the possible mixings considering superselection alone actually happen and which either don't happen at all or are suppressed.

So SM QCD in that respect seems to be broken. It also seems to be broken in other respects. It could be that it is really correct and that its seeming failures are really due to user error by the entire community of QCD theorists. But, the possibility that SM QCD is broken because it allows for possibilities that aren't produced in Nature and doesn't tell us why we don't see them in Nature (like glueball, tetraquarks, pentaquarks and merely suppressed by a short mean lifetime top quark hadrons, and polarization of certain neutron streams) is very real. We don't have 5 sigma confirmation that they can't exist; but we have decades of looking for them in experiments that should be powerful enough to reveal them without every observing one at even a 3 sigma level despite a concerted effort to look for them with experiments specifically tailored to that purpose.

Given that reality, it is worth giving serious thought to what changes to SM QCD would cause QCD to either rule out, or to suppress the frequency of results that QCD permits, but that we don't see.

Thus, I'm asking readers to start with an assumption: suppose that even though SM QCD equations permit glueballs, that in Nature, glueballs either don't exist in either pure form or mixed form, or are so highly suppressed that we can never hope to see them (a bit like baryon and lepton number that the SM violates only in the exceedingly extreme sphaeleron solution). Then, I am asking readers to say, "how could you modify the SM to produce that result?"

If a proposal worked, it would be incorporated into SM QCD even though it isn't part of it now. If a proposal didn't work, then it would go to the obscure part of the scientific literature where plausible theories that nonetheless turn out to be wrong like epicycles and aether and SU(5) GUT theories live.

I would compare the possibility to the Standard Model extension that added neutrino mass. Certainly, the original SM provided that neutrinos has a zero mass and didn't oscillate. Then Pontecorvo came along (before there was experimental evidence to back up the possibility) and said, what if I tweaked the Standard Model to have massive neutrinos who oscillate between different mass states. Then, people did experiments and found that Pontecorvo's suggestion could explain those experiments. When the idea that neutrinos have mass and oscillate between different mass states become widely accepted, it came to be part of the group of concepts that were considered to be "Standard Model physics" rather than "New Physics", even though even today there isn't really a true consensus about exactly which formal mechanism best describes neutrino mass (the Majorana or Dirac mass debate). For example, people include the three neutrino mass state masses and the four parameters of the PMNS matrix as seven of the experimentally determined parameters of the SM these days.

All but the most pedantic people don't make a fuss about calling the SM with massive neutrinos by some other name like the "Revised Standard Model", even though they would have a point. In the same way, QCD with an additional rule or two would be "Revised QCD", but if these modifications ended up working out, people would start calling it just plain "QCD" after a while.

I use the phrase "Quantum Chromodynamics" which QCD abbreviates, simply to refer to the entire universe of theories that describe how quarks and gluons have color charge that causes them to interact in a quantum mechanical way with a coupling strength determined by the strong force coupling constant. This core has lots of collateral assumptions built into it. It assumes Lorentz invariance and Minkowski space. It assumes that the gluon propogator follows basically the same rules as the photon propogator except for the fact that gluons have color charge. It can be formulated with arbitrary integer numbers of flavors that can be fitted to experiments. It assumes CPT invariance with color charge being flipped in a way analogous to electric charge being flipped between matter and anti-matter. It assumes that baryon number is conserved.

If we discovered some day, that B-L rather than B by itself is a conserved quantum number and changed that rule, or added a rule that the number of particles produced in the decay of some hadron was equal to some sum of quantum numbers mod 3, or what have you, it would still be a BSM version of QCD, because it would still be a set of rules explaining the strong force.

Similarly, when they first tried to put the weak force into the SM, they tried a version where the weak force coupled to both left parity and right parity particles. It turned out that another rule (that the weak force couples only to left parity particles and right parity anti-particles) was needed to match reality, so that rule became part of the SM. You could have formulated a very similar gauge theory without that rule, and they tried that for a while, but it had to be tweaked.

Bottom line:

Naively, it is very easy to describe glueballs in paper using SM QCD and very hard to produce what is predicted in real world experiments, and when it comes down to brass tacks, no scientist in the world today can very accurately tell us from first principles SM QCD calculations why this is the case.

But, I have complete faith that it is possible for us to come up with a theory very much like SM QCD that would make it possible to do that, and that might very well have as one of its conclusions that glueballs don't actually exist at all, and that everything that we observe in Nature can be described without resort to glueballs.

Given that possibility, it is worth thinking about what kind of rules would do that.

I suspect that one possibility might look something like one or more generalized OZI rules.

I further suspect that rules like these might flow at a more fundamental level from a change in the step at which we evaluate q^2 and the manner in which we do so, when we are carrying out QCD equations that require us to applying the fact that SM constants run with the energy scale of the interaction in the Standard Model to a particular experimental situation that we are trying to make a theoretical prediction for.

In other words, I suspect that the operational rules we need to add to implement QCD mostly flow from the fact that there is some subtle difference between the way that physicists are currently renormalizing to solve QCD problems, and the way that they should renormalize when solving QCD problems if they are to reproduce what we see experimentally.

If that is indeed the problem, I'm not sure that fixing the way that the renormalization principle is applied in practice to concrete situations from what is standard practice today is such a core element of what it means for a theory to be QCD that it really merits giving the theory a new name. The newspaper report on what the scientist who gets a Nobel prize for figuring it out will say is that the scientist fixed a mistake made by Feynman and his peers in how to renormalize to solve SM QCD equations and by correctly redefining how to evaluate q^2 for purposes of renormalizing.

Of course, I'd also welcome other ideas regarding possible BSM reasons why first principles QCD fails to consistently make accurate predictions (or any predictions at all) regarding certain kinds of experimental outcomes.

 

[arivero]

A combination of two gluons (each living in the adjoint rep. "8") can add up to a color singlet:

[tex]8 \otimes 8 = 1 \oplus 8 \oplus 8 \oplus 10 \oplus \overline{10} \oplus 27[/tex]

So there is one color singlet rep "1".

Now I think about... is this true of the "gluinoball" too, with a pair of gluinos? And of course a "gluogluino ball", of spin 1/2.

 

[The_Duck]

The first calculations had been completed by 1980 and have only been refined modestly since then.

The calculations you refer to are very approximate. They completely neglected the existence of quarks. This makes the problem simpler in a bunch of ways: glueballs are then stable, and don't mix with ##q \bar q## states. But it's not going to give you precise predictions, because glueballs are actually resonances and should mix with lots of ##q \bar q## states. While in principle lattice QCD can handle these complications, incorporating them properly requires more computational power than we have even now.

there is a very well defined target

Not really, because of the above. We don't have precise predictions, so we don't know exactly what the mixings and decay patterns of glueballs (or rather, the mixed states with glueball components) should be.

One problem with QCD, however, is that we seem to lack a very principled way of determining how they mix - even though empirically, only certain discrete particular mixtures with well defined properties, rather than a continuous range of mixture proportions are obsrved.

Mixings can be calculated with lattice QCD in principle, but in practice it is quite hard to do with our finite computational resources. See this paper for an example calculation of the mixing between the ##\eta## and the ##\eta'##.

A comparison to the Higgs boson case is informative. Every aspect of the Higgs boson, except its mass, was predicted precisely by the SM. Similarly, every aspect of glueballs, including their mass is predicted precisely by the SM.

The electroweak sector is *so much easier* though! Everything is weakly interacting, perturbation theory gives good results, there are only a few states, the Higgs resonance has a vanishingly small width, etc. In the low energy strongly interacting sector perturbation theory is useless, there are dozens of states, many of them are very wide, etc.

Witness all the uncertainty evidenced in this PDG mini-review not only about glueballs but about a number of hard-to-pin-down scalar resonances at low energies.

In other words, I suspect that the operational rules we need to add to implement QCD mostly flow from the fact that there is some subtle difference between the way that physicists are currently renormalizing to solve QCD problems, and the way that they should renormalize when solving QCD problems if they are to reproduce what we see experimentally.

I think renormalization is better understood than you give it credit for here. I don't think there's room for us to be making a fundamental mistake in how to renormalize QCD.

--

Finally, I think it's going to be very hard to modify the strong interaction and not violate existing experimental constraints. The reason all speculative BSM research focuses on heavy/weakly interacting is that the existing constraints are pretty tight.

 

[tom.stoer]

Now I think about... is this true of the "gluinoball" too, with a pair of gluinos? And of course a "gluogluino ball", of spin 1/2.

Algebraic structure, representations, multiplets, ... are identical; but this doesn't tell you anything regarding spin, masses, ...

 

[tom.stoer]

theorists should really spend more time pondering if those many discrepancies could be resolved with BSM physics in the QCD sector

I don't agree. The IR sector of QCD is still purely understood (confinement, chiral symmetry breaking, nucleon spin, ...) Therefore my conclusion is that we first have to understand QCD before going beyond QCD.

it could be because QCD fails to describe reality in some important respect (i.e. that QCD is wrong)

Could be, but I don't think that we have much experimental support for this guess.

we have had experiments that are theoretically powerful enough to unambiguously disclose the naive pure glueballs that whose properties have been known for decades for a couple of decades at least, and they haven't made an unambiguous appearance

As said, this seems to be due to the fact that pure glueballs mix with other states in nature.

we have no rule in SM QCD that tells us how to predict those resonances from first principles

Look at QED. Can you derive the properties of high-Tc superconductors (of simply water) from first principles? I bet you can't.

SM QCD does not provide clear guidance regarding which of the possible mixings considering superselection alone actually happen and which either don't happen at all or are suppressed

As said: the IR sector of QCD is still purely understood.

SM QCD in that respect seems to be broken

I can't see any experimental evidence for this statement.

... why first principles QCD fails to consistently make accurate predictions (or any predictions at all) regarding certain kinds of experimental outcomes.

Simply b/c the equations are very hard to solve ;-)

I draw very different conclusion from the state of affairs. Whereas your conclusion is that SM QCD itself is incomplete in some sense, mine is that our understanding of SM QCD is still incomplete.

 

[Haelfix]

It would be very difficult to change details (spectrum/decay branches etc) of the glueball sector of QCD and not hit very strong experimental constraints.

At the very least it would mean that you don't believe in lattice QCD which has calculated several pertinent features of that spectrum already. Also you would have to explicitly alter the symmetry group of pure QCD by hand, to eg suppress/enhance various operators that would normally be there by gauge invariance and the Gellman principle.

 

[nikkkom]

The quantum state of a system of several particles is described by products of single particle states (and possibly linear combinations thereof). The total colour charge is an additive function of the values from each factor in such a product. So, e.g. a bound state consisting of two gluons with colour charges [itex]r\bar{g}[/itex] and [itex]g\bar{r}[/itex], respectively, would be a colour neutral state.

Such a particle would be analogous to a meson. It would have no color charge. Such a state would mix with any flavorless meson, such as J/ψ (charmonium), where we have quark-antiquark pair with new zero color charge. So, in some sense we already "have seen" this kind of glueball - J/ψ must be able to annihilate to it.

I'm saying that _baryon-like_ glueball, one with non-zero color, but with [itex]r\bar{r}[/itex]+[itex]g\bar{g}[/itex]+[itex]b\bar{b}[/itex] color ("white"), is impossible.

 

[arivero]

I'm saying that _baryon-like_ glueball, one with non-zero color, but with [itex]r\bar{r}[/itex]+[itex]g\bar{g}[/itex]+[itex]b\bar{b}[/itex] color ("white"), is impossible.

You need to clarify that do you mean by "baryon-like". If you only mean "Not using anticolor", then already a pair of gluons do the trick, as tom.stoer mentioned. If you want three gluons, again it follows from the product that it is possible, because

8 x 8 x 8 = (8 x 8) x 8 = (1 + 8 +8 + 10 + 10 +27) x 8 = (1 x 8) + (8 x 8) + (8 x 8) + (10 x 8 ) + -- =
= (8) + ( 1 + 8 +8 + 10 + 10 +27) + (1 + 8 +8 + 10 + 10 +27) +...

So you see that there are white singlets in the expansion.