A Bridge Too Far - Some Tetraquarks Are Impossible

QCD Qualitatively Permits Composite Particles With More Than Three Quarks (Background)

In Quantum Chromodynamics (QCD) (which is widely believed to be a complete theory of the strong force, although calculations with it can only be done in approximate form) composite particles called hadrons made of two, three, four, five, sex or more quarks are not qualitatively ruled out.

In practice, almost all composite particles produced, even in very high energy experiments, involve two quark composite particles called mesons, or three quark composite particles called baryons. (The only form of "free" quark observed outside a composite particle is the top quark which generally decays via the weak force before it has time to form any kind of composite particle.)

There are quite a few composite particle resonances that are hard to characterize in a simple constituent quark model including only mesons and baryons, however, and a considerable share of research in experimental QCD is devoted to understanding these anomalous resonances.

For example, there is not a consensus understanding regarding how scalar and axial vector mesons arise and what the nature of their internal structure consists of within the QCD community. There is also a continued failure to experiment to disclose any really definitive examples of "glueballs" which are predicted to exist by QCD, despite decades of searching for them.

A pair of two quark mesons can develop a bond similar to the bond between atoms in a molecule to each other, which is called a "meson molecule". The resonances most convincingly characterized as meson molecules include X(3872), Z_b(10610) and Z_b(10650) in the bottomonium sector, and Z_c(3900) (discovered at the BES III experiment in 2013) and Z_c(4020/4025) in the charmonium sector. 

There have been only a few definitive experimental observations of true tetraquarks (as opposed to mere "meson molecules") which have a strong force bond that connects each of the four quarks to each other: the Z_c(4430) confirmed to be a tetraquark the LHCb experiment in 2014 after being first observed by the Belle collaboration in 2007, is the most convincing candidate. This tetraquark observations does seem to be the real deal.

But, it and other strong tetraquark candidates such as X(4274), X(4500) and X(4700) announced by the LHCb in June of 2016 involve at least some lighter quarks. (The DZero experiment at Fermilab announced that the X(5568) resonance is also a tetraquark in February of 2016, but this finding is in doubt because it has not been confirmed by the LHCb even though it should have been visible at the LHCb by now given the amount of data that the LHCb experiment has collected if it is real.)

Experimental hints of pentaquarks have remained elusively experimentally insignificant for decades, from 1976 through the present, although five quark meson-baryon molecules have been observed, probably including some of the spin combinations of resonances known as P_c(4380)⁺ and P_c(4450)⁺ seen as the LHCb experiment, including particularly the spin 3/2 version of the heavier of the two resonances. The most promising candidate for a pentaquark to date is a spin 5/2 version of the hadron called P_c(4380)⁺, observed in 2015, but it has only been observed by one experiment in one production channel, so it isn't impossible to rule out some sort of seriously systemic error.

But, just as top quark hadrons aren't qualitatively ruled out by QCD even though they are quantitatively incapable of forming bound states (or at a minimum, extremely unlikely to form bound states, which if formed would be shorter lived than any other kind of hadron, even at extremely high energies such as those of the current run of the LHC), the fact that QCD qualitatively allows tetraquarks or higher order composite QCD particles does not mean that they are quantitatively possible.

Four Charm Quark Tetraquarks And Four Bottom Quark Tetraquarks Are Impossible; But Two Charm Quark and Two Bottom Quark Tetraquarks Might Be Possible

A rigorous but not absolutely comprehensive set of QCD calculations suggest that composite particles made of four charm quarks, and composite particles made of four bottom quarks (i.e. fully-heavy tetraquarks) are "unbound". In other words, the strong force mediated by gluons isn't strong enough to hold them together confined in a composite particle, although a bound composite particle made of two charm quarks and two bottom quarks might just barely be possible.

In other words, unless something subtle but important has been left out of the calculation, these fully-heavy tetraquarks are theoretically impossible.

The study hedges that it might have missed a subtle point because there have been some experimental observations which could hint at the existence of fully heavy tetraquarks, although these data points are very tentative and don't amount to a confirmed observation of them.

Generally, a particle is not considered discovered by particle physicists until we have five sigma evidence for it in an experiment, which has not yet happened in the case of any fully heavy tetraquarks.

The abstract of the paper and it citation are as follows:

Multiquark states have been advocated to explain recent experimental data in the heavy-light sector, and there are already speculations about multiquarks containing only heavy quarks and antiquarks. With a rigorous treatment of the four-body problem in current quark models, full-charm (ccc¯c¯) and full-beauty (bbb¯b¯) tetraquarks are found to be unbound. Thus their stability should rely on more subtle effects that are not included in the simple picture of constituent quarks. The case of (bcb¯c¯) might be more favorable if the naive color-additive model of confinement is replaced by a string-inspired interaction.

Jean-Marc Richard, et al., "String dynamics and metastability of fully-heavy tetraquarks" (March 2, 2017).

Analysis And Other Likely Implications Of The Study

Naively, this is a pretty surprising result.

In theory, because gluons are massless, like photons (although they appear to acquire mass dynamically), so they should have an infinite range. And, if gluons had an infinite range, adding more quarks to the mix, even heavy ones, wouldn't obviously overcome the ability of the strong force to bind them. But, given that in practice the strong force is a short range force, because gluons, like quarks, are always bound into hadrons (so "free gluons" are not observed), this is somewhat less surprising.

The reasons that the phenomena of confinement arises are theoretically rich, but heuristically, it has a lot to do with the fact that the strong force gets stronger with distance and energy scale, before it gets weaker again. At short ranges, quarks and gluons are "asymptotically free" (although whether the strength of the strong force trends all of the way down to zero (a "trivial infrared fixed point") or instead to a low but non-zero strength (a "non-trivial infrared fixed point"), in the limit as it approaches zero distance/momentum transfer, is an open question in QCD.

It is likely that the result from this most recent study would generalize to higher order heavy pentaquarks and hexaquarks, etc. as well. So, while QCD may allow for hadrons other than mesons and baryons, the number of composite particles that QCD allows with more than three constituent quarks is finite and quite possibly rather small. The heaviest possible tetraquark probably has a mass on the order of 16 GeV or less, if the result from this most recent study is correct, rather than the mass in excess of 22 GeV that we would expect for a four bottom quark tetraquark.

Indeed, the threshold for pentaquarks and hexaquarks would very plausibly arise with a less massive set of quarks than in the tetraquark case, because there are more quarks involved overall.

Similarly, while QCD allows for "excited states" of even its more ordinary hadrons, at some point there is so much energy in the system that it too becomes unbound as such highly energetic quarks form a quark-gluon plasma instead.

Thus, it should be theoretically possible to make a finite list of all possible composite particles bound by the strong force including all excited states, at some point (i.e. in a matter or years or a decade, not many decades or centuries), from first principles calculations.

The Relatively Narrow Hadron Mass Spectrum

The spectrum of composite particles that are not mere hadron molecules is crowded into quite a narrow mass range of about two orders of magnitude, compared to the fundamental particles whose masses span at least eleven orders of magnitude (from the lightest neutrino to the top quark). The greater range is both because the top quark and massive fundamental bosons are very heavy, and because the neutrinos, the electron, and the light quarks are very light. 

The lightest hadron is roughly 0.14 GeV and the heaviest observed hadron is about 11 GeV, a span of two orders of magnitude. The heaviest theoretically possible tetraquark would be about 22 GeV, and the heaviest theoretically possible pentaquark would be about 27 GeV (193 times as heavy as the lightest one, but still much less than the weak force bosons, the Higgs boson and the top quark). If the result of this most recent paper is correct and can be extrapolated more broadly, the heaviest possible hadron of any kind might be 16 GeV (115 times as heavy as the lighest one).

* Observed mesons range from 0.13957 GeV (the charged pion) to 11.02 GeV (unclassified forms of bottomonium) (which is close to the theoretical maximum for a meson). The heaviest observed meson without bottom quarks has a mass of under 4.7 GeV, and the theoretical maximum mass of a meson without bottom quarks is probably under 5 GeV.

* Observed baryons range from 0.938 GeV (the proton) to resonances (not all fully classified according to the properties and structure) of up to 5.946 GeV (e.g. the bottom Xi), although heavier baryon resonances up to about 15-16 GeV are theoretically possible. The heaviest theoretically possible baryon without bottom quarks would have a mass of under 8 GeV.

* As noted above, the heaviest confirmed or unconfirmed potential exotic hadron resonance observed is less than 5.6 GeV, even though the theoretical maximum is about 16 GeV for tetraquarks if the result from the most recent study is correct and about 22 GeV for tetraquarks if it is incorrect, with the theoretical maximum for pentaquarks and other exotic quarks being even higher. The heaviest possible tetraquark without bottom quarks if this result is correct would be about 10 GeV. 

* The lightest possible tetraquark would hinge on the interpretation given to some scalar meson resonances, some of which are interpreted by some physicists as tetraquarks and some of which has masses as low as 0.5 GeV, although there is no consensus on this point, the lightest really solid candidate has a mass of 3.9 GeV.

* Hypothetical glueballs are predicted to fall in the mass range from 1 to 5 GeV.

Experimental Implications For Hadron Physics

One of the collateral consequences of this narrow theoretically possible mass range is that even a much more powerful collider than the LHC would not be expected to discover many new hadrons simply because it is more energetic. And, the fact that we have built the LHC and created collisions are far more powerful than necessary to create the heaviest hadrons QCD predicts that they should be, without seeing any hadron resonances heavier than QCD predicts that they should be, also confirms that our model appears to be valid over a very great range of validity.

The challenge involved in creating and observing new hadrons largely involves more clever designs for colliders and detectors (e.g. in the GlueX experiment at Jefferson Labs) rather than more raw power.

Unless one is chasing the chimera of a T meson or top eta meson or theta meson (the names for hypothetical hadrons that include a top quark), more power, per se, isn't particularly helpful and can even be a problem, because it creates more noise which makes it harder to distinguish distinct hadron resonances from each other from the resulting jumble.

When it comes to hadron physics we need better experiments, not necessarily bigger ones.

QCD Still Works

In other QCD news, a retrospective analysis of data from one of the Tevatron experiments (which finished collecting data years ago) confirms that the predictions of QCD are matched in detail by experiment in measurements of subset of photons emitted from proton-proton collisions, which are not a kind of measurement that was used to devise QCD in the first place and which involves a highly complex set of underlying calculations.

So, far all its stumbles, for example, in describing some of the more exotic parts of the hadron spectrum, QCD has to be very close to a true descriptions of reality, even if the way that it is operationalized right now is not quite perfect and stumbles now and then.

The abstract and paper are as follows:

A measurement of the inclusive production cross section of isolated prompt photons in proton-antiproton collisions at center-of-mass energy s√=1.96TeV is presented. The results are obtained using the full Run II data sample collected with the Collider Detector at the Fermilab Tevatron, which corresponds to an integrated luminosity of 9.5fb−1. The cross section is measured as a function of photon transverse energy, EγT, in the range 30<EγT<500GeV and in the pseudorapidity region |ηγ|<1.0. The results are compared with predictions from parton-shower Monte Carlo models at leading order in quantum chromodynamics (QCD) and from next-to-leading order perturbative QCD calculations. The latter show good agreement with the measured cross section.

CDF Collaboration, "Measurement of the inclusive-isolated prompt-photon cross section in pp¯ collisions using the full CDF data set" (March 2, 2017).

A Footnote On Author Credits In Article Citations

I heartily endorse the practice of crediting papers in the particle physics field and other fields where stable collaborations of large numbers of people contribute to a corporate collaboration author, such as in the paper above, possibly with a corresponding author who writes up the paper and takes responsibility for it even though others were critical in doing the work, as opposed to the older practice of publishing papers with hundreds of authors who often didn't read the paper (even if they were given an opportunity to) and made a more generalized contribution to the collaboration.

Better still is the rare but worthwhile practice which I have seen in only a handful of papers, of stating in the abstract or introduction to the paper which author was the primary contributor to which part of the total paper.