Friday, January 17, 2014

Meson Molecules (aka Deusons) Have Been Discovered, But Not Tetraquarks


Composite particles made out of quark and/or antiquarks and bound together by gluons are called hadrons.

There are three possible color charges for quarks (called, e.g., red, green and blue), and three possible color charges for antiquarks (called, e.g., antired, antigreen and antiblue).  Gluons have two color charges (a quark color and an antiquark color), or a linear combination of such couplings (there are actually only eight rather than nine possible color combinations for gluons).

All hadrons are color neutral by virtue of having one quark with of each of the three colors or each of the three anticolors, or by virtue of having a quark with one of the three colors and an antiquark with the corresponding anticolor.

The need for all composite particles to be color charge neutral has a number of corollaries.  One is that all quarks are "confined" in a hadron (subject to the exception of the top quark which decays essentially the instant it is formed into a lighter down type quark, almost always a bottom quark).  The second is that all hadrons have integer electric charge (mesons can have a charge of -1, 0 or +1, baryons can have a charge of -2, -1, 0, +1 or +2).

Two kinds of hadrons have been observed experimentally.

Two quark particles called mesons are made out of a quark and an antiquark (in which the antiquark has the antiquark color charge corresponding the the color charge of the quark in the meson) bound directly by gluons and have spins of 0 or 1.  Due to the requirement of color charge neutrality, mesons always have an equal number of quarks and antiquarks, mesons always have a baryon number of zero.

 Three quark particles called baryons are made out of three quarks, (one with each of the three color charges, or three antiquarks, one with each of the three antiquark color charges) bound directly by gluons and have spins of 1/2 or 3/2.  Due to the requirement of color charge neutrality, baryons are always composed of entirely of quarks and have a baryon number of 1, or are composite entirely of antiquarks and have a baryon number of -1.

There are a finite number of possible meson and baryon  ground states, although this is complicated a bit by the fact that some neutral hadrons appear only in linear combinations of each other, and by the fact that hadrons can have "excited states" with the same quark content but higher masses that the ground state for a particular kind of meson or baryon. The vast majority of observed composite particles fit neatly into one of these boxes.

All but a couple of hadrons (the stable proton and the metastable neutron with a mean lifetime of 880 seconds in a free state) are ephemeral, with lifetimes of 10-8 seconds or less.

The stable baryons, protons and neutrons respectively, of course, in turn bind together into atomic nuclei which are held together by a nuclear binding force. This nuclear binding force is derivative of the strong force that holds hadrons together with gluons which use a meson called the pion (the lighest of the mesons which is made only of up and/or down quarks) to carry the force between baryons in the nucleus. Each atom in nature has one electron associated with it for each proton in the nucleus in its unionized state. Atoms, in turn, are often bound to each other in molecules via the electromagnetic forces generated by the protons and electrons in the various atoms. The details of these interactions largely flow from the characteristic way that a particular number of electrons arrange themselves around an atom with the corresponding number of protons.

Quantum chromodynamics (QCD), the part of the Standard Model that explains the strong force that confines quarks together into hadrons, allows for a number of composite particles bound directly by gluons that have not yet been experimentally observed and are hence called "exotic." In principle, QCD allows for the formation of composite particles from any color charge neutral combination of quarks and gluons, subject to limitations that arise because the strong force is a short range force.

Theoretical analysis and experimental searches for exotic composite particles bound by the strong force have focused on three possibilities: Glueballs with zero quarks, tetraquarks made of four quarks, and pentaquarks made of five quarks, in each case, bound to each other directly by gluons and having a neutral color charge.

A more comprehensive review of "unconventional" hadrons can be foundhere.  It adds two more categories to my list.

First, mesons with JPC quantum numbers* not allowed by the constituent quark model (which is not itself strictly a part of QCD proper). Examples of this include any mesons with spins other than 0 or 1, and electrically neutral mesons with JPC quantum numbers of 0--, 0+-, and 1-+.

There are by my calculations, in the ground state in the constituent quark model, 5 kinds of possible baryons with just one quark flavor (all spin 3/2), 80 kinds of baryons with two quark flavors (40 possible sets of constituent quarks with spin 1/2 and spin 3/2 versions of each) and 240 kinds of baryons with three quark flavors (60 possible sets of constituent quarks with one spin 3/2 and two spin 1/2 versions of each), for a total of 325 possible baryon ground states and an equal number of antibaryons. Naively, there ought to be 25 spin 0 mesons and 25 spin 1 mesons, for a total of fifty but due to linear combinations, group theory considerations and the like, this may not be precisely right. A more technical analysis is found here. There are a potentially infinite or near infinite set of excited states as well (including all scalar, axial vector and tensor mesons).

Second, experimentally detected resonances whose masses and quantum numbers are not easily fit to either theoretically predicted QCD hadrons or to excited states of those hadrons. For example, the paper identifies experimentally detected resonances of less than 2 GeV of mass that seem to have JPC quantum numbers of 0++ (i.e. true scalar mesons), but only four theoretical candidates (two ground states and two excited states) with those quantum numbers in that mass range in the "constituent quark model."

* Strictly speaking J which is often loosely called "spin" is total angular momentum. In this context, P is parity, and C is charge conjugation parity.

The Results

The good news is that recent wave of high energy physics experiments have observed a number of hadron-like particles that do not fit neatly into one of the ordinary meson and baryon boxes, and that these exotic particles seem to have at a minimum, a four quark content including a bottom quark, a bottom antiquark, a down type antiquark, and an up quark, with masses on the order of 10.6 GeV/c2 and a width of 15 MeV (implying a mean lifetime of, for example, about a third of the hypothetical Standard Model Higgs boson).

The bad news is that these observations don't appear to be the long hypothesized "genuine tetraquarks" that theorists have been predicting for years. Instead, they seem to be "meson molecules" in which two ordinary mesons become associated with each other.

During the last three years strong experimental evidence from B and charm factories has been accumulating for the existence of exotic hadronic quarkonia, narrow resonances which cannot be made from a quark and an antiquark. Their masses and decay modes show that they contain a heavy quark-antiquark pair, but their quantum numbers are such that they must also contain a light quark-antiquark pair. The theoretical challenge has been to determine the nature of these resonances. The main possibilities are that they are either "genuine tetraquarks", i.e. two quarks and two antiquarks within one confinement volume, or "hadronic molecules" of two heavy-light mesons. In the last few months there as been more and more evidence in favor of the latter.

From Marek Karliner, "Doubly Heavy Tetraquarks and Baryons" (Pre-Print Submitted January 16, 2014).

The body of the paper proposes the name <b>deuson</b> for a "hadronic molecule" made up of two mesons bound together by something very similar to the forces that bind together protons and neutrons in an atom.

Karliner's paper goes on to "provide fairly precise predictions for masses and quantum numbers of the additional exotic states which are naturally expected in the molecular picture but have yet to be observed." The paper also discusses what experimental signatures we should look for because they would reveal even more exotic hadrons beyond the meson molecule model including "genuine tetraquarks."

Discussion and Analysis

As I commented above, this result is the less exciting of the two possibilities, although it is still pretty remarkable in that it represents the first time that something like the nuclear binding force between protons and neutrons in an atom has been observed in a case of hadrons other than protons and neutrons.

The use of the term "molecule" in this context, while apt in conveying the distinction between a true tetraquark and a state in which two separate mesons are bound to each other in a composite particle of some type, clouds the question of whether the force believed to bind the two mesons together is analogous to the nuclear binding force in atomic nuclei, which is derivative of the QCD strong force, or is actually the electromagnetic force that binds atoms together just as it does in ordinary molecules.

The body of the paper, however, resolves this ambiguity and makes clear that the state observed is really analogous to the nucleus of a deuterium atom, in which a single proton and single neutron are bound by the nuclear binding force transmitted via pions, even though term "molecule" which ordinarily refers to two or more atoms which interact electromagnetically, rather than via the strong force or nuclear binding force. As the paper explains at page 2 (citation omitted, some mathematical symbols translated into words, underlining mine):
The most interesting theoretical question is what are these states?

Their quantum numbers are those of a bb ud tetraquark, but such quantum numbers can also be realized by a system consisting of B* anti- B andB*anti- B* "hadronic molecules" loosely bound by pion exchange. The diff erence between these two possibilities is subtle, because they have the same quantum numbers and therefore in principle they can can mix with each other. The extent of the mixing depends on the overlap between the respective wave functions. By a "tetraquark" I mean a state where all four quarks are within the same "bag" or con finement volume, while by "hadronic molecule" I mean a state where there are two color-singlet heavy-light mesons attracting each other by exchange of pions and possibly other light mesons.

The proximity of the two resonances to the B* -anti- B and B*-anti- B* thresholds strongly suggests a parallel with X(3872), whose mass is almost exactly at the D* -anti- D threshold.

It also provides strong support for the the possibility that these state indeed are deuteron-like "molecules" of two heavy mesons quasi-bound by pion exchange. This is because it is very unlikely that two "genuine" tetraquarks just happened to sit at the respective two-meson thresholds
The attraction due to exchange is 3 times weaker in the I=1 channel than in the I=0 channel. Consequently, in the charm system the I=1 state is expected to be well above the D* -anti- D threshold and the I=0 X(3872) is at the threshold. In the bottom system the attraction due to exchange is essentially the same, but the kinetic energy is much smaller by a factor of on about m(B)/m(D) approximately equal to 2.8. Therefore the net binding is much stronger than in the charm system.
[Note that, in the quoted material referenced, B is a reference to a B meson (which means that it contains a bottom quark or bottom anti-quark), B* to an excited state of a B meson, D to a D meson (which contains a charm quark or charm anti-quark, but not a bottom quark or bottom anti-quark), D* to an excited state of a D meson, and anti-B, anti-B*, anti-D and anti-D* refer respectively to the antiparticles of these mesons. "X(3872)" is a temporary name assigned to an experimentally observed particle with a mass of approximately 3.872 GeV whose quark components are not known.]

What the underlined language is referring to is that in all known mesons and baryons made up of quarks directly bound to each other by gluons, the mass of the composite particle is much greater than the mass of the component quarks and is highly dependent upon the overall spin of the composite particle, with more subtle variations that seem related to other characteristics of the particle like the electric charges involved.  Even mesons or baryons with the same quark flavor content can have very different masses.

In contrast, the difference in mass between sum of the masses of the number of protons and neutrons in a particular atomic nuclei and the mass of the entire atomic nucleus after adjusted for the impact of the nuclear binding force is slight (although measureable - the slight differences in the amount of mass attributable to the nuclear binding force between different atomic nuclei is what is converted into the energy that powers nuclear fission reactors).  It seems unlikely therefore that a true tetraquark would have almost exactly the same mass as the sum of the masses of two mesons with the same combined quark content.

The hypothetical nuclear binding force between the two mesons in these systems is about a third as strong as the force binding quarks directly via gluons within a hadron.

Conjectures Re Exotic Strong Force Composite Particles

Will we find genuine tetraquarks or pentaquarks?

My conjecture is that we will not, or at least that they will be many orders of magnitude more rare than hadronic molecules of mesons and baryons with each other.

While these composite particles aren't naively forbidden by QCD, there is a factor that may make deusons, and analogous particles made of a meson and a baryon bound to each other in a similar way, greatly preferred relative to "genuine" tetraquarks and pentaquarks.

This factor is that in any given QCD color charge neutral tetraquark, it is always possible to divide the four quarks in the "color confinement bag" into two independent systems, each with a quark of a particular color and an antiquark with a corresponding color charge.  These two-quark subsystems can maintain their color charge neutrality independently without any need for interaction between the two subsystems.   So, there is no need for the two subsystems to be confined to each other in order to maintain a color charge neutral particle.

Likewise, in the case of quarks that could form a color charge neutral pentaquark, it is always possible to break the whole into a two quark subsystem and a separate three quark subsystem, without a need for interaction between the two subsystems to maintain a color charge neutral particle.

If the subsystems that need to exchange gluons with each other are effectively independent of each other, can't confine each other, and don't really exchange gluons with the other particles in the system, how can they be said to ever be a "genuine" tetraquark or pentaquark.

In contrast, this is not true in the case of either mesons, or baryons.  There are no possible ways that their quark content could be broken up into color charge neutral subsystems.

Therefore, it seems plausible that "genuine" tetraquarks and pentaquarks either do not exist at all, or are so rare relative to much less energetic hadronic molecule states that they cannot be found in statistically significant numbers at existing experiments.

Does the plausibility of interactions between quarks in different subsystems of tetraquarks or pentaquarks defeat this reasoning?

Tentatively, my answer is no.

There is a subtle caveat to the analysis above, but I am not ultimately convinced that this defeats the argument above against the formation of genuine tetraquarks or pentaquarks (which can be applied with equal force to any composite particle system with even more quarks that can fit within the effective range of the strong force).

Suppose that you have a B-anti-B molecule.  If the quarks in the B meson have red and anti-red color charge, and the quarks in the anti-B meson have blue and anti-blue color charge, then there is really no reason that there would be direct gluon exchange between the two mesons at all.  On the other hand, if the quarks in the B meson have red and anti-red color charge, and the quarks in the anti-B meson have red and anti-red color charge, it would make more sense that the gluon exchanges between the four quarks in the system would become intermingled with each other.

In the single color tetraquark case, it still wouldn't be necessary to keep all four quarks in one bag to create a color charge neutral composite particle to confine the quarks, but one might expect about a third of all such four quark systems to have more cross-subsystem interactions than the other two-third would experience.

This subtle distinction is even more relevant in any possible pentaquark system.   The quarks comprising a color neutral pentaquark can always be decomposed into a meson subsystem and a baryon subsystem. Indeed, there are actually no fewer than one and no more than two ways that this can happen in any given color neutral pentaquark.  But, every decomposition of a color neutral pentaquark will involve a situation where one of the quarks in the baryon subsystem can participate in the same gluon exchanges with one of the quarks in the meson subsystem as the other quark in the meson subsystem.

Thus, in a pentaquark, the non-trival interactions between subsystems which we would naively think would be possible in about one-third of tetraquarks, would always be present.

Ultimately, however, the fact that tetraquarks and pentaquarks never need to have all of their components confined in one system, even if components in one subsystem can have non-trivial interactions with components of another subsystem, probably deprives them of the simultaneous unbreakable strong force bond to all of the other components of the system that gives rise to ordinary mesons and baryons.  Mere coincidence in space and interactions between component quarks, without true confinement, does not appear to give rise to a "genuine" hadron.

Will our discoveries about deusons and tetraquarks have more than theoretical relevance?

We live in a work with six quark flavors.

Only five of these quark flavors, however, have been observed experimentally to hadronize, although I remain unconvinced that mesons and baryons containing top quarks are theoretically impossible, as opposed to merely very rare, because the mean lifetime of a top quark is not too profoundly shorter than the time frame required for hadronization, so one would expect some small subset of top quarks (only a modest finite number of which have ever been synthesized in an observable situation at all) to have actual lifetimes long enough to permit them to briefly hadronize.

But, there are few conditions in Nature, or for that matter, in man-made contexts other than particle accelerators, in which energies are so great that the heavier quark flavors actually come into being or have meaningful physical consequences (apart, perhaps, from their potential impact, for example, on the values of the physical constants for the masses of the Higgs boson and weak force bosons in a theory beyond the Standard Model where these physical constants are not themselves truly fundamental).

A single exotic quark flavor (the strange quark) in addition to the up and down quarks, is more than sufficient to explain pretty much all observed natural phenomena and all man-made systems not specifically designed to produce heavier exotic quarks - with the possible exception of the cosmology of the early universe and the inner workings of quark stars, if such things, as distinct from mere neutron stars, really even exist at all - something for which there is not particularly strong evidence from astronomy at this point.

I certainly can't easily think of engineering applications that rely on the existence of D mesons, B mesons, and baryons that include charm and bottom quarks. These more exotic hadrons take often immense energies to create and are also exceedingly short lived, even compared to more ordinary mesons and exotic baryons, which makes their engineering applications extremely limited.

What about glueballs?

Theory and experiment are neck and neck in the race to discover, or come up with a reason why we cannot discover, glueballs.  Increasing experimental power is likely to provide a definitive resolution of this question.

The reasoning advanced above, with regard to tetraquarks and pentaquarks, also tends to disfavor glueballs with sufficiently large numbers of component gluons.  If my conjecture is sound, then any glueball capable of being decomposed into color neutral subsystems will indeed do so.  So, only simpler glueball systems are really possible (or at least really likely to form at a sufficient frequency to be experimentally observed and described).  It follows that experimental efforts to detect glueballs should continue to focus on these simpler cases.

There are other reasons that could be proposed for either the non-existence of glueballs entirely, or for them to be far more rare given the rules of QCD than one might naively expect without really conducting the right kind of analysis.  But, those conjectures are beyond the scope of this post.

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