Do X and Y mesons provide evidence for color excited quarks or squarks?

Now and then come the days when head is completely empty of ideas. One just walks around and gets more and more frustrated. One can of course make authoritative appearances in blog groups and express strong opinions but sooner or later one is forced to look for web if one could find some problem. At this time I had good luck. By some kind of divine guidance I found myself immediately in Quantum Diaries and found a blog posting with title Who ordered that?! An X-traordinary particle?

Not too many unified theorists take meson spectroscopy seriously. Although they are now accepting low energy phenomenology (the physics for the rest of us) as something to be taken seriously, meson physics is for them a totally uninteresting branch of botany. They could not care less. As a crackpot I am however not well-informed about what good theoretician should do and shouldn't do and got interested. Could this give me a problem that my poor crackpot brain is crying for?

The posting told me that in the spectroscopy of ccbar type mesons is understood except for some troublesome mesons christened imaginatively with letters X and Y plus brackets containing their mass in MeVs. X(3872) is the firstly discovered troublemaker and what is known about it can be found in the blog posting and also in Particle Data Tables. The problems are following.

1. First of all, these mesons should not be there.
2. Their decay widths seem to be narrow taking into account their mass.
3. Their decay characteristics are strange: in particular the kinematically allow decays to DDbar dominating the decays of Ψ(3770) with branching ratio 93 per cent has not been observed whereas the decay to DDbarπ⁰ occurs with a branching fraction >3.2× 10^-3. Why the pion is needed?
4. X(3872) should decay to photon and charmonium state in a predictable way but it does not.

One of the basic predictions of TGD is that both leptons and quarks should have color excitations (see this). In the case of leptons there is a considerable support as carefully buried anomalies: the first ones come from seventies. But in the case of quarks this kind of anomalies have been lacking. Could these mysterious X:s and Y:s provide the first signatures about the existence of color excited quarks. An alternative proposal is that X and Y are meson like states formed from superpartners of charmed quark and antiquark. Consider for definiteness the option based on color excited quarks.

1. The first basic objection is that the decay widths of intermediate gauge bosons do not allow new light particles. This objection is encountered already in the model of leptohadrons. The solution is that the light exotic states are possible only if they are dark in TGD sense having therefore non-standard value of Planck constant and behaving as dark matter. The value of Planck constant is only effective and has purely geometric interpretation in TGD framework.
2. The basic objection is that light quarks do not seem to have such excitations. The answer is that gluon exchange transforms the exotic quark pair to ordinary one and vice versa and considerable mixing of the ordinary and exotic mesons takes place. This kind of coupling between gluon octet, color triplet and D-dimensional triality one representation is possible for D=6bar and D=15 (note that standard Lie-algebra coupling of gluons is not in question). At low energies where color coupling strength becomes very large and this gives rise to mass squared matrix with very large non-diagonal component and the second eigenstate of mass squared is tachyon and therefore drops from the spectrum. For heavy quarks situation is different and one expects that charmonium states have also exotic counterparts.

3. The selection rules can be also understood. The decays to DDbar involve at least two gluon emissions decaying to quark pairs and producing additional pion unlikes the decays of ordinary charmonium state involving only the emission of single gluon decaying to quark pair so that DDbar results.

   The decay of lightest X to photon and charmonium is not possible in the lowest order since at least one gluon exchange is needed to transform exotic quark pair to ordinary one. Exotic charmonia can however transform to exotic charmonia. Therefore the basic constraints seem to be satisfied.

The above arguments apply with minimal modifications also to squark option and at this moment I am not able to to distinguish between this options. The SUSY option is however favored by the fact that it would explain why SUSY has not been observed in LHC in terms of shadronization and subsequent decay to hadrons by gluino exhanges so that the jets plus missing energy would not serve as a signature of SUSY. Note that the decay of gluon to dark squark pair would require a phase transition to dark gluon first.

For details and background see the article Do X and Y mesons provide evidence for color excited quarks or squarks? and the chapter The Recent Status of Leptohadron Hypothesis of "p-Adic Length Scale Hypothesis and Dark Matter Hierarchy".