**Authors:** Matti Pitkänen

This article was motivated by a blog posting in Quantum Diaries with the title "Who ordered that?! An X-traordinary particle?". The learned that in the spectroscopy of ccbar type mesons is understood except for some troublesome mesons christened with letters X and Y. 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.

- These mesons should not be there.
- Their decay widths seem to be narrow taking into account their mass.
- 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 DDbarπ
^{0}occurs with a branching fraction >3.2× 10^{-3}. Why the pion is needed? - 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. 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?

- 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.
- Second 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. At low energies where color coupling strength becomes very large 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.
- 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 the 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.

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[v1] 1 Nov 2011

[v2] 2012-01-30 09:33:04

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