Tetraquark States: Exploring Beyond the Quark Model

[Safinaz]

Hi all,

I were wonder how the particles which consisting of four quarks like Z(4430) state ( $c\bar{c}d\bar{u}$ ) can be theoretically explained ?

Of course, this is beyond the the quark model, where the SU(3) group has for example, representations with dimensions 3 (corresponding to baryons), 8 (octets) ,10 (decuplets), and etc.. So what are the other alternative scenarios to accommodates these exotic particles, are
there theories assuming a group like SU(4) ?

Bests,
S.

 

[Einj]

When you talk about "tetraquarks" you usually refer to "four-quark states". There are different models going on that try to explain these "exotic mesons". However, none of them assumes any new group usually, it's all withing the Standard Model.

The main models developed during the years are:

1) "Compact tetraquark": exactly as mesons and baryons are made by $q\bar q$ and $qqq$, you can build objects made by $qq\bar q\bar q$. In fact, from a group theory point of view quarks belong to the representation $3$ of $SU(3)_{color}$ while anti-quarks belong to the $\bar 3$. Now, it is well-known (see for example the one-gluon-exchange approximation) that you can bind two quarks together in a $\bar 3$ representation (in fact $3\times 3=\bar 3+6$) and this configuration is attractive. You can also do the same thing for two anti-quarks in a $3$, forming the so-called (anti-)diquarks. Binding the diquark and the anti-diquark together you can obtain a colorless structure $[qq]_{\bar 3}[\bar q\bar q]_3\to [qq\bar q\bar q]_1$.
The problem with this model is that, even if it can nicely explain the current spectrum of exotic mesons, it also predicts a bunch of other exotic particles that have not been seen yet.

2) "Meson molecule": nothing but two mesons bound together in a molecule via strong forces. For example a $DD^*$ bound state. The problem with this model is that it requires for the mass of the exotic meson to be close to the sum of the masses of the components of the molecule (in order not to have a too large binding energy). Not all the observed exotic particles lie reasonably close to this threshold.

3) "Hadro-charmonium": the idea is smilar to that of an ordinary atom. You can have a nucleus composed by an ordinary charmonium (for example a $J/\psi$) sorrounded by a "cloud" of light quarks with the same quantum numbers of a light meson (for example a pion). The interaction between the nucleus and the cloud would be via a residual strong Van Der Waals force.

4) "Hybrid": I honestly don't know much about this model. If I remember correctly it assumes for the particle to be composed by two valence quarks and a valence gluon. But I'm not sure.

I hope this is clear enough and answers your question.
In my opinion the question about the nature of these "exotic mesons" is one of the most interesting and exciting in nowadays particle physics. The beautiful aspect is that is it strongly contrained by data and hence developing a model that properly describes all the properties of this particles is a very hard task. People should probably put a little more effort in solving this problem... we still don't know if it might contain new physics.

 

[Safinaz]

Yes .. thanks, that's helped me in understanding ..