# Could a tetraquark $q \bar{q} q \bar{q}$ be colorless?

CERN just posted this article where it informs that it was found an hadron which cannot be classified within the traditional quark model. What other models are there to explain this result? Or is it possible to introduce a correction to the quark model to explain such find?

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The particle they found is a Tetraquark. The traditional quark model only had particles with 3 quarks or a quark-antiquark pair. –  George G Apr 9 at 13:58
The Z(4430) is believed to be made up of quarks, or at least no-one is suggesting differently. It's just that it appears to be made up of four quarks not three. –  John Rennie Apr 9 at 13:58
But then it can't be color neutral if it's composed by $c \bar{c}d \bar{u}$. I thought all hadrons had to be neutral. –  PML Apr 9 at 14:07
Why can't $c \bar c d \bar u$ be color neutral? Doesn't $3\times\bar3\times3\times\bar3$ contain a singlet? –  innisfree Apr 9 at 14:15
$rgb$ isn't the only colorless combination. $r\bar{r} g \bar{g}$ and other such 4-quark states are colorless as well. –  Jordan Apr 9 at 15:50

There are three flavours of quarks in the fundamental $3$ representation of $SU(3)$, the QCD gauge group. Their antiparticles are in the conjugate representation $\bar3$ or $3^\star$.

QCD is confining; the quarks form bound, colorless states, which are singlets in $SU(3)$.

• Mesons are $q\bar q$. The general tensor $3\times\bar 3$ can be decomposed into irreducible represetations; $3\times\bar 3 = 1 +8$. Note that this contains a singlet.
• Tetra-quarks are $q\bar q q\bar q$. Since $3\times\bar 3 = 1 +8$, $3\times\bar 3 \times 3\times\bar 3$ clearly contains a singlet.

Decomposition of an arbitrary tensor doesn't always contain a singlet e.g. $3\times3=\bar6+3$.

The discovery of a tetra-quark does not require the model of quarks and their interactions to be adjusted.

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A tetraquark (and pentaquark) had been previously predicted as extensions of known mesons (and baryons, respectively). There is no reason why they cannot be colour neutral. e.g. in RBG the quarks could be R 255 G 0 B 0 R 0 G 255 B 0 R 0 G 0 B 128 R 0 G 0 B 127

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This is nonsense... Quarks don't have RGB in the same way a computer does. There is no "half blue" charge. –  JeffDror Apr 17 at 10:27