= Four-flavour meson multiplet
{title2=$\mathbf4\otimes\overline{\mathbf4}=\mathbf{15}\oplus\mathbf1$}
Four <quark flavours> in the defining <representation> of flavour <SU(4)> and their <antiquarks> give sixteen <meson> flavour states. The <trace> of $M^i{}_j=q^i\bar q_j$ is the <trivial representation>; its traceless part is the <Adjoint representation>. Under light-flavour <SU(3)>, the full content is $\mathbf8\oplus\mathbf3\oplus\overline{\mathbf3}\oplus2\mathbf1$. Relative to the light-flavour nonet, the new states are $u\bar c,d\bar c,s\bar c,c\bar u,c\bar d,c\bar s,c\bar c$. Inside the traceless fifteen-dimensional multiplet the additional singlet is instead $(u\bar u+d\bar d+s\bar s-3c\bar c)/\sqrt{12}$. The pure $c\bar c$ state is a linear combination of this state and the full <SU(4)> singlet. The classification concerns flavour; it does not imply degenerate physical <masses> or fix spin.
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