quarks).

Baryon wave functions {#sec:Baryon}
=====================

We need the baryon states of $J^P={1/2}^+$:

1.  $\Xi^+_c$: $\frac{1}{\sqrt{2}} \,c    \,(us - su)$, and the spin wave function will be the mixed antisymmetric, $\chi_{MA}$, for the two light quarks. Thus, the spin reads $\chi_c \frac{1}{\sqrt{2}}(\uparrow \downarrow - \downarrow \uparrow)$, with $\chi_c =\, \uparrow \, \textrm{or}\, \downarrow$ for $S_z=1/2$ or $-1/2$;

2.  $\Xi^0_c$: the same as $\Xi^+_c$, changing $(us - su) \to (ds - sd)$;

3.  $\Xi^{\prime\,+}_c$: $\frac{1}{\sqrt{2}} c (us + su)$, and now the spin wave function for the three quarks will be the mixed symmetric, $\chi_{MS}$, in the last two quarks

    $$\label{ms}
    \chi_{MS}=
    \left\{
      \begin{array}{rl}
        \hbox{$\displaystyle \frac{1}{\sqrt{6}}(\uparrow\uparrow\downarrow + \uparrow\downarrow\uparrow - 2 \downarrow\uparrow\uparrow)$}, & \hbox{for $S_z=1/2$}, \\
        \hbox{$\displaystyle -\frac{1}{\sqrt{6}}(\downarrow\uparrow\downarrow + \downarrow\downarrow\uparrow - 2 \uparrow\downarrow\downarrow)$}, & \hbox{for $S_z=-1/2$};
      \end{array}
    \right.$$

4.  $\Xi^{\prime\,0}_c$: the same as $\Xi^{\prime}_c$, changing $(us+su) \to (ds+sd)$;

5.  $\Omega^0_c$: $css$, and the spin wave function $\chi_{MS}$ in the last two quarks, like that for $\Xi^{\prime}_c$ ;

6.  $\Xi^0$: to be consistent with the chiral Lagrangians one has to use a different phase convention with respect to Ref. [@close], where the $\Sigma^+$, $\Xi^0$ and $\Lambda$ change sign with respect to Ref. [@close]. The correct assignment for the $\phi_{MA}$ are given in Table 