Considering the pentaquark $P = (uudt\bar{c})$, with orbital angular momentum $L = 0$, and assuming a space-spin wavefunction that corresponds to the maximum-J state, I want to know the isospin multiplet to which $P$ belongs.
First of all, the maximum-J state would be $J = \frac{5}{2}^-$, as we are dealing with a pentaquark (a combination of a proton and a meson here).
At this point, for the $J$ above, the maximum isospin $I$ for $P$'s multiplet would be $I = \frac{3}{2}$, since the only particles that account for the isospin are the quarks $u$ and $d$ and their respective antiquarks. Therefore, the asked multiplet would be the following quadruplet:
$$|dddt\bar{c}>$$ $$|uddt\bar{c}>$$ $$|uudt\bar{c}>\;=P$$ $$|uuut\bar{c}>$$
Is this procedure at all correct?
