Solution
= Solution
Each <quark> has <baryon number> $1/3$, and each <antiquark> has <baryon number> $-1/3$. A strange <quark> has <strangeness> $-1$, a strange <antiquark> has <strangeness> $+1$, and the light $u,d$ have zero <strangeness>. The <isospin> projections of $u,d,s$ are $+1/2,-1/2,0$, with the opposite values for their <antiquarks>. Thus
$$
B=\frac{n_q-n_{\bar q}}3,\qquad
S=n_{\bar s}-n_s,\qquad
I_z=\frac{n_u-n_d-n_{\bar u}+n_{\bar d}}2.
$$
For three <valence quarks>, $B=1$ and $Y=B+S=1-n_s$. The <baryon octet> is reproduced by the following <quark model> assignments:
|| <Baryon>
|| <Valence quarks>
|| $I_z$
|| $B+S$
| <Neutron> $n$
| $udd$
| $-1/2$
| $1$
| <Proton> $p$
| $uud$
| $+1/2$
| $1$
| <Sigma baryon> $\Sigma^-$
| $dds$
| $-1$
| $0$
| <Sigma baryon> $\Sigma^0$
| $uds$
| $0$
| $0$
| <Lambda baryon> $\Lambda^0$
| $uds$
| $0$
| $0$
| <Sigma baryon> $\Sigma^+$
| $uus$
| $+1$
| $0$
| <Xi baryon> $\Xi^-$
| $dss$
| $-1/2$
| $-1$
| <Xi baryon> $\Xi^0$
| $uss$
| $+1/2$
| $-1$
Consequently the top-left and top-right states in the source diagram are $\boxed{X=n,\quad Y=p}$. Here the source's label $Y$ means the unknown particle at the top right; the conventional symbol $Y=B+S$ elsewhere in this solution denotes <flavor hypercharge>.
\Image[/past-exam-of-the-nuclear-and-particle-physics-course-of-the-university-of-oxford/2022-flavour-weight-diagrams.png]
{title=Original baryon-octet and pseudoscalar-meson-nonet weight diagrams in the full hypercharge convention}