Half-hypercharge convention ($Y=(B+S)/2$)

Some formulas write $Q=I_3+Y$ rather than $Q=I_3+Y_{\mathrm{usual}}/2$. Then $Y=(B+S)/2$, where $B$ is baryon number and $S$ is strangeness. The light-quark weights are $u:(1/2,1/6)$, $d:(-1/2,1/6)$, $s:(0,-1/3)$. Baryon weight rows therefore have half the usual vertical coordinates. This is a flavour convention, distinct from weak hypercharge.

The baryon octet has rows $Y=1/2,0,-1/2$ with isospins $1/2$, $1\oplus 0$, $1/2$. The central weight has two states, ${\Sigma }^0$ and ${\Lambda }^0$. The baryon decuplet has rows $Y=1/2,0,-1/2,-1$ with isospins $3/2,1,1/2,0$. The three-quark flavour singlet has one state at the origin. Both abstract octet copies in $3^{\otimes 3}$ share the same weights.