= Equal Sigma and Xi hyperfine splittings
{title2=$M_{qqs,3/2}-M_{qqs,1/2}=M_{qss,3/2}-M_{qss,1/2}=3A'/(2m_qm_s)$}
Use dimensionless <spin angular momentum> operators with $\hbar=1$ and the common-coefficient <baryon hyperfine mass formula>. The identical pair has total spin one, so its pair expectation is $1/4$. For total baryon spin $1/2$, the two mixed-flavour pair expectations sum to $-1$; for total spin $3/2$, they sum to $1/2$. Their difference is $3/2$, giving the title formula for either repeated-flavour choice. The equality assumes the same effective coefficient $A'$ in the two flavour configurations; different spatial overlaps can change it.
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