From the hyperfine calculation we find that the mass of the vector mesons are heavier than pseudoscalar meson, as the following proves.
The magnetic moment is proportional to the spin and inversely proportional to the mass. The hyperfine interaction correction is proportional to the dot product of the two moments, $$ \Delta E_{i j}=k \frac{\vec{S_i} \cdot \vec{S_j}}{m_i m_j}, $$ so the mass of the meson is $$ \begin{gathered} m=m_i+m_j+\Delta E_{i j} \\ S^2=\left(\vec{S_i}+\vec{S_j}\right)^2=S_i^2+S_j^2+2 \vec{S_i} \cdot \vec{S_j}. \end{gathered} $$
So we predict that vector mesons are heavier than pseudoscalar mesons.
However, strong forces favour the aligned spins, and it’s said here that the binding energy is larger for aligned spins.
Does the strong force increase or decrease with aligned spins?
Since vector mesons have aligned spins, they should have higher binding energy, hence smaller mass. How is that consistent with the hyperfine correction?