  The complete analytical $O(m_l^3\alpha^5/m_p^2\times (\log{m_\pi},
\log{\Delta}, \log{m_l}))$ contribution to the Hyperfine splitting is given. It
can explain about 2/3 of the difference between experiment and the pure QED
prediction when setting the renormalization scale at the $\rho$ mass. The
suppression of the polarizability piece with respect the Zemach one seems to
be, to a large extent, a numerical accident. We give an estimate of the
matching coefficient of the spin-dependent proton-lepton operator in heavy
baryon effective theory.
