Learning about the chiral structure of the proton from the hyperfine splitting

Abstract

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.