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Leading Chiral Logarithms to the Hyperfine Splitting of the Hydrogen and Muonic Hydrogen
We study the hydrogen and muonic hydrogen within an effective field theory
framework. We perform the matching between heavy baryon effective theory
coupled to photons and leptons and the relevant effective field theory at
atomic scales. This matching can be performed in a perturbative expansion in
alpha, 1/m_p and the chiral counting. We then compute the O(m_{l_i}^3
alpha^5/m_p^2 x logarithms) contribution (including the leading chiral
logarithms) to the Hyperfine splitting and compare with experiment. They can
explain about 2/3 of the difference between experiment and the pure QED
prediction when setting the renormalization scale at the rho mass. We give an
estimate of the matching coefficient of the spin-dependent proton-lepton
operator in heavy baryon effective theory.Comment: 17 pages, LaTeX, minor changes, one reference adde