Leading Chiral Logarithms to the Hyperfine Splitting of the Hydrogen and Muonic Hydrogen

Abstract

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.

17 pages, LaTeX, minor changes, one reference added

Cited by in corpus (28)

• The proton charge radius
• The Electromagnetic Self-Energy Contribution to M_p - M_n and the Isovector Nucleon Magnetic Polarizability
• 2S Hyperfine splitting of muonic hydrogen
• The two-photon exchange contribution to muonic hydrogen from chiral perturbation theory
• Proton structure corrections to electronic and muonic hydrogen hyperfine splitting
• Forward virtual Compton scattering and the Lamb shift in chiral perturbation theory
• Zemach and magnetic radius of the proton from the hyperfine splitting in hydrogen
• Non-relativistic bound states at finite temperature (II): the muonic hydrogen
• Two-photon exchange correction to the Lamb shift and hyperfine splitting of S levels
• Muonic hydrogen ground state hyperfine splitting
• The chiral structure of the Lamb shift and the definition of the proton radius
• Two-photon exchange contribution to elastic $e^{-}$-proton scattering: Full dispersive treatment of $\pi N$ states and comparison with data
• The proton radius (puzzle?) and its relatives
• The Lamb shift in muonic hydrogen and the proton radius from effective field theories
• Two-photon exchange correction to the hyperfine splitting in muonic hydrogen
• Model-independent determination of the two-photon exchange contribution to hyperfine splitting in muonic hydrogen
• Nuclear structure corrections in the energy spectra of electronic and muonic deuterium
• Forward two-photon exchange in elastic lepton-proton scattering and hyperfine-splitting correction
• Forward doubly-virtual Compton scattering off the nucleon in chiral perturbation theory: II. Spin polarizabilities and moments of polarized structure functions
• Two-photon exchange corrections to elastic $e^{-}$-proton scattering: Full dispersive treatment of $\pi N$ states at low momentum transfers
• On HQET and NRQCD Operators of Dimension 8 and Above
• Model independent determination of the muonic hydrogen Lamb shift and proton radius
• Hyperfine splitting in ordinary and muonic hydrogen
• Precision calculation of the recoil--finite-size correction for the hyperfine splitting in muonic and electronic hydrogen
• Two-photon exchange on neutron and the hyperfine splitting
• Elements of QED-NRQED Effective Field Theory: I. NLO scattering at leading power
• $\Delta (1232)$-Resonance in the Hydrogen Spectrum
• Elements of QED-NRQED Effective Field Theory: II. Matching of Contact Interactions