Forward virtual Compton scattering and the Lamb shift in chiral perturbation theory

Abstract

We compute the spin-independent structure functions of the forward virtual-photon Compton tensor of the proton at one loop using heavy baryon chiral perturbation theory and dispersion relations. We study the relation between both approaches. We use these results to generalize some sum rules to virtual photon transfer momentum and relate them with sum rules in deep inelastic scattering. We then compute the leading chiral term of the polarizability correction to the Lamb shift of the hydrogen and muonic hydrogen. We obtain -87.05/n^3 Hz and -0.148/n^3 meV for the correction to the hydrogen and muonic hydrogen Lamb shift respectively.

13 pages, 1 figure. Minor changes, misprints corrected, two referenced added

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• The third-order QCD corrections to deep-inelastic scattering by photon exchange
• Dispersion relations in real and virtual Compton scattering
• The form factors of the nucleon at small momentum transfer
• Proton structure effects in muonic hydrogen
• Generalized Sum Rules for Spin-Dependent Structure Functions of the Nucleon
• Muon capture by a proton in heavy baryon chiral perturbation theory
• Proton polarizability effect in the Lamb shift of the hydrogen atom
• Virtual Compton scattering off the nucleon at low energies
• Higher-Order Nuclear-Polarizability Corrections in Atomic Hydrogen
• The chiral structure of the Lamb shift and the definition of the proton radius
• Leading Chiral Logarithms to the Hyperfine Splitting of the Hydrogen and Muonic Hydrogen
• Proton polarizability and the Lamb shift in muonic hydrogen
• Proton Polarization Shifts in Electronic and Muonic Hydrogen
• Virtual Compton scattering off spin-zero particles at low energies
• Nucleon Polarizability Contribution to the Hydrogen Lamb Shift and Hydrogen -- Deuterium Isotope Shift
• Q^2 Evolution of Generalized Baldin Sum Rule for the Proton
• Learning about the chiral structure of the proton from the hyperfine splitting

Cited by in corpus (41)

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• Model independent analysis of proton structure for hydrogenic bound states
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• Subtracted dispersion relation formalism for the two-photon exchange correction to elastic electron-proton scattering: comparison with data
• Constraints on muon-specific dark forces
• The two-photon exchange contribution to muonic hydrogen from chiral perturbation theory
• $\mu -H$ Lamb shift: dispersing the nucleon-excitation uncertainty with a finite energy sum rule
• Gold-plated moments of nucleon structure functions in baryon chiral perturbation theory
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• Two-photon exchange correction to the Lamb shift and hyperfine splitting of S levels
• Proton radius from electron-proton scattering and chiral perturbation theory
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• Hadron Polarizabilities
• Nucleon spin-averaged forward virtual Compton tensor at large $Q^2$
• The proton radius (puzzle?) and its relatives
• Review of experimental and theoretical status of the proton radius puzzle
• The Lamb shift in muonic hydrogen and the proton radius from effective field theories
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• Two-photon exchange correction to $2S$-$2P$ splitting in muonic helium-3 ions
• Forward two-photon exchange in elastic lepton-proton scattering and hyperfine-splitting correction
• Two-photon exchange corrections to elastic $e^{-}$-proton scattering: Full dispersive treatment of $\pi N$ states at low momentum transfers
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• The recoil correction to the proton-finite-size contribution to the Lamb shift in muonic hydrogen
• Model independent determination of the muonic hydrogen Lamb shift and proton radius
• Lattice QCD calculation of the two-photon exchange contribution to the muonic-hydrogen Lamb shift
• Hyperfine splitting in ordinary and muonic hydrogen
• Cottingham formula and nucleon polarizabilities
• Forward doubly-virtual Compton scattering off the nucleon in chiral perturbation theory: the subtraction function and moments of unpolarized structure functions
• Nucleon in a periodic magnetic field
• Two-photon exchange on neutron and the hyperfine splitting
• The chromo-polarizabilities of a heavy quark at weak coupling
• Elements of QED-NRQED Effective Field Theory: I. NLO scattering at leading power
• Elements of QED-NRQED Effective Field Theory: II. Matching of Contact Interactions
• Finite volume corrections to forward Compton scattering off the nucleon
• Hadronic deuteron polarizability contribution to the Lamb shift in muonic deuterium
• Brief review of the theory of the muonic hydrogen Lamb shift and the proton radius
• Comment on "Nucleon spin-averaged forward virtual Compton tensor at large Q^2"
• Improved description of the pion-nucleon scattering phenomenology in covariant baryon chiral perturbation theory