The two-photon exchange contribution to muonic hydrogen from chiral perturbation theory

Abstract

We compute the spin-dependent and spin-independent structure functions of the forward virtual-photon Compton tensor of the proton at one loop using heavy baryon effective theory including the Delta particle. We compare with previous results when existing. Using these results we obtain the leading hadronic contributions, associated to the pion and Delta particles, to the Wilson coefficients of the lepton-proton four fermion operators in NRQED. The spin-independent coefficient yields a pure prediction for the two-photon exchange contribution to the muonic hydrogen Lamb shift, $\Delta E_{\mathrm{TPE}}(\pi \&\Delta )=34(13)$ $\mu$eV. We also compute the charge, $⟨r^n⟩$, and Zemach, $⟨r^n{⟩}_{(2)}$, moments for $n\ge 3$. Finally, we discuss the spin-dependent case, for which we compute the difference between the four-fermion Wilson coefficients relevant for hydrogen and muonic hydrogen.

arXiv comment43 pages, 6 figures. Minor corrections, references added, misprints corrected, Eq. (3.19) added, results unchanged. To meet journal version

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• Comprehensive theory of the Lamb shift in light muonic atoms
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• Dispersion Theory in Electromagnetic Interactions
• Nuclear structure corrections to the Lamb shift in ${\mu }^3$He${}^{+}$ and ${\mu }^3$H
• Model-independent determination of the two-photon exchange contribution to hyperfine splitting in muonic hydrogen
• 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
• Nucleon form factors in dispersively improved Chiral Effective Field Theory II: Electromagnetic form factors
• $\eta$ and ${\eta }^{\prime }$ decays into lepton pairs
• Experiments towards resolving the proton charge radius puzzle
• On HQET and NRQCD Operators of Dimension 8 and Above
• 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
• Sum rules across the unpolarized Compton processes involving generalized polarizabilities and moments of nucleon structure functions
• Hyperfine splitting in ordinary and muonic hydrogen
• Corrections of two-photon interactions in the fine and hyperfine structure of the P-energy levels of muonic hydrogen
• Two-photon-exchange effects in the unpolarized $\mu p$ scattering within the hadronic model
• 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
• Radiative and chiral corrections to elastic lepton-proton scattering in chiral perturbation theory
• $\Delta (1232)$-Resonance in the Hydrogen Spectrum
• Elements of QED-NRQED Effective Field Theory: I. NLO scattering at leading power
• Finite volume corrections to forward Compton scattering off the nucleon
• Elements of QED-NRQED Effective Field Theory: II. Matching of Contact Interactions
• Nucleon in a periodic magnetic field: Finite-volume aspects
• Two-photon exchange in (muonic) deuterium at N3LO in pionless effective field theory
• Radiative corrections to elastic proton-electron scattering measured in coincidence
• Zemach and Friar radii of the proton and neutron from lattice QCD
• Precision Nuclear-Spin Effects in Atoms: EFT Methods for Reducing Theory Errors
• Laser excitation of the 1s-hyperfine transition in muonic hydrogen