Proton polarisability contribution to the Lamb shift in muonic hydrogen at fourth order in chiral perturbation theory

Abstract

We calculate the amplitude T_1 for forward doubly-virtual Compton scattering in heavy-baryon chiral perturbation theory, to fourth order in the chiral expansion and with the leading contribution of the gammaNDelta form factor. This provides a model-independent expression for the amplitude in the low-momentum region, which is the dominant one for its contribution to the Lamb shift. It allows us to significantly reduce the theoretical uncertainty in the proton polarisability contributions to the Lamb shift in muonic hydrogen. We also stress the importance of consistency between the definitions of the Born and structure parts of the amplitude. Our result leaves no room for any effect large enough to explain the discrepancy between proton charge radii as determined from muonic and normal hydrogen.

arXiv comment9 pages, 2 figures; added discussion of matching ChPT form factor onto dipole form at non-zero Q^2; no significant changes in results

References in corpus (38)

• Chiral Dynamics in Nucleons and Nuclei
• High-precision determination of the electric and magnetic form factors of the proton
• Reparameterisation Invariance Constraints on Heavy Particle Effective Field Theories
• Electromagnetic excitation of the Delta(1232)-resonance
• Global analysis of proton elastic form factor data with two-photon exchange corrections
• Chiral Perturbation Theory and Baryon Properties
• The chiral effective pion-nucleon Lagrangian of order p^4
• The HQET/NRQCD Lagrangian to order alpha/m^3
• Effective theory of the Delta(1232) in Compton scattering off the nucleon
• The form factors of the nucleon at small momentum transfer
• Proton structure effects in muonic hydrogen
• Using effective field theory to analyse low-energy Compton scattering data from protons and light nuclei
• Higher order proton structure corrections to the Lamb shift in muonic hydrogen
• Determination of the chiral coupling constants c3 and c4 in new pp and np partial-wave analyses
• Consistent Calculation of the Nucleon Electromagnetic Polarizabilities in Chiral Perturbation Theory Beyond Next-to-Leading Order
• Lamb Shift in Light Muonic Atoms - Revisited
• Chiral Effective-Field Theory in the Delta(1232) Region: Pion Electroproduction on the Nucleon
• Delta(1232) and the Polarizabilities of the Nucleon
• The Electromagnetic Self-Energy Contribution to M_p - M_n and the Isovector Nucleon Magnetic Polarizability
• Model independent analysis of proton structure for hydrogenic bound states
• Lamb Shift in Muonic Hydrogen. I. Verification and Update of Theoretical Predictions
• Spin structure of the nucleon at low energies
• Aspects of Nucleon Compton Scattering
• Signatures of Chiral Dynamics in Low Energy Compton Scattering off the Nucleon
• Generalized Drell-Hearn-Gerasimov Sum Rule at Order {\cal O}(p^4) in Chiral Perturbation Theory
• Forward virtual Compton scattering and the Lamb shift in chiral perturbation theory
• Generalized polarizabilities and the spin-averaged amplitude in virtual Compton scattering off the nucleon
• Lamb Shift in Muonic Hydrogen. II. Analysis of the Discrepancy of Theory and Experiment
• Proton polarizability effect in the Lamb shift of the hydrogen atom
• Novel analysis of chiral loop effects in the generalized Gerasimov-Drell-Hearn sum rule
• Virtual Compton scattering off the nucleon at low energies
• Natural Resolution of the Proton Size Puzzle
• The chiral structure of the Lamb shift and the definition of the proton radius
• Electromagnetic Polarisability of the Nucleon in Chiral Perturbation Theory
• Small Momentum Evolution of the Extended Drell--Hearn--Gerasimov Sum Rule
• Compton scattering from the proton at NLO in the chiral expansion
• Virtual Compton scattering off spin-zero particles at low energies
• Comment on "Complete One-Loop Analysis of the Nucleon's Spin Polarisabilities"

Cited by in corpus (82)

• Baryons as relativistic three-quark bound states
• Muonic hydrogen and the proton radius puzzle
• The Proton Radius Puzzle
• Theory of the 2S-2P Lamb shift and 2S hyperfine splitting in muonic hydrogen
• The proton charge radius
• Theoretical Constraints and Systematic Effects in the Determination of the Proton Form Factors
• Nucleon Polarizabilities: from Compton Scattering to Hydrogen Atom
• Model independent extraction of the proton magnetic radius from electron scattering
• Compton scattering from the proton in an effective field theory with explicit Delta degrees of freedom
• Chiral perturbation theory of muonic hydrogen Lamb shift: polarizability contribution
• The NRQED lagrangian at order 1/M^4
• Subtracted dispersion relation formalism for the two-photon exchange correction to elastic electron-proton scattering: comparison with data
• Theory of the n=2 levels in muonic deuterium
• Constraints on muon-specific dark forces
• The two-photon exchange contribution to muonic hydrogen from chiral perturbation theory
• New insights into the spin structure of the nucleon
• Nuclear structure contribution to the Lamb shift in muonic deuterium
• The proton structure in and out of muonic hydrogen
• Three-photon exchange nuclear structure correction in hydrogenic systems
• Comprehensive theory of the Lamb shift in light muonic atoms
• $\mu -H$ Lamb shift: dispersing the nucleon-excitation uncertainty with a finite energy sum rule
• Nuclear polarization corrections in the mu-4He+ Lamb shift
• Expanding Nuclear Physics Horizons with the Gamma Factory
• New Measurement of Compton Scattering from the Deuteron and an Improved Extraction of the Neutron Electromagnetic Polarizabilities
• Improved estimates of the nuclear structure corrections in $\mu$D
• Two-photon exchange correction in elastic unpolarized electron-proton scattering at small momentum transfer
• Two-photon exchange correction to the Lamb shift and hyperfine splitting of S levels
• Proton radius from electron-proton scattering and chiral perturbation theory
• Ab initio calculation of nuclear structure corrections in muonic atoms
• Two-photon exchange contribution to elastic $e^{-}$-proton scattering: Full dispersive treatment of $\pi N$ states and comparison with data
• Theory of the Lamb shift and Fine Structure in muonic ${}^4\mathrm{He}$ ions and the muonic ${}^3\mathrm{He}{-}^4\mathrm{He}$ Isotope Shift
• Hadron Polarizabilities
• The deuteron-radius puzzle is alive: A new analysis of nuclear structure uncertainties
• The proton radius (puzzle?) and its relatives
• Nucleon spin-averaged forward virtual Compton tensor at large $Q^2$
• Two-photon exchange correction to muon-proton elastic scattering at low momentum transfer
• Review of experimental and theoretical status of the proton radius puzzle
• Nucleon Compton scattering in the Dyson-Schwinger approach
• 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
• Two-photon exchange correction to $2S$-$2P$ splitting in muonic helium-3 ions
• Dispersion Theory in Electromagnetic Interactions
• The Triton Charge Radius to Next-to-next-to-leading order in Pionless Effective Field Theory
• Nuclear structure corrections to the Lamb shift in ${\mu }^3$He${}^{+}$ and ${\mu }^3$H
• Dispersive estimate of the electromagnetic charge symmetry violation in the octet baryon masses
• Forward two-photon exchange in elastic lepton-proton scattering and hyperfine-splitting correction
• Nucleon resonances in Compton scattering
• Two-photon exchange corrections to elastic $e^{-}$-proton scattering: Full dispersive treatment of $\pi N$ states at low momentum transfers
• Theory of the n=2 levels in muonic helium-3 ions
• Experiments towards resolving the proton charge radius puzzle
• Dispersive evaluation of the Lamb shift in muonic deuterium from chiral effective field theory
• Nonidentical protons
• On HQET and NRQCD Operators of Dimension 8 and Above
• Forward sum rule for the $2\gamma$-exchange correction to the charge radius extraction from elastic electron scattering
• 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
• Compton Scattering from the Deuteron below Pion-Production Threshold
• The magnetic moments and electromagnetic form factors of the decuplet baryons in chiral perturbation theory
• Lattice QCD calculation of the two-photon exchange contribution to the muonic-hydrogen Lamb shift
• Hyperfine splitting in ordinary and muonic hydrogen
• A self-consistent value of the electric radius of the proton from the Lamb shift in muonic hydrogen
• Two-photon-exchange effects in the unpolarized $\mu p$ scattering within the hadronic model
• 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
• 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
• $\Delta (1232)$-Resonance in the Hydrogen Spectrum
• Elements of QED-NRQED Effective Field Theory: I. NLO scattering at leading power
• Proton Compton Scattering from Linearly Polarized Gamma Rays
• Electromagnetic proton-neutron mass difference
• Finite volume corrections to forward Compton scattering off the nucleon
• Elements of QED-NRQED Effective Field Theory: II. Matching of Contact Interactions
• Low energy doubly-virtual Compton scattering from di-lepton electroproduction on a nucleon
• Nuclear Quasi-Elastic Electron Scattering Limits Nucleon Off-Mass Shell Properties
• Two-photon exchange in (muonic) deuterium at N3LO in pionless effective field theory
• New sum rule for the nuclear magnetic polarizability
• Forward doubly-virtual Compton scattering off an unpolarised deuteron in pionless effective field theory
• Virtual Compton scattering at low energies with a positron beam
• Disperon QED
• Soft-photon radiative corrections to the $e^{-}p\to e^{-}p{l}^{-}{l}^{+}$ process
• Comment on "Nucleon spin-averaged forward virtual Compton tensor at large Q^2"