Ab initio calculation of nuclear structure corrections in muonic atoms

Abstract

The measurement of the Lamb shift in muonic hydrogen and the subsequent emergence of the proton-radius puzzle have motivated an experimental campaign devoted to measuring the Lamb shift in other light muonic atoms, such as muonic deuterium and helium. For these systems it has been shown that two-photon exchange nuclear structure corrections are the largest source of uncertainty and consequently the bottleneck for exploiting the experimental precision to extract the nuclear charge radius. Utilizing techniques and methods developed to study electromagnetic reactions in light nuclei, recent calculations of nuclear structure corrections to the muonic Lamb shift have reached unprecedented precision, reducing the uncertainty with respect to previous estimates by a factor of 5 in certain cases. These results will be useful for shedding light on the nature of the proton-radius puzzle and other open questions pertaining to it. Here, we review and update calculations for muonic deuterium and tritium atoms, and for muonic helium-3 and helium-4 ions. We present a thorough derivation of the formalism and discuss the results in relation to other approaches where available. We also describe how to assess theoretical uncertainties, for which the language of chiral effective field theory furnishes a systematic approach that could be further exploited in the future.

arXiv comment62 pages, 15 figures, 8 tables

References in corpus (57)

• An accurate nucleon-nucleon potential with charge-independence breaking
• CODATA Recommended Values of the Fundamental Physical Constants: 2010
• Chiral effective field theory and nuclear forces
• Accurate Charge-Dependent Nucleon-Nucleon Potential at Fourth Order of Chiral Perturbation Theory
• CODATA Recommended Values of the Fundamental Physical Constants: 2014
• Quantum Monte Carlo Calculations of $A\le 6$ Nuclei
• The two-nucleon system at next-to-next-to-next-to-leading order
• Theory of Light Hydrogenlike Atoms
• High-precision determination of the electric and magnetic form factors of the proton
• Muonic hydrogen and the proton radius puzzle
• Benchmark Test Calculation of a Four-Nucleon Bound State
• Local three-nucleon interaction from chiral effective field theory
• New measurement of the $1S-3S$ transition frequency of hydrogen: contribution to the proton charge radius puzzle
• On the rms-radius of the proton
• Dispersion analysis of the nucleon form factors including meson continua
• Response Functions from Integral Transforms with a Lorentz Kernel
• High Precision Measurement of the Proton Elastic Form Factor Ratio ${\mu }_p{G}_E/G_M$ at low $Q^2$
• The Lorentz Integral Transform (LIT) method and its applications to perturbation induced reactions
• State Dependent Effective Interaction for the Hyperspherical Formalism
• Uncertainty analysis and order-by-order optimization of chiral nuclear interactions
• Frequency metrology in quantum degenerate helium: Direct measurement of the 2 3S1 - 2 1S0 transition
• Higher order proton structure corrections to the Lamb shift in muonic hydrogen
• Proton polarisability contribution to the Lamb shift in muonic hydrogen at fourth order in chiral perturbation theory
• Lamb Shift in Light Muonic Atoms - Revisited
• Frequency metrology of helium around 1083 nm and determination of the nuclear charge radius
• State Dependent Effective Interaction for the Hyperspherical Formalism with Noncentral Forces
• On the pi pi continuum in the nucleon form factors and the proton radius puzzle
• Proton radii and two-photon exchange
• Modern Ab Initio Approaches and Applications in Few-Nucleon Physics with A \ge 4
• alpha-particle photoabsorption with a realistic nuclear force
• Shell-model calculations for the three-nucleon system
• Simultaneous measurement of the photodisintegration of 4He in the giant dipole resonance region
• Theory of the n=2 levels in muonic deuterium
• The ${}^4$He total photo-absorption cross section with two- plus three-nucleon interactions from chiral effective field theory
• Nuclear structure corrections in muonic deuterium
• Nuclear structure contribution to the Lamb shift in muonic deuterium
• Proton Polarizability Contribution: Muonic Hydrogen Lamb Shift and Elastic Scattering
• Missing and Quenched Gamow Teller Strength
• Three-photon exchange nuclear structure correction in hydrogenic systems
• Nuclear polarization corrections in the mu-4He+ Lamb shift
• Deuteron charge radius and Rydberg constant from spectroscopy data in atomic deuterium
• Improved estimates of the nuclear structure corrections in $\mu$D
• Nuclear structure effects in light muonic atoms
• Nuclear Polarization Corrections to mu-d Atoms in Zero-Range Approximation
• 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
• The deuteron-radius puzzle is alive: A new analysis of nuclear structure uncertainties
• Nucleon spin-averaged forward virtual Compton tensor at large $Q^2$
• Higher-Order Nuclear-Size Corrections in Atomic Hydrogen
• Two-photon exchange correction to $2S$-$2P$ splitting in muonic helium-3 ions
• An efficient method for evaluating energy-dependent sum rules
• Nuclear structure corrections to the Lamb shift in ${\mu }^3$He${}^{+}$ and ${\mu }^3$H
• Lamb shift in muonic ions of lithium, beryllium and boron
• Near-threshold measurement of the 4He(g,n) reaction
• Nuclear Polarization Corrections for the S--Levels of Electronic and Muonic Deuterium
• The Piecewise Moments Method: A Generalized Lanczos Technique for Nuclear Response Surfaces
• Theory of the n=2 levels in muonic helium-3 ions
• Update on nuclear structure effects in light muonic atoms

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• From bound states to the continuum
• Nuclear matrix elements from lattice QCD for electroweak and beyond-Standard-Model processes
• The proton structure in and out of muonic hydrogen
• Comprehensive theory of the Lamb shift in light muonic atoms
• Benchmark calculations of electromagnetic sum rules with a symmetry-adapted basis and hyperspherical harmonics
• Dispersive evaluation of the Lamb shift in muonic deuterium from chiral effective field theory
• Zemach moments and radii of 2,3H and 3,4He
• Probing uncertainties of nuclear structure corrections in light muonic atoms
• Uncertainty quantification in electromagnetic observables of nuclei
• Hyperfine structure of S-states in muonic ions of lithium, beryllium and boron
• Revisiting the helium isotope-shift puzzle with improved uncertainties from nuclear structure corrections
• Reduced Theoretical Error for QED Tests with 4He+ Spectroscopy
• Bayesian analysis of nuclear polarizability corrections to the Lamb shift of muonic H-atoms and He-ions
• Two-photon exchange in (muonic) deuterium at N3LO in pionless effective field theory
• A theory vade mecum for PSI experiments
• Hyperfine structure of P states in muonic ions of lithium, beryllium and boron
• Generation of arbitrarily polarized muon pairs via polarized $e^{-}{e}^{+}$ collision
• Radiative Corrections and the Renormalization Group for the Two-Nucleon Interaction in Effective Field Theory
• A reassessment of nuclear effects in muonic deuterium using pionless effective field theory at N3LO
• Relativistic fine structure of the (He4,mu) ion 2p-levels