Bayesian analysis of nuclear polarizability corrections to the Lamb shift of muonic H-atoms and He-ions

Abstract

The extraction of nuclear charge radii from spectroscopy experiments in muonic atoms is currently limited by the large uncertainties associated with the theoretical evaluation of the nuclear polarizability effects. To facilitate calculations, these polarizability corrections are conventionally expressed as an expansion in a dimensionless parameter $\eta$, which has been argued in previous literature to hold an approximate value of 0.33 in light-nuclear systems. In this work, we check this claim by doing a Bayesian analysis of the nuclear-polarizability corrections to the Lamb shift in ${\mu }^2$H and ${\mu }^3$H atoms and in ${\mu }^3$He${}^{+}$ and ${\mu }^4$He${}^{+}$ ions at various orders in the $\eta$-expansion. Our analysis supports the claim that $\eta \ll 1$ in these systems and finds truncation uncertainties that are similar to the previous estimate, the only exception being the truncation uncertainties in the ${\mu }^3$He${}^{+}$ ion, which are found to be larger.

Published in JPG

References in corpus (8)

• Accurate Determination of the Neutron Skin Thickness of ${}^{208}$Pb through Parity-Violation in Electron Scattering
• Local three-nucleon interaction from chiral effective field theory
• Local chiral effective field theory interactions and quantum Monte Carlo applications
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• Improved estimates of the nuclear structure corrections in $\mu$D
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Cited by in corpus (6)

• Comprehensive theory of the Lamb shift in light muonic atoms
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• Revisiting the helium isotope-shift puzzle with improved uncertainties from nuclear structure corrections
• Two-photon exchange in (muonic) deuterium at N3LO in pionless effective field theory
• Bayesian method for fitting the low-energy constants in chiral perturbation theory
• A reassessment of nuclear effects in muonic deuterium using pionless effective field theory at N3LO