Lattice QCD calculation of the two-photon exchange contribution to the muonic-hydrogen Lamb shift

Abstract

We develop a method for lattice QCD calculation of the two-photon exchange contribution to the muonic-hydrogen Lamb shift. To demonstrate its feasibility, we present the first lattice calculation with a gauge ensemble at $m_{\pi }=142$ MeV. By adopting the infinite-volume reconstruction method along with an optimized subtraction scheme, we obtain $\Delta E_{\text{TPE}}=-28.9(4.9)\mu \text{eV}+93.72\mu \text{eV}/{\text{fm}}^2\cdot ⟨r_p^2⟩$, or $\Delta E_{\text{TPE}}=37.4(4.9)\mu$eV, which is consistent with the previous theoretical results in a range of 20-50 $\mu$eV.

7 pages + 3 pages supplemental material, 12 figures

References in corpus (5)

• Proton polarisability contribution to the Lamb shift in muonic hydrogen at fourth order in chiral perturbation theory
• Forward virtual Compton scattering and the Lamb shift in chiral perturbation theory
• Field sparsening for the construction of the correlation functions in lattice QCD
• Forward doubly-virtual Compton scattering off the nucleon in chiral perturbation theory: the subtraction function and moments of unpolarized structure functions
• Low energy doubly-virtual Compton scattering from di-lepton electroproduction on a nucleon

Cited by in corpus (9)

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• Comprehensive theory of the Lamb shift in light muonic atoms
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• First lattice QCD calculation of $J/\psi$ semileptonic decay containing $D$ and $D_s$ particles
• Radiative corrections to leptonic decays using infinite-volume reconstruction
• Looking at QED with Dyson-Schwinger equations: basic equations, Ward-Takahashi identities and the two-photon-two-fermion irreducible vertex
• Lattice study of $J/\psi \to \gamma {\eta }_c$ using a method without momentum extrapolation
• Lattice QCD calculation of the Compton amplitude subtraction function