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.

Comments: 7 pages + 3 pages supplemental material, 12 figures