Single pion contribution to the hyperfine splitting in muonic hydrogen

Abstract

A detailed discussion of the long-range one-pion exchange (Yukawa potential) contribution to the 2S hyperfine splitting in muonic hydrogen which had, until recently, been disregarded is presented. We evaluate the relevant vertex amplitudes, in particular ${\pi }^0{\mu }^{+}{\mu }^{-}$, combining low energy chiral expansions together with experimental data on ${\pi }^0$ and $\eta$ decays into two leptons. A value of $\Delta E_{HFS}^{\pi }=-(0.09\pm 0.06)\mu \mathrm{eV}$ is obtained for this contribution.

v2: Expanded and completed version

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Cited by in corpus (12)

• The proton structure in and out of muonic hydrogen
• Lamb shift in muonic ions of lithium, beryllium and boron
• The contribution of axial-vector mesons to hyperfine structure of muonic hydrogen
• Dissecting the hadronic contributions to $(g-2{)}_{\mu }$ by Schwinger's sum rule
• The contribution of pseudoscalar mesons to hyperfine structure of muonic hydrogen
• Corrections of two-photon interactions in the fine and hyperfine structure of the P-energy levels of muonic hydrogen
• Two-photon-exchange effects in the unpolarized $\mu p$ scattering within the hadronic model
• Left-right model for dark matter
• Axial-vector exchange contribution to the Hyperfine Splitting
• The light-by-light contribution to the muon anomalous magnetic moment from the axial-vector mesons exchanges within the nonlocal quark model
• Novel approach to measure the leptonic eta(')->mu+mu- decays via charmed meson decays
• The contribution of pseudoscalar and axial-vector mesons to hyperfine structure of muonic hydrogen