Unraveling the proton puzzle: The discrepancy between the proton size deduced from the Lamb shift in muonic hydrogen and the average, textbook value based on regular (electronic) hydrogen has puzzled physicists for nearly a decade. One possible resolution could be that electrons interact with protons in a different way than muons do, which would require “new physics.” Bezginov et al. measured the Lamb shift in electronic hydrogen, which allowed for a direct comparison to the Lamb shift measured in muonic hydrogen. The two results agreed, but the discrepancy with the averaged value remains. Science , this issue p. 1007

Because molecules can have their orientation locked when embedded into a solid rare-gas matrix, their hyperfine structure is strongly perturbed relative to the freely rotating molecule. The addition of an electric field further perturbs the structure, and we have found an interesting effect: the Stark shift of the hyperfine states in these molecules depends on the molecular orientation. These shifts enable the selective detection of molecules with different orientations relative to the axes of a rare-gas crystal, which will be an important ingredient of an improved electron electric dipole moment measurement using large ensembles of polar molecules trapped in rare-gas matrices. We outline an experimental procedure exploiting the orientation-dependent detection, which could be used for a significantly improved measurement of the electron electric dipole moment.

The line center of a resonance is affected by the presence of neighboring resonances due to quantum interference between the two resonant processes. Such shifts must be accounted for in high-precision measurements but are easily overlooked. In the present work, we develop an analytic formulation for the effect in the simplest case of a three-level atom. The shifts in this model system are large enough to be of concern for precision measurements.

We present tables for the bound-state energies for atomic hydrogen. The tabulated energies include the hyperfine structure and thus this work extends the work of Mohr et al. [P. J. Mohr et al., Rev. Mod. Phys. 84, 1527 (2012)], which excludes the hyperfine structure. The tabulation includes corrections of the hyperfine structure due to the anomalous moment of the electron, due to the finite mass of the proton, and due to off-diagonal matrix elements of the hyperfine Hamiltonian. These corrections are treated incorrectly in most other works. Simple formulas valid for all quantum numbers are presented for the hyperfine corrections. The tabulated energies have uncertainties of less than 1 kHz for all states. This accuracy is possible because of the recent precision measurement [R. Pohl et al., Nature (London) 466, 213 (2010)] of the proton radius. The effect of this radius on the energy levels is also tabulated and the energies are compared to precision measurements of atomic hydrogen energy intervals.

We propose a very sensitive method for measuring the electric dipole moment of the electron using polar molecules embedded in a cryogenic solid matrix of inert-gas atoms. The polar molecules can be oriented in the $\widehat{\mathrm{z}}$ -direction by an applied electric field, as has recently been demonstrated by Park et al. The trapped molecules are prepared into a state that has its electron spin perpendicular to $\widehat{\mathrm{z}}$ , and a magnetic field along $\widehat{\mathrm{z}}$ causes precession of this spin. An electron electric dipole moment $d_e$ would affect this precession due to the up to 100 GV/cm effective electric field produced by the polar molecule. The large number of polar molecules that can be embedded in a matrix, along with the expected long coherence times for the precession, allows for the possibility of measuring $d_e$ to an accuracy that surpasses current measurements by many orders of magnitude. Because the matrix can inhibit molecular rotations and lock the orientation of the polar molecules, it may not be necessary to have an electric field present during the precession. The proposed technique can be applied using a variety of polar molecules and inert gases, which, along with other experimental variables, should allow for careful study of systematic uncertainties in the measurement.

Precisely measured electron-proton elastic scattering cross sections [ Phys. Rev. Lett. 105, 242001 (2010)] are reanalyzed to evaluate their strength for determining the rms charge radius ($R_{\mathrm{E}}$) of the proton. More than half of the cross sections at lowest $Q^2$ are fit using two single-parameter form-factor models, with the first based on a dipole parametrization, and the second on a linear fit to a conformal-mapping variable. These low-$Q^2$ fits extrapolate the slope of the form factor to $Q^2=0$ and determine $R_{\mathrm{E}}$ values of approximately 0.84 and 0.89 fm, respectively. Fits spanning all $Q^2$, in which the single constants are replaced with cubic splines at larger $Q^2$, lead to similar results for $R_{\mathrm{E}}$. We conclude that the scattering data are consistent with $R_{\mathrm{E}}$ ranging from at least 0.84 to 0.89 fm, and therefore is consistent with both of the discrepant determinations of $R_{\mathrm{E}}$ made using muonic and electronic hydrogen-atom spectroscopy.