Evidence of Two-Source King Plot Nonlinearity in Spectroscopic Search for New Boson

Optical precision spectroscopy of isotope shifts can be used to test for new forces beyond the standard model, and to determine basic properties of atomic nuclei. We measure isotope shifts on the highly forbidden ${{}^{2}S}_{1/2}\to {{}^{2}F}_{7/2}$ octupole transition of trapped ${}^{168,170,172,174,176}\mathrm{Yb}$ ions. When combined with previous measurements in ${\mathrm{Yb}}^{+}$ and very recent measurements in Yb, the data reveal a King plot nonlinearity of up to $240\sigma$. The trends exhibited by experimental data are explained by nuclear density functional theory calculations with the Fayans functional. We also find, with $4.3\sigma$ confidence, that there is a second distinct source of nonlinearity, and discuss its possible origin.

Figure 1

Frequency-normalized King plot (top) and residuals (bottom, blue) for the $\gamma$ (${{}^{2}S}_{1/2}\to {{}^{2}F}_{7/2}$) transition and reference transition $\alpha$ (${{}^{2}S}_{1/2}\to {{}^{2}D}_{5/2}$) for even-neighbor pairs ($A^{\prime }=A+2$) of ${\mathrm{Yb}}^{+}$ isotopes. A deviation from linearity (red line) by 41 standard deviations $\sigma$ is observed. For reference, residuals for the $\beta$ (${{}^{2}S}_{1/2}\to {{}^{2}D}_{3/2}$) transition [19], magnified 20-fold, are also plotted in gray. The error bars indicate $2\sigma$ uncertainties; for correlations between the errors, see Supplemental Material [24].

Figure 2

Decomposition of the measured nonlinearity (solid ellipses, 95% confidence interval) onto the (${\lambda }_{+}$, ${\lambda }_{-}$) basis for the transitions $\alpha :{{}^{2}S}_{1/2}\to {{}^{2}D}_{5/2}$ in ${\mathrm{Yb}}^{+}$ (blue) [19], $\beta :{{}^{2}S}_{1/2}\to {{}^{2}D}_{3/2}$ in ${\mathrm{Yb}}^{+}$ (green) [19], $\epsilon :{{}^{1}S}_0\to {{}^{1}D}_2$ (dark gray) in Yb [22], and $\gamma :{{}^{2}S}_{1/2}\to {{}^{2}F}_{7/2}$ in ${\mathrm{Yb}}^{+}$ (red, this work). The corresponding frequency-normalized King plot is generated with the reference transition $\delta :{{}^{1}S}_0\to {{}^{3}P}_0$ in Yb [21] (${\lambda }_{\pm }^{(\delta )}$) that has been measured with the highest frequency accuracy. The red dotted ellipse indicates a previous preliminary measurement for the $\gamma$ transition [61]. The dashed lines indicate the ratio ${\lambda }_{+}/{\lambda }_{-}$ that would arise solely from a new boson (light blue dashed line) or the QFS (pink dash-dotted line). The brown solid line is a single-source fit to all four transitions $\alpha$, $\beta$, $\gamma$, $\epsilon$, yielding evidence for a second nonlinearity source with $4.3\sigma$ significance (${\chi }^2=25.4$). The largest inset shows the nonlinearity in a King plot with $\alpha$ as the reference transition (${\lambda }_{\pm }^{(\alpha )}$). Open symbols indicate the nonlinearity due to ${\delta ⟨r^4⟩}^{A{A}^{\prime }}$ from nuclear DFT calculations with SV-min (square), RD-min (diamond), UNEDF1 (circle), and Fy($\mathrm{\Delta }r$) (star) energy density functionals. Short bold lines indicate the uncertainty in electronic-structure calculations (see Supplemental Material [24]).

Figure 3

(a) Comparison plot of derived values for the ratio of the mean-square nuclear radius differences between $(A,A+2)$ isotope pairs. Open symbols mark the values derived from nuclear calculations using SV-min, RD-min, UNEDF1, and Fy($\mathrm{\Delta }r$) energy density functionals (see Fig. 2 for symbol assignments). The red filled square symbols are values derived from measured ISs on the 411 nm transition in combination with mass shifts from configuration interaction (CI) [69, 70, 71, 72] calculations. (b) Plot of derived values for the ratio of the mean square nuclear radius between sequential isotope pairs as a function of $K_{\alpha }$, showing very weak dependence on $K_{\alpha }$. (c),(d) Derived values of $F_{\beta }$, $F_{\gamma }$, $F_{\delta }$, $F_{\epsilon }$ ($K_{\beta }$, $K_{\gamma }$, $K_{\delta }$, $K_{\epsilon }$) as a function of $F_{\alpha }$ ($K_{\alpha }$), using the experimentally determined ratios $F_{\kappa \alpha }$ ($K_{\kappa \alpha }$) for $\kappa =\beta ,\gamma ,\delta ,\epsilon$. In (b), (c), and (d), dashed (dotted) vertical lines and round (square) markers indicate values from CI calculations using GRASP2018 [73] (ambit [74]). Dash-dotted lines and open triangle markers correspond to CI and many-body perturbation theory ($\mathrm{CI}+\mathrm{MBPT}$) [75] calculations using ambit.

Figure 4

Product of coupling constants $y_e{y}_n$ of a new boson with spin $s$ versus boson mass $m_{\varphi }$, derived from generalized-King-plot analyses [14, 76] of groups of three transitions $(\alpha ,\gamma ,\delta )$ (blue), $(\gamma ,\delta ,\epsilon )$ (red), and $(\beta ,\gamma ,\delta )$ (green), assuming that the observed second nonlinearity is dominated by a new boson. Dashed lines indicate the lower bounds of $y_e{y}_n$’s excluded magnitude. Solid lines and shaded areas are center values and confidence intervals for configuration-interaction calculations using ambit. [we show the $\approx 95\%$ confidence interval (see Supplemental Material [24]) that arises from the statistical uncertainty in the measured ISs. The systematic uncertainty due to the atomic structure calculations is larger; the dash-dotted line shows the center value of $y_e{y}_n$ for the $(\alpha ,\gamma ,\delta )$ transition combination using GRASP2018 calculation results, for comparison.] The yellow line indicates the bound derived from electron $g_e-2$ measurements [77, 78, 79, 80] in combination with neutron scattering measurements [81, 82, 83, 84] from Ref. [10].