Constraining new physics models with isotope shift spectroscopy

Isotope shifts of transition frequencies in atoms constrain generic long- and intermediate-range interactions. We focus on new physics scenarios that can be most strongly constrained by King linearity violation such as models with $B-L$ vector bosons, the Higgs portal, and chameleon models. With the anticipated precision, King linearity violation has the potential to set the strongest laboratory bounds on these models in some regions of parameter space. Furthermore, we show that this method can probe the couplings relevant for the protophobic interpretation of the recently reported Be anomaly. We extend the formalism to include an arbitrary number of transitions and isotope pairs and fit the new physics coupling to the currently available isotope shift measurements.

Figure 1

Constraints on a $Z^{\prime }$ gauge boson from $U(1{)}_{B-L}$. KLV bound from existing IS data: ${\mathrm{Ca}}^{+}$ with uncertainty $\sigma \simeq 0.1\mathrm{MHz}$ (397 nm vs 866 nm [32], solid red line). KLV projections for $\sigma =1\mathrm{Hz}$ assuming linearity in ${\mathrm{Ca}}^{+}$ ($S\to D$ transitions, red, dashed), ${\mathrm{Sr}}^{+}$ (blue, dotted), $\mathrm{Sr}/{\mathrm{Sr}}^{+}$ (blue, dashed), and ${\mathrm{Yb}}^{+}$ (black, dash-dotted) [26]. For comparison, bounds from fifth-force searches via the Casimir effect [44, 45] (blue), neutron scattering [46, 47, 48] (orange), Rydberg states [49, 50, 51] (dark blue), energy level shifts in H and He [11] (turquoise), $\nu -e$ scattering at GEMMA and Borexino [41] (purple), and beam dump experiments [2, 3, 52] (green). Astrophysical and cosmological probes (beige): supernova 1987A with $\mathcal{O}(1)$ uncertainties [53, 54, 55] (SN, the area below the dotted line), horizontal branch stars [53, 56, 57, 58, 59] (HB, the area left of the dashed line) and Big Bang nucleosynthesis (BBN) via $N_{\mathrm{eff}}$ [42, 60] (the area above the solid line).

Figure 2

Existing bounds on the neutron coupling $g_n$ of a new boson $\varphi$ from the neutron-electron scattering length in Pb, Bi, and noble gases denoted as neutron optics [46] (orange, dashed); $n\text{−}{}^{208}\mathrm{Pb}$ scattering at neutron energies of $E_n\sim 1-26\mathrm{keV}$ [61] (green, dotted), 10 eV–10 keV [46] (blue, solid) and up to 20 keV including interference of resonant and nonresonant amplitudes [48] (purple, dotted); and the comparison of the total to the forward-scattering cross section of neutrons on nuclei [47] (red, dash-dotted). For discussion see Sec. 4a1.

Figure 3

Bounds of 95% C.L. on $y_e$ and $y_n$ for a protophobic vector boson of mass $m_X=17\mathrm{MeV}$. The gray region represents the required and allowed couplings to explain the ${}^8\mathrm{Be}$ anomaly. The dashed lines show the projected upper bounds on the couplings from KLV measurements in $\mathrm{Sr}/{\mathrm{Sr}}^{+}$ and ${\mathrm{Yb}}^{+}$.