Parity-violating interactions of cosmic fields with atoms, molecules, and nuclei: Concepts and calculations for laboratory searches and extracting limits

We propose methods and present calculations that can be used to search for evidence of cosmic fields by investigating the parity-violating effects, including parity nonconservation amplitudes and electric dipole moments, that they induce in atoms. The results are used to constrain important fundamental parameters describing the strength of the interaction of various cosmic fields with electrons, protons, and neutrons. Candidates for such fields are dark matter (including axions) and dark energy, as well as several more exotic sources described by standard-model extensions. Calculations of the effects induced by pseudoscalar and pseudovector fields are performed for H, Li, Na, K, Cu, Rb, Ag, Cs, Ba, ${\mathrm{Ba}}^{+}$, Dy, Yb, Au, Tl, Fr, and ${\mathrm{Ra}}^{+}$. Existing parity nonconservation experiments in Cs, Dy, Yb, and Tl are combined with these calculations to directly place limits on the interaction strength between the temporal component, $b_0$, of a static pseudovector cosmic field and the atomic electrons, with the most stringent limit of $|b_0^e|<7\times {10}^{-15}\mathrm{GeV}$, in the laboratory frame of reference, coming from Dy. From a measurement of the nuclear anapole moment of Cs, and a limit on its value for Tl, we also extract limits on the interaction strength between the temporal component of this cosmic field, as well as a related tensor cosmic-field component $d_{00}$, with protons and neutrons. The most stringent limits of $|b_0^p|<4\times {10}^{-8}\mathrm{GeV}$ and $|d_{00}^p|<5\times {10}^{-8}$ for protons and $|b_0^n|<2\times {10}^{-7}\mathrm{GeV}$ and $|d_{00}^n|<2\times {10}^{-7}$ for neutrons (in the laboratory frame) come from the results using Cs. Axions may induce oscillating parity- and time reversal-violating effects in atoms and molecules through the generation of oscillating nuclear magnetic quadrupole and Schiff moments, which arise from $P$- and $T$-odd intranuclear forces and from the electric dipole moments of constituent nucleons. Nuclear spin-independent parity nonconservation effects may be enhanced in diatomic molecules possessing close pairs of opposite-parity levels in the presence of time-dependent interactions.

Figure 1

Fundamental vertex for the interaction of an electron with a pseudoscalar cosmic field $\varphi$ via the coupling (1).

Figure 2

Fundamental vertex for the interaction of an electron with a pseudovector cosmic field $b_{\mu }$ via the coupling (10).

Figure 3

Example Feynman–Goldstone diagram for the contribution to the cosmic PNC transition (33) in thallium arising from the double core polarization by the PNC cosmic-field (cross) and the electric-dipole (dot) interaction. The 6s state is treated as a state in the core. The wavy line is the Coulomb interaction with multipolarity $k$.