Sensitivity of EDM experiments in paramagnetic atoms and molecules to hadronic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>C</mml:mi><mml:mi>P</mml:mi></mml:math> violation
V. V. Flambaum, M. Pospelov, Adam Ritz, Y. V. Stadnik
Abstract
Experiments searching for the electric dipole moment (EDM) of the electron ${d}_{e}$ utilize atomic/molecular states with one or more uncompensated electron spins, and these paramagnetic systems have recently achieved remarkable sensitivity to ${d}_{e}$. If the source of $CP$ violation resides entirely in the hadronic sector, the two-photon exchange processes between electrons and the nucleus induce $CP$-odd semileptonic interactions, parametrized by the Wilson coefficient ${C}_{\mathrm{SP}}$, and provide the dominant source of EDMs in paramagnetic systems instead of ${d}_{e}$. We evaluate the ${C}_{\mathrm{SP}}$ coefficients induced by the leading hadronic sources of $CP$ violation, namely, nucleon EDMs and $CP$-odd pion-nucleon couplings, by calculating the nucleon-number-enhanced $CP$-odd nuclear scalar polarizability, employing chiral perturbation theory at the nucleon level and the Fermi-gas model for the nucleus. This allows us to translate the ACME EDM limits from paramagnetic ThO into novel-independent constraints on the QCD theta term $|\overline{\ensuremath{\theta}}|<3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}$, proton EDM $|{d}_{p}|<2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}23}\text{ }\text{ }e\text{ }\mathrm{cm}$, isoscalar $CP$-odd pion-nucleon coupling $|{\overline{g}}_{\ensuremath{\pi}NN}^{(1)}|<4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$, and color EDMs of quarks $|{\stackrel{\texttildelow{}}{d}}_{u}\ensuremath{-}{\stackrel{\texttildelow{}}{d}}_{d}|<2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}24}\text{ }\text{ }\mathrm{cm}$. We note that further experimental progress with EDM experiments in paramagnetic systems may allow them to rival the sensitivity of EDM experiments with neutrons and diamagnetic atoms to these quantities.