Implications of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>R</mml:mi></mml:math>-parity violating supersymmetry for atomic and hadronic electric dipole moments

Abstract

We calculate the electric dipole moments (EDM) of the neutral $^{199}\mathrm{Hg}$ atom, deuteron, nucleons and neutral hyperons $\ensuremath{\Lambda}$, ${\ensuremath{\Sigma}}^{0}$ and ${\ensuremath{\Xi}}^{0}$ in the framework of a generic SUSY model without $R$-parity conservation (${\mathrm{R\ensuremath{\llap{\not\;}}}}_{p}\mathrm{SUSY}$) on the basis of the SU(3) version of chiral perturbation theory (ChPT). We consider $CP$-violation in the hadronic sector induced by the chromoelectric quark dipole moments and $CP$-violating 4-quark effective interactions. From the null experimental results on the neutron and $^{199}\mathrm{Hg}$ atom EDMs we derive limits on the imaginary parts of certain products $\mathrm{Im}({\ensuremath{\lambda}}^{\ensuremath{'}}{\ensuremath{\lambda}}^{\ensuremath{'}*})$ of the trilinear ${\mathrm{R\ensuremath{\llap{\not\;}}}}_{p}$-couplings and demonstrate that they are more stringent than those existing in the literature. Using these limits we give predictions for the EDMs of neutral hyperons. We also estimate the prospects of future storage ring experiments on the deuteron EDM and show that the expected improvement of the above limits in these experiments may reach several orders of magnitude.