A new bound on the electron's electric dipole moment

Abstract: The Standard Model cannot explain the dominance of matter over anti-matter in our universe. This imbalance indicates undiscovered physics that violates combined CP symmetry. Many extensions to the Standard Model seek to explain the imbalance by predicting the existence of new particles. Vacuum fluctuations of the fields associated with these new particles can interact with known particles and make small modifications to their properties; for example, particles which violate CP symmetry will induce an electric dipole moment of the electron (eEDM). The size of the induced eEDM is dependent on the masses of the new particles and their coupling to the Standard Model. To date, no eEDM has been detected, but increasingly precise measurements probe new physics with higher masses and weaker couplings. Here we present the most precise measurement yet of the eEDM using electrons confined inside molecular ions, subjected to a huge intra-molecular electric field, and evolving coherently for up to 3 s. Our result is consistent with zero and improves on the previous best upper bound by a factor $\sim2.4$. Our sensitivity to $10^{-19}$ eV shifts in molecular ions provides constraints on broad classes of new physics above $10^{13}$ eV, well beyond the direct reach of the LHC or any other near- or medium-term particle collider.

• The paper establishes a refined upper bound of |d_e| < 4.1e-30 e.cm, improving previous limits by a factor of 2.4.
• The study employs quantum projection noise-limited spectroscopy on HfF+ ions trapped in a Paul trap, achieving sensitivity to energy shifts as low as 10⁻¹⁹ eV.
• The improved eEDM constraint challenges theories beyond the Standard Model, narrowing viable CP-violating extensions such as supersymmetry and multi-Higgs models.

Overview of the Electron Electric Dipole Moment Measurement

The paper under discussion presents an important advancement in the field of particle physics by providing a new, more precise upper limit on the electron's electric dipole moment (eEDM). This research effort is crucial because the existence of an eEDM signals CP symmetry violation, a phenomenon not fully accounted for by the Standard Model of particle physics. The Standard Model predicts an eEDM well below current experimental sensitivity, so the detection of a larger-than-expected eEDM could indicate new physics.

Experimental Methodology

The authors performed their experiment by confining electrons within molecular ions and subjecting them to strong intra-molecular electric fields. Specifically, they utilized HfF$^+$ molecular ions cooled and trapped in a radiofrequency Paul trap. The orientation of the electron's spin relative to the molecular axis in such an environment can lead to observable energy shifts if the eEDM is non-zero.

To measure these shifts, the authors employed quantum projection noise-limited spectroscopy across hundreds of molecular ions, with interrogation times extending up to 3 seconds. The method allowed for extreme sensitivity to energy shifts on the order of $10^{-19}$ eV, making it possible to probe potential new physics at energy scales exceeding those accessible by current particle accelerators, such as the LHC.

Results

The result of the measurement was consistent with zero, yielding $d_e = \si[parse-numbers=false]{-1.3 \pm 2.0_{\rm stat} \pm 0.6_{\rm syst}} \times 10^{-30}$ e.cm. Correspondingly, the upper bound at 90% confidence is $|d_e|< \SI{4.1e-30}{\electron\centi\meter}$. This result surpasses the previous measurements by a factor of approximately 2.4, which enhances the mass reach for new particles by 1.5 times.

Implications

The improved upper bound on the electron's eEDM has significant implications. It constrains several theories beyond the Standard Model, especially those predicting new particles or forces that violate CP symmetry. Such constraints are essential, as the current matter-antimatter asymmetry in the universe suggests that CP violation must occur beyond what is described by the Standard Model.

Moreover, the result narrows down the parameter space for various extensions of the Standard Model, such as supersymmetry and multi-Higgs models, where CP-violating effects could generate an eEDM within experimental reach. Specifically, the experiment sets a sensitivity limit that corresponds to new particle masses on the order of $M/g \gtrsim 40$ TeV, considering the phase ($\phi_{CP}$) responsible for CP violation is close to unity.

Future Directions

The research opens several avenues for future exploration. Experimental efforts could focus on enhancing sensitivity further by possibly using molecular species with even larger effective electric fields or by improving coherence times. From a theoretical perspective, more rigorous determination of underlying coupling constants and CP-violation parameters remains necessary. As tighter constraints are established, it encourages refinement or reconsideration of new physics models accounting for CP violation.

In summary, the study represents a methodical stride in detecting or confining violations of CP symmetry through precise eEDM measurements. It sets a foundation for continued exploration into the unknown physics that might elucidate the fundamental imbalances in the universe.