EDMeDM (Electric Dipole Moment of the Electron in Diatomic Molecules) Principal Investigator: Timo Fleig, Collaborators: Malaya K. Nayak (Mumbai), Trond Saue (Toulouse), Mikhail G. Kozlov (St. Petersburg) Students: Malika Denis The Search for Physics Beyond the Standard Model State of the Art The Standard Model (SM) of elementary particle physics is not the final microscopic theory of the universe. Its success being beyond question, the SM exhibits striking shortcomings. Apart from the fact that it does not unify all four forces of nature in one common framework, the SM fails to explain the very origin of matter. According to the SM, both particles and their antiparticles should have been produced in (nearly) equal amounts in the early stages of the universe. Yet, we observe an enormous surplus of denominational matter over antimatter, the so-called Baryon Asymmetry of the Universe (BAU). This is one of the great unsolved problems in physics. Electric Dipole Moments (EDMs) as Source of P and T Violation The existence of electric dipole moments of elementary particles (in particular of leptons) would indicate P.and.T-violation and by virtue of the CPT theorem, (CP)-violation. This is one of Sakharov's three conditions which have to be met for explaining the BAU. If an electron, for instance, had a non-vanishing electric dipole moment, the ensuing interaction with an external electric field would be Parity (P) and Time-reversal (T) violating. Such a dipole moment is assumed to be induced by fundamental interactions with other particles. Within the framework of the SM, the EDM of the electron could have a non-zero value. However, since the only known CP-violating mechanism in the SM involves mesons with non-zero strangeness or bottomness, higher-order loop diagrams with virtual quark-antiquark pairs are required for producing an electron EDM. Its value is in this context therefore immeasurably small, on the order of 10-38 e cm. Extensions to the SM such as Grand Unified Theories (GUT) and SuperSymmetric models comprise new sources of (CP)-violation which entails many orders of magnitude larger values of particle EDMs. In Minimal Supersymmetric Extensions to the SM a host of new particles is assumed to exist which would allow for one-loop induced EDMs, boosting the electron's value to an order of 10-27 e cm. Such a value reaches into the measurable range of today's modern experiments. Electric dipole moments are unparalleled probes for new (CP)-violation with a sensitivity beyond the reach of the Large Hadron Collider (LHC) for direct detection! What are we heading for ? The search for EDMs of elementary particles is, therefore, also the search for New Physics (NP) beyond the SM. However, not only the spectacular goal of detecting an EDM is of interest. NOT detecting an EDM in a certain range of values is one important of many guides on how possible extensions to the SM, consistent NP theories, should be conceived. Other symmetry-violating interactions accessible by our methods are the scalar-pseudoscalar electron nucleon interaction (ENSPS, P.and.T-odd), the nuclear magnetic quadrupole moment - electronic magnetic field interaction (P.and.T-odd), and the nuclear anapole moment (P-odd).

Theory Project The EDM of the electron cannot be measured directly. In all modern experiments an energy shift or a transition energy in an atom or molecule due to an EDM is measured, from which the particle's EDM can be interpreted by means of a many-body calculation. The determination of this factor which relates the atomic physics to the particle physics scale is one of the major objectives of our work. Thus, the knowledge of the internal electric field interacting with the electron in the many-particle system is required. We have recently implemented the respective P,T-odd interaction Hamiltonian into our Kramers-Restricted Configuration Interaction method. This method allows for the computation of P,T-odd matrix elements as expectation values over correlated four-component relativistic CI wavefunctions. The new method has been and is currently being applied to various diatomic molecules which have been identified as promising candidates in the search for the electron EDM. Among them are HfF+, ThO, ThF+, and WC. The currently most constraining upper bound to the electron EDM has been obtained from experimental and theoretical studies on ThO (ACME collaboration and own work). The measure for the P,T-odd interaction is the effective electric field at the position of an unpaired electron in the molecule (for an electron pair in a closed shell the energy shifts cancel out). The studies on heavy-element molecules are challenging and typically require an accurate description of molecular electronically excited states, including the effects of special relativity. Our approaches take all atomic electrons into account explicitly, and limit the number of explicit electrons for correlation calculations to valence and outer core shells. If the experimental upper bound to the molecular EDM is interpreted in terms of the electron EDM by dividing this upper bound by the calculated effective electric field, the electron EDM upper bound results. It currently (January 2019) has the value |de| < 1.3 x 10-29 e cm. The figure to the left shows the ensuing constraint on theories going beyond the SM (click on the image). Strictly speaking, only theories to the right of the eEDM bar are still valid possibilities as extensions to the SM. However, accidental cancellations of for instance eEDM and ENSPS effects may lead to a too low upper bound. Moreover, NP theories are susceptible to varying predictions of EDMs based on freedom in their parameter spaces. News Section (12-2016) TaO+ proposed as promising candidate for New Physics searches (11-2016) New electron EDM and ne-SPS interaction constants for ThO determined. (04-2015) TaN spectrum and P,T-odd constants determined (06-2013) ANR grants financing for EDMeDM as one of 15 projects and the only theory project on the principal list (A list). Recent Publications Model-independent determinations of the electron EDM and the role of diamagnetic atoms Timo Fleig and Martin Jung J High Energy Phys (JHEP) 07 (2018) 012 arXiv:1802.02171 (please refer to full JHEP paper, above) P,T-Odd and Magnetic Hyperfine Interaction Constants and Excited-State Lifetime for HfF+ Timo Fleig Phys Rev A 96 (2017) 040502(R) arXiv:1706.02893 (please refer to full PRA paper, above) TaO+: A candidate molecular ion for searches of physics beyond the standard model Timo Fleig Phys Rev A 95 (2017) 022504 arXiv:1611.08741 (please refer to full PRA paper, above) Topic Related Bibliography The Electric dipole moment of the Electron. E. D. Commins and D. DeMille , Advanced Series on Directions in High-Energy Physics - Vol. 20, Chapter 14 (2009) Electric dipole moments in the {MSSM} reloaded. J. Ellis, J. S. Lee, and A. Pilaftsis, J. High Energy Phys. 10 (2008) 49 Electric dipole moments as probes of new physics. M. Pospelov and A. Ritz, Ann. Phys. 318 (2005) 119 Electric Dipole Moments of Leptons. E. D. Commins, Adv. Mol. Opt. Phys. 40 (1999) 1 CP Violation Without Strangeness. I. B. Khriplovich and S. K. Lamoreaux, Springer (Berlin, Heidelberg), 1997 Topic Related Links Advanced Cold Molecule Electron EDM (ACME) Collaboration. DeMille (Yale), Doyle (Harvard), Gabrielse (Harvard) JILA electron EDM search using trapped molecular ions. Cornell (Boulder)