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The implications of a precise electron measurement

14 November 2018

A recent determination of the electron’s electric dipole moment constrains supersymmetric and other theories of new physics.

ACME optics
Lasers in the ACME experiment orient and excite molecules so that researchers can probe the electron’s electric dipole moment. Credit: Loic Anderegg

Six years after CERN’s Large Hadron Collider (LHC) discovered the Higgs particle, the last missing piece of the standard model, many of the biggest mysteries in physics remain. For instance, why is gravity so dramatically weak compared with the other fundamental forces? And why does our universe contain ordinary matter but almost none of the antimatter with opposite electric charge?

Very precise measurements of the electron might help us answer such questions. Andrei Sakharov showed that obtaining more matter than antimatter in the universe requires the violation of CP symmetry, which in quantum field theory is equivalent to time-reversal symmetry T (see the article by Helen Quinn, Physics Today, February 2003, page 30). The standard model does have a CP-violating parameter, called the Cabibbo-Kobayashi-Maskawa (CKM) phase, but it is not sufficient to explain the matter–antimatter asymmetry. Physics beyond the standard model is needed. We expect that new physics might lie near the weak mass scale of about 100 GeV, around the masses of the W and Higgs bosons, which would offer the additional benefit of explaining why the weak force is so much stronger than gravity.

One kind of experiment plays a leading role in testing for CP violation at, or even beyond, energies associated with the weak scale: measurements of the electric dipole moment of the electron. A new limit on electron EDM from the Advanced Cold Molecule Electron EDM (ACME) collaboration, reported recently in Nature, places important constraints on theories that introduce new physics, including supersymmetry theories. Subsequent EDM measurements, which are performed in quarters far more confined than a particle accelerator, will either rule out other theories or confirm a fresh source of CP violation. Indeed, an office-size experiment in a basement could change the course of particle physics.

The EDM is a quantity proportional to the spin of a particle. The corresponding Hamiltonian, H = d · E (d is the EDM and E is an electric field), breaks parity and time-reversal symmetry, so it has potential to explain the matter–antimatter asymmetry.

Electron EDM illustration
In this illustration, virtual particles surround an electron as it spins on its axis. Credit: Nicolle R. Fuller, NSF

Researchers including the ACME collaboration at Harvard University’s Jefferson Laboratory have measured the electron EDM for years. The effort is motivated by the fact that the standard model cannot give a large enough electron EDM to be observed even in future measurements. The discovery of a nonzero EDM would clearly indicate new physics. Theoretical models that introduce additional CP violation typically generate sizable EDMs through quantum loops of virtual new particles (see the article by Norval Fortson, Patrick Sandars, and Steve Barr, Physics Today, June 2003, page 33).

The ACME team is led by David DeMille of Yale University, John Doyle of Harvard University, and Gerald Gabrielse of Northwestern University. In 2013 their collaboration placed the world’s strongest upper limit on the electron EDM. This year they broke their own record. The upper limits are actually for the EDM of the thorium monoxide molecule, but by a reliable molecular calculation, we can relate this molecular EDM to the electron EDM de. (For details about the experimental methods, we recommend a recent interview with Doyle.) The new experimental bound is | de | < 1.1 × 10–29 e cm, almost a factor of 9 better than the 2013 limit.

The measured limit is extremely small. So what does it mean for physics beyond the standard model? In addition to potentially flagging a new source of CP violation, the EDM is sensitive to two aspects of new particles: their mass and the degree to which they interact with the electron. The EDM scales as the inverse square of a heavy particle mass, because heavy particles can influence the electron only through highly virtual quantum fluctuations. Thus, every order of magnitude improvement in the EDM constraint effectively triples the mass reach. Notably, the mass reach of EDM experiments is increasing much more quickly than that of collider experiments.

ACME can rule out new particles that interact directly with the electron (generating the EDM at “one loop” order in perturbation theory) up to a whopping 50 TeV. Compare that with LHC constraints, which at most reach a few TeV. The most exciting aspect of ACME may be its ability to see even more indirect interactions. Any new particles that interact with the Higgs boson and weak gauge bosons can produce an EDM at two-loop order. ACME tests such particles up to about 3 TeV. Hence it rules out very general new physics with electroweak interactions at energies comparable to or higher than what the LHC can test.

The figure below shows how the versatility of an experiment—the variety of new physics it can test—compares with its mass reach. The LHC has less reach in mass but can see particles that don’t violate any symmetry, whereas EDMs have better reach but need CP violation. Other “flavor physics” experiments that look for one type of quark changing into another can probe even higher masses but in even more restricted types of theories.

Mass reach vs genericity
Various methods of finding new physics trade off the detectable range of masses with the exoticness of the physics at work. The Large Hadron Collider can find very generic kinds of particles up to a few TeV. Electric dipole moment searches can probe masses an order of magnitude higher, but only if there is CP violation. Credit: Yuichiro Nakai and Matthew Reece

Supersymmetry (SUSY), which exchanges bosons with fermions, is a top candidate for new physics. The SUSY extension of the standard model contains many superpartner particles and allows for many CP-violating interactions. The mass estimates in the figure also apply to SUSY, as we showed in detail in a recent study. For example, the electron’s superpartner, the selectron, produces an EDM at one loop and must be very heavy. More sophisticated variations on SUSY, including natural SUSY and split SUSY, can produce a dominant EDM at two loops, but even those theories are more strongly constrained by ACME than by the LHC.

All of this, of course, assumes that SUSY violates CP. A key question for future research is whether appealing theories of SUSY exist that predict small enough CP violation to avoid EDM constraints while remaining compatible with the measured CKM phase and the large and growing set of LHC results.

With its improved upper limit on the electron EDM, the ACME collaboration has constrained the new-physics models that are possible in the presence of CP violation. A future discovery of a nonzero value for the electron EDM (or the EDM of the proton or one of the other particles under study) would have a gigantic impact on particle physics. Measuring a nonzero EDM would not tell us exactly what new physics generated the EDM. We would need a more direct test. Thus the discovery of EDMs could become a driving force for constructing a new high-energy collider. In the meantime, there are proposals by the ACME collaboration and others to measure EDMs even more precisely in the near future.

Yuichiro Nakai is a high-energy theorist at Rutgers University. Matthew Reece is a theoretical particle physicist and John L. Loeb Associate Professor of the Natural Sciences at Harvard University. They are coauthors of a theoretical analysis of the ACME results; neither is part of the ACME team.

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