The ultra-cautious quest to find the shape of the electron

Studies that test certain physical properties with pinpoint accuracy are gaining popularity these days because many physicists are intensely looking for small flaws too small for them to notice without taking a closer look in a powerful yet incomplete theory. This is the standard model of particle physics.

It predicts the existence of different particles; the last of these to be found was the Higgs boson, in 2012. But while the model is incomplete, its zoo of particles and their combined interactions haven’t been able to explain much about nature and the universe. For example, the model does not say what dark matter is and cannot explain dark energy. He doesn’t know why the Higgs boson is so heavy or why gravity is so much weaker than the other fundamental forces.

Where did the antimatter go?

The model also predicts that when the universe was created it should have contained equal amounts of matter and antimatter, which is clearly not the case.

Equal amounts of the two substances would have annihilated each other, releasing energy in the form of light, so the universe should have been full of light. Yet today the universe contains large amounts of matter and no antimatter. This is an important avenue of research in the quest to find a flaw in the Standard Model, an edge that is incomplete and could pave the way for new physics to solve some or all of these mysteries.

In a new study Posted in Science, researchers at the University of Colorado, Boulder, reported that they could not find evidence for certain types of this new physics in an experiment with electrons. This experiment researched the evidence with the greatest precision to date.

The negative result is important because it will tell physicists which alternative theories are feasible. For example, if a theory predicts that an electron would make X in the presence of a very strong electric field, but the results of new studies disagree, then physicists now know how to modify their theory to prevent this possibility. The previous result of a different experiment told physicists that the evidence they were looking for would not be found at the Large Hadron Collider in Europe.

Sakharov’s conditions

In 1967, Soviet physicist (and Nobel Peace Prize laureate) Andrei Sakharov examined the problem of matter-antimatter asymmetry and proposed a set of conditions which, if fulfilled, would allow the universe to produce more matter and antimatter. These are (i) the violation of the number of baryons, (ii) the violation of C and CP symmetries, and (iii) the rate of production of baryons must be slower than the rate of expansion of the universes.

One of the fundamental particles that make up matter is the quark. A baryon is a particle made up of three quarks. Examples include the proton and the neutron. Each baryon is assigned a baryon number: the number of quarks minus the number of antiquarks, divided by 3. When a baryon interacts with another particle according to the rules of the Standard Model, the number of baryons is preserved, i.e. the total number of baryons at the start of the interaction must equal the number at the end.

But Sakharov’s first condition is that for matter to take over antimatter, this rule must be broken in an interaction. That is, this interaction should produce more baryons than anti-baryons (i.e. a baryon composed of anti-quarks).

C symmetry is short for charge conjugation symmetry. Charge conjugation is a process that replaces a particle with its antiparticle and therefore reverses its charge (positive to negative or negative to positive). If symmetry C is violated, then there will also be more process which produce baryons than those which produce anti-baryons.

Like C symmetry, P symmetry refers to parity symmetry: if a particular interaction between particles is valid, then its mirror image, i.e. how you might see the interaction in a mirror, should also be valid. CP symmetry refers to an interaction that together violates C symmetry and P symmetry.

Sakharov’s final condition is that the rate at which baryons and anti-baryons are produced must be exceeded by the expansion of the universes. This follows from a simple principle. Consider a hypothetical chemical reaction: A + B VS + D. During the reaction, the amount of A + B will decrease as the amount of VS + D will accumulate. This could cause the reaction to be reversed: VS + D A + B. To prevent such an inversion, the simplest thing to do is to identify a condition that allows A + B VS + D But no VS + D A + Blike, for example, maintaining a high temperature and then applying this condition.

Similarly, Sakharov’s third condition states that the universe must expand faster than the rate at which baryons are produced, so that a compensatory reverse process does not occur that increases the number of anti-baryons.

So far, physicists have discovered C and CP symmetry violation, but only in particles containing quarks. The resulting matter-antimatter asymmetry is insufficient to explain the dominance of matter in the universe today. This means that there should be new physics, i.e. an extension of the Standard Model, which allows more violation of CP symmetry.

The electronic dipole moment

CP symmetry is a dyadic symmetry, it has two parts that are actually part of a larger triadic symmetry called CPT. T is for time, and the symmetry T means that a particle interaction in a direction that is favored in forward time must be favored in the reverse direction as time flows backward. In other words, the laws of physics are the same forwards and backwards in time. Violation of CP symmetry is considered equivalent to violation of T symmetry.

In their new study, researchers from the University of Colorado checked whether the electric charge of an electron is located in its center or slightly offset to one side. If it is well extinguished, the electron would have a dipole: more negative charge on one side of the particle and more positive charge on the other. And such a dipole will defy T symmetry.

The dipole has a force, called the dipole moment, which depends on the offset of the charge of the electrons. If time were reversed, (an electron spin) would reverse and the (electric dipole moment) would not, looking fundamentally different from before the time reversal, independent physicists Mingyu Fan and Andrew Jayich of the University of California, Santa Barbara wrote in a comment accompanying the new paper in Science.

The standard model allows the electron to have an electric dipole moment of up to 10^-38e cm (e is the electron charge). Anything more than that and the model will break, signaling the effect of new physics.

The electron electric dipole moment (eEDM) finding experiment measured the energy difference between two states of an electron one when its spin is in the direction of an external electric field and the other when its spin is aligned opposite to that of the field. In the absence of eEDM, the energy difference should be zero. If an eEDM is present, one of the electronic states should have a little more energy, and the difference can be used to calculate its value.

Sophisticated techniques

The difference is more pronounced when the external electric field is stronger. Technology has advanced so much that physicists can apply extremely strong fields in their labs, but the strongest still exist in nature. In the new study, physicists investigated valence electrons in hafnium fluoride (HfF) molecules, which exerted an electric field of about 23 billion V/cm more than 10,000 times stronger than what researchers can create in the lab, albeit over shorter distances.

The study is easier explained than done, requiring a suite of sophisticated instruments and techniques, some to make the measurements, others to reduce noise and uncertainty in the resulting data, given the small values ​​involved. The research team ionized thousands of HfF molecules and held them in a trap, using lasers to bring them to particular energy states. An external magnetic field was applied to cancel noise in certain parts of the trap. A small electric field was also applied to orient the molecules.

Once the setup was ready, the team created the electrons in both energy states and then measured the energy difference between them using a technique called Ramsey spectroscopy.

According to a paper 2013 by Huanqian Loh, then a PhD student at the University of Colorado, an eEDM measurement is more sensitive if the external electric field is stronger, if the measurement is coherent for longer, and if the signal-to-noise ratio is higher (that is, if an electron switches more often between the two states). So, in order to make a more sensitive measurement, the team had to optimize for all of these attributes.

In the end, the team estimated the electron eEDM to be less than 4.1 10^-30e cm with a confidence level of 90%. The team’s paper said the result is consistent with zero and improves on the previous best upper bound by a factor of about 2.4. The measurement is still eight orders of magnitude above the limit allowed by the Standard Model, but it is useful because it approximates the previous measurement.

Since the result is consistent with zero up to a certain energy level, it also rules out the existence of new hypothetical physical particles up to that level. Drs. Fan and Jayich hailed the involvement when they compared the team’s feat, achieved with a device that fits on a table, to that of the Large Hadron Collider at CERN, which costs about $4.75 billion to build and $1 billion to operate each year, and probes nature down to a lower energy level, albeit differently.

Insights from eEDM measurements on multiple systems would help guide requirements for a future high-energy particle collider that could create the time-symmetry violating particles responsible for the matter-antimatter asymmetry in the early universe, the commentary notes.