The ultra-careful quest to find the shape of the electron’s charge

Scientists are trying hard to find a flaw in a powerful yet incomplete theory of physics, and the electron plays an important role in it.

July 24, 2023 10:30 am | Updated July 25, 2023 10:02 am IST

Representative illustration.

Representative illustration. | Photo Credit: geralt/Pixabay

Studies that test some physical property to an extreme precision are gaining in popularity these days because many physicists are intently looking for small chinks – too small for them to have noticed without a closer look – in a theory that is both powerful yet incomplete. This is the Standard Model of particle physics.

It predicts the existence of different particles; the last of them 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 many things about nature and the universe. For example, the Model doesn’t say what dark matter is and can’t explain dark energy. It 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 had equal quantities of matter and antimatter – which is clearly not the case.

The equal quantities 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 has large amounts of matter and no antimatter. This is one important line of inquiry in the quest to find a flaw in the Standard Model, an edge that is incomplete and could lead the way to a ‘new physics’ to resolve some or all of these mysteries.

In a new study published in Science, researchers from the University of Colorado, Boulder, have reported that they couldn’t find evidence of certain kinds of such ‘new physics’ in an experiment with electrons. This experiment looked for the evidence at the highest 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 do X in the presence of a very strong electric field, but the new study’s results disagree, then physicists now know to modify their theory to prevent this possibility. The previous such result from a different experiment told physicists that the evidence they were looking for wouldn’t be found at the Large Hadron Collider in Europe.

The Sakharov conditions

In 1967, the Soviet physicist (and Nobel Peace Prize laureate) Andrei Sakharov considered the matter-antimatter asymmetry problem and came up with a set of conditions that, if they’re met, would allow the universe to produce more matter and antimatter. These are (i) baryon number violation, (ii) C- and CP-symmetry violation, and (iii) baryon production rate must be slower than the universe’s expansion rate.

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

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

C-symmetry is short for ‘charge conjugation symmetry’. Charge conjugation is a process that replaces a particle with its anti-particle, and as a result flips its charge (positive to negative or negative to positive). If C-symmetry is violated, then there will also be more processes that produce baryons than those that 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 be equally valid. CP-symmetry refers to an interaction violating C-symmetry and P-symmetry together.

The final Sakharov condition is that the rate at which baryons and anti-baryons are produced should be outpaced by the universe’s expansion. This arises from a simple principle. Consider a hypothetical chemical reaction: A + BC + D. As the reaction proceeds, the quantity of A + B will dwindle while the quantity of C + D will accumulate. This could cause the reaction to reverse itself: C + DA + B. To prevent such a reversal, the simplest thing to do is to identify some condition that allows A + BC + D but not C + DA + B, like, for example, maintaining a high temperature, and then apply that condition.

Similarly, the third Sakharov condition stipulates that the universe should expand faster than the rate at which baryons are produced, so that a compensatory reverse process doesn’t arise that increases the number of anti-baryons.

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

The electron dipole moment

CP-symmetry is a dyadic symmetry – it has two parts – that is actually part of a larger triadic symmetry called CPT. ‘T’ is for time, and T-symmetry means that a particle interaction in one direction that is favoured in forward time should be favoured in the reverse direction when time flows backwards. That is, the laws of physics are the same forward and backward in time. CP-symmetry violation is considered to be equivalent to T-symmetry violation.

In their new study, the University of Colorado researchers checked whether the electric charge of an electron is located at its centre or is slightly off to one side. If it is indeed off, 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 strength, called the dipole moment, depending on how off-centre the electron’s charge is. “If time were reversed, [an electron’s spin] would flip and the [electric dipole moment] would not, looking fundamentally different from before time-reversal,” independent physicists Mingyu Fan and Andrew Jayich, of the University of California, Santa Barbara, wrote in a commentary 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’s charge). Anything more than this and the Model will break, signalling the effect of some ‘new physics’.

The experiment to look for the electron electric dipole moment (eEDM) 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 an eEDM, the energy difference should be zero. If an eEDM is present, one of the electron states should have slightly 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 to the extent that physicists can apply extremely powerful fields in their labs, but the most powerful still exist in nature. In the new study, the physicists studied valence electrons in molecules of hafnium fluoride (HfF), which exerted an electric field of around 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 smallness of values involved. The research team ionised 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 negate noise in 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 the two energy states and then measured the energy difference between them using a technique called Ramsey spectroscopy.

According to a 2013 paper by Huanqian Loh, then a doctoral 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 (i.e. if an electron flips more often between the two states). So in order to make a more sensitive measurement, the team had to optimise for all these attributes.

Ultimately, the team estimated that the electron’s eEDM to be lower than 4.1 × 10-30e cm at a 90% confidence. The team’s paper stated that the “result is consistent with zero and improves on the previous best upper bound by a factor of ~2.4.” The measurement is still eight orders of magnitude above the limit that the Standard Model allows, yet it is useful because it steps closer from the previous measurement.

Since the result is “consistent with zero” up to a certain energy level, it also precludes the existence of hypothetical ‘new physics’ particles up to that level.

“The new results don’t definitively exclude whole classes of hypotheses, but rather make the models that hypothesise the existence of particles with mass less than 4 TeV that much more improbable,” Eric Cornell, an adjoint professor at the University of Colorado and head of the group that made the new measurement, said. (To compare, a proton’s mass is 0.000938 TeV at rest.)

Drs. Fan and Jayich commended this implication when they compared the team’s feat, achieved with an “apparatus 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 run annually,” and probes nature up to a lower energy level, albeit differently.

“Knowledge from eEDM measurements across multiple systems would help guide the requirements of 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 noted.

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