Standard model of particle physics tested by the fine-structure constant

A highly precise measurement of a physical constant known as the fine-structure constant provides a stringent test of the standard model of particle physics, and sets strong limits on the existence of speculative particles.
Holger Müller is in the Department of Physics, University of California, Berkeley, Berkeley, California 94720, USA.

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Every physicist knows the approximate value (1/137) of a fundamental constant called the fine-structure constant, α. This constant describes the strength of the electromagnetic force between elementary particles in the standard model of particle physics and is therefore central to the foundations of physics. For example, the binding energy of a hydrogen atom — the energy required to break apart the atom’s electron and proton — is about α2/2 times the energy associated with an electron’s mass. Moreover, the magnetic moment of an electron is subtly larger than that expected for a charged, point-like particle by a factor of roughly 1 + α/(2π). This ‘anomaly’ of the magnetic moment has been verified to ever-increasing accuracy, becoming “the standard model’s greatest triumph”1. Writing in Nature, Morel et al.2 report a measurement of α with an accuracy of 81 parts per trillion (p.p.t.), a 2.5-fold improvement over the previous best determination3.

The measurement of α involves three steps. First, a laser beam makes an atom absorb and emit multiple photons and, in doing so, recoil (Fig. 1a). The mass of the atom is deduced by measuring the kinetic energy of this recoil. Second, the electron’s mass is calculated using the precisely known ratio of the atom’s mass to the mass of an electron4,5 (Fig. 1b). Third, α is determined from the electron’s mass and the binding energy of a hydrogen atom, which is known from spectroscopy6 (Fig. 1c).

Figure 1

Figure 1 | Process for measuring the fine-structure constant. Morel et al.2 report a highly precise determination of the fine-structure constant — the physical constant that defines the strength of the electromagnetic force between elementary particles. a, In the measurement of this constant, a beam of light from a laser causes an atom to recoil. The red and blue colours correspond to the light wave’s peaks and troughs, respectively. The kinetic energy of the recoil is used to deduce the atom’s mass. b, The value of the atom’s mass is then combined with the precisely known ratio of the atom’s mass to the electron’s mass4,5 to infer the mass of an electron. c, Finally, the electron’s mass and the binding energy of a hydrogen atom are used to determine the fine-structure constant. The binding energy is known from spectroscopy6, whereby light emitted from a hydrogen atom is analysed.

However, the recoil energy is tiny and therefore hard to measure. Laser-based cooling of atoms has enabled physicists to carry out atom interferometry — a measurement technique that uses the interference of matter waves associated with the atoms. In an atom interferometer, atoms have a 50% probability of interacting with photons from laser pulses. Consequently, such atoms exist in two quantum states simultaneously: one in which they are at rest and the other in which they move, having absorbed the momentum of the photons.

This situation is equivalent to the production of two partial matter waves that move away from each other. These matter waves are recombined by firing more laser pulses, generating constructive or destructive interference (whereby the waves reinforce or cancel each other) and therefore a high or low probability of observing the atoms. The phase shift between the interfering waves — the displacement of one wave with respect to the other — is proportional to their travel time and the recoil energy.

Subsequent improvements to this approach have realized long travel times and interactions with many photons. In 2011, the research group behind the current breakthrough, at the Kastler–Brossel Laboratory in Paris, used the technique to determine α with an accuracy7 of 660 p.p.t. In the following year, scientists carried out a measurement of the electron’s anomalous magnetic moment to derive a standard-model prediction for α with an accuracy8 of 250 p.p.t. And in 2018, my team at the University of California, Berkeley, published an atom-interferometry determination of α that agreed with the previous one but pushed the accuracy3 to 200 p.p.t.

Now, Morel et al. have improved the accuracy to 81 p.p.t. In another triumph for the standard model, the measured value of α agrees with the standard-model prediction from the anomalous magnetic moment, even at such precision. This result confirms, for example, that the electron has no substructure and is truly an elementary particle. If it were made of smaller constituents, it would have a different magnetic moment, contrary to observation.

The measurement also places strong bounds on the existence of certain dark-sector particles, a speculative family of particles, some of which might constitute dark matter — the unseen matter component of the Universe. In quantum field theory, empty space is a sea of ‘virtual’ particles that spring into a brief existence. Virtual dark-sector particles would shift the electron’s magnetic moment in subtle, yet measurable ways.

However, there is a remaining puzzle. Although there is only a slight tension between each of the determinations of α and the standard-model prediction from the anomalous magnetic moment, there is a strong tension between Morel and colleagues’ latest measurement and its two predecessors. As shown in Figure 1 of their paper2, this situation is possible because the latest measurement and its predecessors deviate from the standard-model prediction in opposite directions.

The authors suggest that the difference between their research group’s own measurements could be caused by speckle — small-scale spatial variations of the laser intensity — or by a phase shift arising in electronic-signal processing. However, it is no longer possible to evaluate such a shift in the group’s earlier experiment, and speckle should produce a variation between the measurements in the opposite direction to that needed to explain the discrepancy.

Morel and colleagues also leave open the reason for the disparity with the 2018 measurement. The two experiments differ in the use of rubidium versus caesium atoms, in the types of atom–light interaction used and in how the laser beams are prepared and aligned. These choices imply different influences of the environment on the atoms.

For example, the largest corrections applied to data taken in both experiments arise from the laser beams. Both the speckle mentioned earlier and the overall beam profiles affect the magnitude and direction of the atom recoil. The discrepancy between the results could be explained if my team had over-corrected for these effects or Morel et al. had under-corrected. Most probably, it will take further experimental work to tell.

Experimenters are therefore gearing up to clarify the origin of this discrepancy and to challenge the standard model yet again. For example, my team is aiming to further improve the precision in the measured value of α by building an atom interferometer that enables unprecedented control over the laser-beam shape. Moreover, necessary improved measurements of atomic masses are already under way5. And finally, a refined determination of the electron’s anomalous magnetic moment is being prepared at Northwestern University in Illinois9. Together, these improvements will allow physicists to approach an accuracy of 10 p.p.t. At that point, the effects of the tau lepton — a heavier cousin of the electron — will be observed in the experiments and many hypothesized dark-sector theories could be probed.

Nature 588, 37-38 (2020)


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