New calculation of electron self-energy improves determination of fundamental constants

After World War II, when quantum electrodynamics, the quantum field theory of electrons and photons, was being developed, one of the big challenges for theorists was the Lamb shift (the transition of an electron from one hydrogen The purpose was to calculate the value of (the energy of the photon produced by). Converts a hyperfine energy level to another level.

This effect was first detected in 1947 by Willis Lamb and Robert Rutherford. The emitted photon has a frequency of 1,000 megahertz, which corresponds to the wavelength of a photon of 30 cm and an energy of 1/4 millionth of an electron volt. microwave spectrum. It happened when one electron of a hydrogen atom transitioned from the 2P1/2 energy level to the 2S1/2 level. (The leftmost number is the principal quantum number, much like the Bohr atom’s discrete but increasing circular orbits.)

Traditional quantum mechanics has no such transition, and Dirac’s relativistic Schrödinger equation (of course called the Dirac equation) also has no such hyperfine transition. Because the shift is the result of interaction with the vacuum, and Dirac’s vacuum was an “ocean”. ” did not interact with real particles.

When theorists were working to create a viable quantum electrodynamics (QED) theory, QED calculations involved some of the theory’s notable complications, such as divergent integrals and singularities at both low and high energies. Predicting the ram shift was a big challenge because of the problems involved.

On Lamb’s 65th birthday in 1978, Freeman Dyson said to him, “Those days when Lamb shifts were the central theme of physics were the golden years for all physicists of my generation.” You are the first to see this small change, so elusive and difficult to measure, that it clarifies the way we think about particles and fields.

Accurately predicting Lamb shifts and the anomalous magnetic moments of electrons has been a challenge for every generation of theorists ever since. The theoretically predicted values ​​of the shifts allow us to measure the fine structure constants with uncertainties of less than parts in a million.

A new step in the evolution of Lamb shift calculations has now been published in Physical Review Letters by a group of three scientists from Germany’s Max Planck Institute for Nuclear Physics. More precisely, they calculated the self-energy of a “two-loop” electron.

Self-energy is the energy that a particle (here an electron) has as a result of the changes it causes in its environment. For example, the electrons in a hydrogen atom attract the atomic nucleus, the proton, so the effective distance between them changes.

QED has a prescription for calculating self-energy, and it is easiest to use Feynman diagrams. “Two-loop” refers to the Feynman diagram that describes this quantum process: two virtual photons from the quantum vacuum that affect the behavior of the electron. They fly out of the vacuum, stay for less time than dictated by Heisenberg’s uncertainty principle, and are then absorbed into the 1S electronic state with spin 1/2.

The two-loop self-energy description is one of three mathematical terms to describe the Lamb shift, but it is the major issue that most affects the outcome of the Lamb energy shift.

Lead author Vladimir Yerokhin and his colleagues determined that increase in accuracy from numerical calculations. Importantly, we calculated two-loop corrections for all orders of the key parameter Zα, which describes the interaction with the nucleus. (Z is the atomic number of the nucleus. The atom still has only one electron, but for generalization it contains a nucleus larger than hydrogen. α is the fine structure constant.)

Although computationally challenging, this trio adds to previous two-loop calculations of the electron self-energy that reduce the hydrogen 1S-2S Lamb shift by a frequency difference of 2.5 kHz and reduce its theoretical uncertainty. brought about significant improvements. In particular, this reduces the value of the Rydberg constant by a factor of one trillion.

This number was introduced by the Swedish spectroscopist Johannes Rydberg in 1890 and appears in a simple equation for the spectral lines of hydrogen. The Rydberg constant is a fundamental constant, one of the most precisely known constants in physics, containing 12 significant digits and previously having a relative uncertainty of about 2 parts in a trillion.

Overall, they conclude that “the computational approach developed in this letter allows us to improve the numerical accuracy of this effect by more than an order of magnitude and extend calculations to lower the nuclear charge (Z) further than previously possible. ” he wrote. This also affects the Rydberg constant.

Their methodology also influences other prominent QED calculations. Other two-loop corrections to the Lamb shift affect the two-loop QED effect, especially the anomalous magnetic moments of electrons and muons, also known as the “g-factor.” ” Significant experimental effort is currently being devoted to precisely determining the g-factor of muons, such as Fermilab’s muon g-2 experiment, which points the way to physics beyond the Standard Model. Because it’s possible.

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