Muonic Helium HFS

Introduction: A Unique Three-Body Atom

Beyond the familiar atoms of the periodic table lies a class of “exotic atoms” that provide a unique window into the fundamental laws of physics. One such atom is muonic helium ($\mu$He), formed when a negative muon (μ−) displaces one of the two electrons orbiting a helium nucleus. The muon, being 200 times heavier than an electron, settles into an orbit so close to the nucleus that it effectively screens one unit of the nuclear charge, creating a “pseudonucleus” with the magnetic properties of a muon. The resulting neutral atom—consisting of the helium nucleus, a negative muon, and one remaining electron—can be considered a very heavy isotope of hydrogen. This simple, yet exotic, three-body system is an ideal laboratory for testing bound-state Quantum Electrodynamics (QED) and for precisely determining the fundamental properties of the negative muon.

The Scientific Motivation: A Precision Test of CPT Invariance

The primary motivation for measuring the hyperfine structure (HFS) of muonic helium is to perform one of the most sensitive tests of CPT (Charge, Parity, Time) invariance—a fundamental symmetry of nature which states that the laws of physics should be the same if a particle is interchanged with its antiparticle, its spatial coordinates are inverted, and the direction of time is reversed.

By precisely measuring the HFS of muonic helium, we can determine the magnetic moment and mass of the negative muon. The MuSEUM collaboration’s muonium experiments, in turn, provide the same properties for the positive muon (the antimuon). A direct comparison of the properties of the muon and antimuon provides a stringent test of CPT symmetry for the second generation of leptons. Any deviation would be a monumental discovery and a clear signal of new physics.

The Experimental Approach at J-PARC: Overcoming Challenges

The experiment is performed at the MUSE D-line facility at J-PARC, which delivers the world’s most intense pulsed negative muon beam. This high intensity is crucial for overcoming one of the main challenges of the measurement: the very weak signal. The process of forming a muonic helium atom is violent, and the muon loses most of its initial spin polarization, leaving only a small fraction (~5%) to produce the measurable signal.

The experiment uses the same apparatus developed for the muonium HFS measurements. A key innovation in the recent work was the use of a small admixture of methane (CH4​) gas in the helium target. The methane acts as an efficient electron donor to neutralize the newly formed muonic helium ion ([μ−4He++]+). This method is significantly more effective than previous attempts that used xenon, as the lower atomic number of methane prevents it from capturing the incoming muons before they can form muonic helium. The measurement then proceeds using a microwave magnetic resonance technique: a microwave field is used to induce spin-flips between the HFS levels, which are detected by observing the change in the angular distribution of electrons from the muon’s decay.

New, High-Precision Results: A Milestone Achieved

After nearly 40 years since the last measurements, the MuSEUM collaboration has performed new, high-precision spectroscopy of the muonic helium-4 ground-state HFS. By taking data at several different gas pressures (3, 4, and 10.4 atm) and carefully extrapolating the results to zero pressure to account for atomic collision effects, the collaboration determined the HFS interval to be Δν=4464.980(20) MHz.

This result, with a precision of 4.5 parts per million (ppm), is a significant achievement. It is three times more precise than the previous direct measurement at weak field and is also more precise than the previous indirect measurement at high field, making it the most accurate determination of the muonic helium HFS to date.

Future Outlook: The Road to Higher Precision

While the recent result is a major step forward, the collaboration is preparing for the next generation of experiments to further improve the test of CPT symmetry.

High-Field Measurements: Preparations are underway for measurements in a strong magnetic field at the new H-line, which will provide 10 times the muon beam intensity. The goal is to achieve a precision below 100 parts per billion (ppb) for the HFS, which would allow for a determination of the negative muon’s magnetic moment and mass with a precision of under 1 ppm.

Advanced Techniques: A new experimental approach is being investigated to recover the muon polarization lost during the atom’s formation. This involves using lasers to repolarize the atoms through a spin-exchange optical pumping technique, which could improve measurement precision by nearly another order of magnitude. These future steps promise to provide one of the most stringent tests of CPT invariance in the lepton sector and continue the search for physics beyond the Standard Model.