Researchers at ETH Zurich and the Paul Scherrer Institute in Villigen, Switzerland, have produced a high-intensity beam of muonium atoms in a cold state, an experimental advance that could enable a direct test of whether gravity acts differently on second-generation matter. The peer-reviewed study in Nature Physics describes a new method for generating muonium in superfluid helium. The resulting atoms travel at similar speeds and almost parallel to one another, properties required for a future interferometer that would measure the tiny influence of gravity on muonium.

The study did not conduct that gravitational measurement or find evidence that gravity departs from its expected behavior for ordinary matter; it instead developed the beam source needed for the proposed test. The experiment is designed to examine the universality of free fall and the equivalence of gravitational and inertial mass, a cornerstone of Albert Einstein’s theory of gravitation. In ordinary matter, bodies fall at the same rate at a given point within a gravitational field, while the equivalence principle links gravitational mass with inertial mass.

According to the research team, this principle has so far been demonstrated only with ordinary matter or first-generation antimatter. Muonium is a neutral atom formed from a positively charged antimuon and a negatively charged electron, making it a second-generation probe. A gravity experiment with this exotic atom would test whether the equivalence continues to hold for particles outside the first generation.

Muonium has two characteristics that make it useful for this test: it is neutral, and it belongs to a heavier and less familiar generation of particles. A neutral object allows gravitational behavior to be studied without the weak gravitational signal being masked by stray electromagnetic fields, which can dominate the behavior of charged particles. At the same time, muonium is exceptionally difficult to produce and control.

Its constituent muon decays after only about 2.2 microseconds. Earlier sources generated muonium atoms that flew off in many directions at different speeds and were therefore unsuitable for the precision required in a gravity experiment. The researchers addressed this problem by creating a cold, intense and well-directed beam.

The antimuons were directed into a thin layer of superfluid helium that had been cooled close to absolute zero, at minus 273 degrees Celsius. Superfluid helium is a quantum fluid in which individual helium atoms lose their identity and in which impurities are not tolerated. Lead author Jesse Zhang said the researchers used the superfluid as an “atomic cannon,” exploiting the conversion of chemical potential into kinetic energy to propel the newly formed muonium atoms out of the liquid.

When an antimuon encounters a free electron in the superfluid helium, it forms a neutral muonium atom with positive chemical potential. The atom is forced out of the liquid, and as it reaches the surface, that chemical potential is converted into kinetic energy. The resulting boost sends the muonium vertically out of the helium.

Importantly, the atoms must move through the quantum liquid at a suitable speed without collisions, because excessive scattering would prevent them from reaching the surface within their very short lifetime. The high-intensity antimuon beam from PSI allows many muonium atoms to be generated for the planned experiments. Anna Soter, a professor of physics at ETH Zurich and member of the research team, said the cold state is what makes the proposed gravity experiment possible.

In this context, “cold” does not mean that the atoms are motionless; it means that they propagate at similar speeds and nearly parallel to one another. This improved control over direction and velocity is important because the planned instrument will use the wave properties of the atoms to create an interference pattern. A very small shift in that pattern caused by Earth’s gravitational pull would provide a measure of gravity’s effect on muonium.

The study establishes the upstream beam capability rather than reporting the result of that comparison. The next stage of the program is the development of a muonium interferometer. According to the researchers, they hoped to test the method for the first time with the atomic beam in the year of the announcement and, if that worked as expected, to carry out the actual gravity experiment two or three years later.

Those are planned milestones rather than completed measurements. If the interference pattern of muonium shifts differently from the pattern expected for ordinary matter, Soter said the result would be surprising and could, among other theoretical possibilities, point toward the existence of a fifth force. No fifth force has been proven, and the present work provides no evidence for one.

The team’s primary aim is to measure whether the equivalence between gravitational and inertial mass applies to a second-generation particle. Physics recognizes four fundamental interactions: gravity, electromagnetism, the strong interaction and the weak interaction. A fifth force has been proposed repeatedly, but it has never been established.

Soter emphasized that the researchers are open-minded about what the measurement may show while keeping the immediate objective focused on the first such test. The new beam is therefore an enabling experimental result, not a demonstration that Einstein’s theory has been challenged or overturned. Beyond the planned gravity measurement, the high-intensity muonium beam is expected to enable more precise laser-spectroscopy experiments.

These could allow muonium to be measured more accurately than in previous work and provide information about the muon’s mass and fundamental physical constants, which are stated goals of the research group. The same experimental source can thus serve two purposes: supplying a cold, directed beam for a gravitational comparison and providing a larger, better-controlled population of muonium for detailed spectroscopic study. The reported advance addresses a major technical obstacle while leaving the central scientific question unresolved.

A successful gravitational test will still require an interferometer capable of resolving a minuscule shift in an interference pattern while dealing with muonium’s short lifetime, beam quality and other sources of uncertainty. The study’s demonstrated result is the generation of a high-intensity, superthermal muonium beam in superfluid helium, with atoms emerging in the cold state needed for future work. Whether muonium falls exactly as expected for ordinary matter remains to be measured.

The beam nevertheless supplies the experimental foundation for testing gravitational universality in a second-generation particle, a comparison that had not previously been carried out with muonium.

Subject of Research: A cold muonium beam developed for future tests of gravitational universality and laser spectroscopy

Article Title: Novel particle beam could challenge Einstein’s Theory of Gravity

Article References: Novel particle beam could challenge Einstein’s Theory of Gravity. Original publication (Bibliographic details unavailable.)

Image Credits: AI Generated

DOI: Not provided

Keywords: muonium, muon beam, gravity, gravitational universality, equivalence principle, interferometry, superfluid helium, laser spectroscopy, ETH Zurich, Paul Scherrer Institute, Novel, particle

Neutral mesons, the fleeting particles that endlessly oscillate between matter and antimatter forms, have just acquired a strikingly new mathematical lens. In a theoretical study published in The European Physical Journal C, physicist Swarup Sangiri of the Indian Institute of Technology Kharagpur has constructed a fresh class of geometric objects, called connected sequential Bargmann invariants, that encode how two different decay channels of an entangled meson pair relate to one another inside the projective geometry of quantum states. The work extends an earlier framework and shows that when decay-projected states are wired directly into a cyclic chain of quantum overlaps, the resulting quantities behave in a fundamentally different way near the boundary where CP violation switches off.

To appreciate why this matters, it helps to recall what makes neutral meson systems so special. Particles such as the neutral kaon, the D meson, and the two neutral B mesons are produced as flavor eigenstates but propagate as mixtures of heavy and light eigenstates, conventionally written as combinations of the meson and its antiparticle with coefficients p and q. When the magnitudes of p and q differ, the two propagation eigenstates are no longer orthogonal, and this nonorthogonality is the hallmark of indirect CP violation, the subtle asymmetry between matter and antimatter that was famously discovered in kaons in 1964. Because any physical observable must be independent of arbitrary phase conventions attached to quantum states, the natural language for describing interference in these systems is one of rephasing-invariant quantities.

Bargmann invariants provide exactly that language. For a closed sequence of quantum states, the nth-order Bargmann invariant is the product of overlaps taken around the cycle, and it remains unchanged under independent phase redefinitions of each state. Its phase is a geometric phase, the kind of holonomy familiar from the Berry phase, accumulated along a closed loop in the space of rays. Earlier work had applied this machinery to correlated neutral meson decays, constructing third-order invariants that probe single-channel interference and fourth-order invariants that correlate two decay channels through the heavy and light propagation eigenstates. Those constructions linked the geometric picture to conventional flavor observables, including Jarlskog-type structures, without introducing any new phenomenological parameters.

The new study asks a deceptively simple question: what happens if the two decay-projected states themselves are connected directly inside the cyclic overlap chain? When one meson of an entangled pair, produced for example in the decay of a phi or Upsilon resonance, decays into a channel f, its partner is projected into a conditional state determined by the decay amplitudes. A second channel g prepares a different conditional state. The connected sequential fourth-order Bargmann invariant follows the loop from the heavy eigenstate to the f-conditioned state, then directly to the g-conditioned state through their mutual overlap, then to the light eigenstate, and finally back to the heavy one. The crucial new ingredient is the overlap between the two conditional states, a quantity built purely from the decay amplitudes that measures how similar the two post-selected meson states are in projective Hilbert space.

This change in connectivity has dramatic consequences for how the geometric quantities scale as CP violation becomes small. The previously studied disconnected fourth-order invariant, when normalized by the product of two third-order invariants, produced a ratio that blows up quadratically, scaling as the inverse square of the mixing asymmetry, the difference between the squared magnitudes of p and q. The connected sequential ratio, by contrast, carries only a single factor of that asymmetry in its denominator, so its enhancement near the CP-conserving limit is merely linear. Physically, replacing one propagation-mediated link with a direct overlap between the projected states removes one power of the heavy-light suppression, placing the two classes of geometric correlation in distinct scaling classes.

A second new ratio compares the sequential invariant directly with the disconnected one. This comparison ratio behaves in the opposite manner: it is proportional to the mixing asymmetry itself, vanishing in the exact CP-symmetric limit. Its behavior is governed by a competition between two effects, the shrinking of the heavy-light overlap on one side and the possible alignment of interference phases between the two decay channels on the other. When the conditional states prepared by the two channels become geometrically aligned, the suppression can be weakened, revealing that the connected structure is sensitive not only to mixing asymmetry but also to the relative coherence of the decay projections.

To make these statements precise, the analysis is carried out in terms of the standard rephasing-invariant interference parameters lambda, the products of the mixing ratio q over p and the ratios of decay amplitudes to their CP-conjugates. A systematic small-asymmetry expansion, with the squared magnitudes of p and q written as one half plus or minus a small parameter, shows that the sequential ratio depends explicitly on the phase difference between the two channels through the numerator structure. This dependence has no analogue in the disconnected construction, where the channels communicate only through the propagation eigenstates. It means the connected sequential geometry probes the relative orientation of the decay-conditioned rays themselves, a piece of interference information that conventional observables do not isolate on their own.

The geometric interpretation is perhaps the most elegant part of the story. Both the disconnected and the sequential fourth-order invariants involve the same four rays, the heavy and light propagation eigenstates and the two decay-projected states, yet they define different closed paths through projective Hilbert space. A Bargmann invariant depends not just on which states participate but on how they are stitched together, so rewiring the cycle produces a genuinely different geometric correlation. In the CP-conserving limit the heavy and light eigenstates become orthogonal, one link of every cycle collapses, and the entire cyclic structure degenerates, which is why the invariants vanish there. The formalism thus ties the very existence of these CP-sensitive geometric objects to the nonorthogonality of the propagation eigenstates.

Crucially for experiment, none of this requires new physics inputs. The sequential invariant and both ratios can be written entirely in terms of the mixing parameters and decay amplitudes already extracted from time-dependent flavor analyses at flavor factories such as the KLOE experiment with entangled kaons and the BABAR and Belle measurements with entangled B mesons. The framework simply reorganizes the same accessible information into cyclic geometric quantities. The neutral kaon system, with its small indirect CP violation and long-lived interference phenomena, is flagged as a particularly natural arena where the linear enhancement of the sequential ratio could be pronounced, with candidate channels including two-pion, semileptonic, and multi-pion final states. The B meson systems, including channels like B decays to J/psi kaons and to pion pairs, offer rich phase-dependent interference structures, while the D system, where both mixing and CP violation remain tiny in the Standard Model, could serve as a sensitive testing ground for small deviations from exact symmetry.

The study stops short of claiming a new dynamical observable. The author is careful to note that the sequential construction does not add an extra propagation stage in the manner of conventional cascade CP analyses; it is a reorganization of overlap geometry within a single meson system. Even so, the result establishes a hierarchy of Bargmann invariant structures, from single-channel triangles through disconnected quadrilaterals to directly connected sequential cycles, each capturing a different layer of CP-sensitive interference. As precision flavor physics continues to squeeze ever tighter constraints on the origins of matter-antimatter asymmetry, geometric tools of this kind may reveal correlation patterns hiding in plain sight within data that experiments already collect.

Subject of Research: Geometric Bargmann invariant structures and CP-sensitive interference in correlated neutral meson systems

Article Title: Connected sequential Bargmann invariants and (\mathcal CP~)-sensitive geometric correlation structures in neutral meson systems

Article References: Sangiri, S. (2026). Connected sequential Bargmann invariants and $$\mathcal CP~$$-sensitive geometric correlation structures in neutral meson systems. The European Physical Journal C, 86(9), Article 1056. https://doi.org/10.1140/epjc/s10052-026-16308-5

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16308-5

Keywords: Bargmann invariants, neutral mesons, CP violation, geometric phase, quantum interference, meson mixing, projective Hilbert space, kaons, B mesons, rephasing invariance, entangled meson pairs, flavor physics