An analysis of η′ mesons produced in carbon has found an excess on the lower-mass side of the expected η′ signal when the mesons carried lower momentum. The authors interpret the pattern as an in-medium spectral change, and a density-based simulation translates it into a possible η′ mass reduction of 57.5 MeV/c² at normal nuclear density. The uncertainty on that estimate is asymmetric, at +5.7/−27.8 MeV/c².
The study set out to answer a narrow question: can the η′ invariant mass, reconstructed from its decay products, change while the meson is inside a nucleus? It looked directly through η′→γγ, reconstructing the candidate mass from the two photons.
How the signal was isolated
Data were collected with a 20 mm carbon target and a tagged photon beam spanning 1.3 to 2.4 GeV. Candidate events were required to contain exactly two BGOegg photons and no more than one charged particle, the selection used for quasi-free γN→η′N events.
Monte Carlo estimates were used to choose the momentum boundary by optimizing the expected in-medium-to-other-event ratio. The choice was kept blind to the significance of any line-shape signal. The final groups were Pγγ below 1.0 GeV/c and 1.0 to 1.5 GeV/c.
In the 780 to 1080 MeV/c² mass range used for the main fits, the carbon sample contained 64,000 low-momentum events and 50,000 high-momentum events.
A lower-mass excess at low momentum
The first comparison used a no-medium model with three pieces: the vacuum quasi-free η′ signal, a multi-meson background and an ω background. It had seven free fit parameters, providing a baseline for testing whether known processes accounted for the observed line shape.
The model described the high-momentum spectrum well, with χ²=48.7 for 54 degrees of freedom. It fit the low-momentum spectrum less well, with χ²=69.2, leaving an excess around 910 MeV/c² in the lower tail. The analysis excluded the 885 to 925 MeV/c² interval for a separate check.
That excluded-region test gave a 4.7σ result. Moving either boundary by ±5 MeV/c² gave values from 4.1σ to 4.8σ. Sigma is a statistical way of expressing how far a result lies from the no-signal expectation, rather than a measurement of the mass itself.
Researchers then compared the data with detector-response templates from a simulation that allowed the η′ mass and total width to vary with nuclear density. The best fit favored k1=0.06, with χ²=52.4 for 53 degrees of freedom. The added component had a nominal significance of 4.1σ, based on Δχ²=16.8 for one additional degree of freedom; a conservative treatment gave 3.7σ. The quoted k1 uncertainty was −0.029/+0.006.
Under that model, k1 corresponds to a 57.5 MeV/c² reduction at normal nuclear density, with an uncertainty of +5.7/−27.8 MeV/c². This is an inferred parameter value, not a model-independent measurement of an η′ mass inside every nucleus.
Tests that narrow the claim
The pattern did not depend entirely on the simulated template. Replacing it with a Gaussian gave a maximum low-momentum significance of 4.0σ at a mean of 925 MeV/c² and a width of 21.4 MeV/c². Its conservative significance was 3.7σ, while the high-momentum result was below 1.3σ.
Several controls found no comparable excess. The high-momentum control significance did not exceed 1.4σ, ten low-momentum η reference samples gave less than 0.9σ, and low-momentum liquid-hydrogen data gave χ²=23.1 for 24 degrees of freedom with simulated-signal significance below 1.1σ.
The fitted ratio of signal yield to vacuum yield rose as lower Pγγ thresholds were selected, following the momentum dependence of the in-medium simulation. Matching the observed scale required a factor of 14.3.
The mass estimate rests on several modeling choices. The simulation assumed a linear density dependence for both mass and total width, used a Woods-Saxon nuclear-density profile, fixed k2 at 105, equivalent in the model to 20 MeV of width broadening, and kept the partial γγ width at its vacuum value.
The evidence is therefore specific to a carbon-target measurement and to the simulation framework used to interpret it. It does not establish a model-independent mass value at normal density or show that the same spectral behavior applies across nuclei, densities, momenta or decay channels.
The narrowest reading is a statistically strong, low-momentum spectral excess under the tested analyses, while the size of a corresponding mass reduction depends on the chosen density and width model. Additional measurements across targets, momenta and decay channels are needed to test how broadly the result applies.
Paper data and sources
Original title: Direct measurement of the in-medium $η^{\prime}$ mass spectrum through the $γγ$ decay channel
Authors: Y. Matsumura, N. Muramatsu, T. A. Hashimoto et al.
Journal/Repository: Phys. Rev. Lett. 137, 051901 (2026)
Status: Peer-reviewed
First online: 2026-08-25
DOI: 10.1103/x414-n6g9
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