The experimental setup was deliberately simple in concept but demanding in execution. A 1.5-metre-long target, corresponding to 13 interaction lengths of molybdenum and tungsten, was followed by a 2.4-metre iron hadron absorber. Downstream sat a spectrometer tracker built from four drift-tube stations and a magnet that deflected charged particles in the horizontal plane, while resistive plate chambers served as a muon tagger. The geometric acceptance was defined by a polar angle of 0.054 radians with respect to the beam, corresponding to a pseudorapidity of 3.6. Over the run, the collaboration accumulated a data set corresponding to (3.25 plus or minus 0.07) times 10 to the 11 protons on target, with beam intensities kept below 3 times 10 to the 6 protons per second.

The analysis focused on events in which two or more tracks were fully reconstructed. Candidate J/psi events were required to contain two tracks with momenta between 20 and 300 GeV/c, with the lower threshold motivated by the severe multiple scattering of low-momentum tracks and the upper threshold suppressing so-called ghost tracks. Requiring at least one track with transverse momentum above 1.0 GeV/c significantly enhanced the J/psi contribution relative to the low-mass background. The invariant mass distribution was fitted with two models, one based on Crystal Ball functions and one on Bukin functions with asymmetric tails, and the differences between the two fit results were folded into the systematic uncertainties.

Two effects had to be corrected before the data could be interpreted. The muons travel through up to 1.5 metres of target material and 2.4 metres of iron before reaching the spectrometer, losing on average about 10 GeV of energy as determined by Geant4 simulations. In addition, multiple scattering changes the direction of the reconstructed momentum between the J/psi production point and the momentum measurement in the tracker. The collaboration partly mitigated this by replacing the track-fit direction with the direction defined by the target centre and the first measured point. Because the energy loss is non-Gaussian with large tails, correcting only for the mean energy loss means the fitted J/psi mass does not match the Particle Data Group value, but the deviations in data and simulation were found to be similar, which the collaboration judged sufficient.

The headline comparison concerns the ratio of observed to simulated yields. For the low-mass resonance background, dominated by decays of eta, omega, rho-zero and phi mesons as well as muon pairs from photon conversions, the data-to-simulation ratio was 1.03 plus or minus 0.03, an essentially perfect agreement. For the J/psi signal, however, the ratio was 0.22 plus or minus 0.01: the simulation, based on Pythia v8 with only primary J/psi production, overpredicts the observed charmonium rate by roughly a factor of five. The collaboration notes that Pythia is known to predict charm production at low beam energies rather poorly, and that the two generator versions, Pythia v6 and Pythia v8, give markedly different transverse-momentum and rapidity distributions for J/psi mesons, for reasons that are not understood.

For SHiP itself, this overprediction is good news rather than a problem. J/psi mesons decaying to muon pairs are expected to be a major source of high-transverse-momentum muons, which are a significant background for the experiment because muons with large transverse momentum are more difficult to deflect with the active muon shield that protects the detector from beam-induced muon flux. A real J/psi rate well below the Monte Carlo expectation therefore reduces the shielding challenge. The di-muon rate overall, including the low-mass contributions, is in reasonable agreement with the Pythia v8-based simulation, so the discrepancy is specific to the charmonium component.

To quantify the charmonium production, the collaboration extracted differential cross sections as a function of centre-of-mass rapidity and of the polar angle in the Collins-Soper reference frame. The signal yield was fitted in bins of each kinematic variable, corrected for acceptance and efficiency, and corrected for migration between true and reconstructed rapidity using a migration matrix derived from the simulation. The acceptance-times-efficiency product rises from a centre-of-mass rapidity of about 0.3 and reaches roughly 40 percent at a rapidity of about 1.0, reflecting the limited angular coverage of the apparatus. Differences between the generated and reconstructed yields in the simulation were taken as a systematic error on the final result.

In the rapidity interval with the largest overlap with the earlier NA50 measurement, 0.3 to 0.6 in centre-of-mass rapidity, the collaboration obtained a J/psi production cross-section per nucleon, including the branching ratio of J/psi decays into muons, of (1.18 plus or minus 0.04 plus or minus 0.10) nb per nucleon. The NA50 experiment had measured J/psi production with 400 GeV protons on a series of much thinner targets made of beryllium, aluminium, copper, silver, tungsten and lead, and its result extrapolated with the NA50 parametrisation gives (0.99 plus or minus 0.04) nb per nucleon in the same interval. The two values agree within the systematic errors.

This agreement carries a substantive physics message. Because the SHiP target is several interaction lengths long, particles produced in the initial proton-nucleus collision can themselves undergo subsequent interactions and produce charmonium in secondary collisions, an effect that a thin-target measurement cannot capture. Comparing the thick-target result with the extrapolated thin-target NA50 value allows that secondary contribution to be bounded. Within the systematic errors, no significant enhancement from secondary J/psi production inside the target is observed, and an upper limit of less than 32 percent at 90 percent confidence level is placed on any such contribution. The collaboration also reports that production extends up to high rapidity, close to the kinematic limit, and that the Collins-Soper angular distribution shows no significant polarisation, with a polarisation parameter of 0.11 plus or minus 0.14 plus or minus 0.02, compatible with zero.

Several caveats frame the result. The mass resolution in data is considerably worse than in the simulation, which the authors attribute to a larger spread of energy loss or stronger multiple scattering than Geant4 predicts, an effect they flag as worth further study with regard to the active muon shield. The fitted psi(2S) contribution was constrained to be small, at (0.7 plus or minus 0.9) percent of the J/psi yield with an upper limit of 2.1 percent at 90 percent confidence level, consistent with the 1.5 to 1.9 percent contribution NA50 resolved with its superior mass resolution. The Drell-Yan contribution in the 2.9 to 4.5 GeV/c-squared mass range is of similar order and partially accounted for in the background. The measurement was performed as CERN experiment NA67, approved in April 2024, and its datasets are available from the corresponding author on reasonable request. For the SHiP collaboration, the practical conclusion is twofold: the muon flux modelling underlying the experiment’s design has now been tested against charmonium data in a realistic thick target, and nature appears kinder to the shielding design than the simulations had assumed.

Subject of Research: J/psi di-muon production measured with 400 GeV protons on a thick SHiP target replica at CERN

Article Title: Measurement of di-muons from 400 GeV/c protons interacting in a thick molybdenum/tungsten target

Article References: The SHiP Collaboration, Aksoy, A., Albanese, R., Albrecht, K., Alessio, F., Alexandrov, A., Aloschi, F., Arndt, T., Arutinov, D., Ballarino, A., Baudin, L., Bautin, V., Bay, A., Bekman, I., Betancourt, C., Bezshyiko, I., Bezshyyko, O., Bick, D., Birch, M., … Zholdybayev, T. (2026). Measurement of di-muons from 400 GeV/c protons interacting in a thick molybdenum/tungsten target. The European Physical Journal C, 86(10), Article 1231. https://doi.org/10.1140/epjc/s10052-026-16148-3

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16148-3

Keywords: SHiP, J/psi, charmonium, di-muon, CERN SPS, fixed-target, Pythia, Monte Carlo, muon shield, NA50, cross-section, secondary production