High-Precision Cross-Sections for Galactic Cosmic Rays: Highlights from XSCRC2024 and Follow-Up Actions

Abstract

The interpretation of high-precision Galactic cosmic-ray data from AMS-02, CALET, DAMPE, etc., is fundamentally limited by nuclear cross-sections uncertainties. This proceeding highlights the results presented at the XSCRC2024 workshop, which aims at bringing together the cosmic-ray, nuclear, and particle physics communities, with the goal of improving cross-section measurements across various domains, from nuclei production for constraining cosmic-ray transport parameters, to antiproton and anti-deuteron production for dark matter searches. This workshop lead to a comprehensive roadmap for new cross-section measurements in the next decade, as well as other outcomes.

1. Introduction

Galactic cosmic rays (GCRs) provide unique insights into astrophysical processes (acceleration and transport) and help unveil the nature of dark matter (DM). Among the many candidates, Weakly Interacting Massive Particles (WIMPs) in the GeV-to-TeV mass range are prime targets for DM indirect detection [1]. Their annihilations produce antiprotons, positrons, and other particles that add up to standard astrophysical production. Current high-precision spectrometers (e.g., AMS-02) and calorimeters (e.g., CALET and DAMPE) achieve percent-level precision and multi-TeV energies on numerous GCR fluxes. However, the interpretation of their data is severely limited by uncertainties on nuclear cross-sections (XS). Indeed, GCR transport studies involve a large network of productions XS. Meanwhile, unveiling a DM signal critically depends on the modelling of the GCR astrophysical background, which also depends on antimatter production XS. Overall, the current nuclear data precision is 10–20%, while percent-level precision for many reactions would be necessary in the hundreds of MeV/n to several GeV/n.

This proceeding synthesises the main results and discussions at the third edition of the XSCRC workshop (Cross-Sections for Cosmic-Rays at CERN), in 2024, after the successful 2017 and 2019 editions. We briefly present the astrophysical and particle physics challenges in Section 2. We highlight the main results presented at XSCRC2024 in Section 3. We then conclude in Section 4, highlighting some important outcomes of this workshop: they include a roadmap for acquiring the necessary high-precision data in the coming decade, proposals to perform some of these measurements at existing or future facilities, and the next XSCRC edition, possibly in 2026!

2. GCR Challenges and XS Limitations

CRs are mostly protons, helium, and traces of heavier nuclei, up to the heaviest stable nuclei. Their spectrum have been measured from ${10}^7$ eV up to ${10}^{20}$ eV, and GCRs have energies below ∼${10}^{15}$ eV. The latter are accelerated via diffusive shock acceleration, then diffuse in the turbulent magnetic fields of the Galaxy, where nuclear interactions on interstellar matter (mostly H and He) and other processes occur. For those not escaping the Galaxy (after wandering over tens of millions of years), the last part of their journey involves crossing the Solar cavity (Solar modulation) and being detected in one of the CR detectors in space or onboard balloons.

2.1. Astrophysical Challenges

Despite having the general picture to explain GCR data, unveiling their sources and explaining their detailed abundances and maximum energy are still questions challenging this field of research. For instance, the discovery of spectral anomalies in recent GCR data triggered a lot of efforts in order to link the microphysics to the phenomenologically derived transport parameters. Secondary-to-primary ratios (e.g., B/C, ¹⁰Be/⁹Be, sub-Fe/Fe) are used for constraining these parameters. These ratios directly probe the amount of material traversed by GCRs during their propagation, making the predictions critically dependent on accurate production XS. Indeed, current uncertainties in these XS (typically 10–20%) dominate the systematic errors in transport parameter determination. The few-percentage precision of AMS-02 B/C data cannot be fully exploited. Furthermore, these nuclear uncertainties affect our understanding of fundamental astrophysical questions. These include the presence of primary deuterium and lithium components in GCRs, the existence of a residual grammage from gas cocoons surrounding the sources, etc.

2.2. New Physics Challenges

Searches for DM signatures through rare CR channels ($e^{+}$, $\overline{p}$, $\overline{d}$, diffuse $\gamma$-rays) face similar limitations. The separation of potential DM signals from astrophysical backgrounds requires precise modelling of the secondary production. Antiproton and anti-deuteron background uncertainties stem primarily from production XS uncertainties in p+H and p+He interactions, but transport uncertainties—from the LiBeB production XS uncertainties—are as significant (∼20% on anti-nuclei). Also, the DM signal uncertainties (factor ∼2 on antimatter fluxes) arise from the diffusive halo size uncertainties. These are themselves related to the ^9,10Be production XS uncertainties. Finally, the recent report of possible anti-helium events in AMS-02 data further emphasises the urgent need for better understanding of anti-nuclei production mechanisms.

3. XSCRC2024 Highlights

This XSCRC workshop series takes place at CERN, to benefit its visibility, accessibility, organisational support, as well as to maximise the interactions with the particle physics community. The first workshop was held in 2017 [2], bringing together the CR, nuclear, and particle physics communities, with the aim of triggering actionable projects, based on the CR community needs and the particle and nuclear physics instruments’ capabilities. The second edition, in 2019 [3], demonstrated that fruitful collaborations had already started, with promising results. The results of the last edition to date, XSCRC2024 [4], are highlighted in this section. We stress that more than 50–60 researchers attended each of these editions. In particular, XSCRC2024 had 17 invited talks and 15 contributed talks, with many discussion sessions.

3.1. Recent Results from Direct Detection CR Experiments

The workshop featured comprehensive overviews of the results of current CR direct detection experiments. There were talks on AMS-02 [5] (on the International Space Station, ISS, since 2011), a spectrometer providing exceptional charge separation (Fe/Co discrimination better than 1 in ${10}^6$) and $e^{+}{e}^{-}$ separation up to TeV energies. We also had talks on CALET [6] (on the ISS since 2015) and DAMPE [7] (onboard a satellite since 2015), spectrometers with larger acceptance, extending measurements to the PeV frontier (e.g., ∼30 radiation lengths for CALET), albeit with poorer charge separation compared to spectrometers, and no $e^{+}{e}^{-}$ separation; see the top panel of Figure 1.

The results presented included high-precision measurements of heavy nuclei (AMS-02), the discovery of a second rigidity break in p and He spectra (CALET), and the first overlapping data points between direct and indirect detection experiments for the all-particle spectrum (DAMPE). These added to the plethora of results already published by these experiments (200 GV spectral break, $e^{+}$ and $e^{-}$ fluxes, antiproton fluxes, daily time series, etc.).

Notably, AMS-02 and DAMPE have measured inelastic and production XS directly from flight data [8,9], enabling valuable cross-comparisons with beam test data and Monte Carlo simulations (see the bottom panel of Figure 1). These measurements were performed in the context of existing normalisation issues between spectrometric and calorimetric flux measurements.

3.2. Production XS for Nuclei and Facilities

Several presentations at the workshop stressed the critical role of production XS to interpret several secondary-to-primary ratio data (²H/He, ³He/He, LiBeB/C, F/Si). Ranking the highest-priority nuclear reactions to measure was a project that started with XSCRC2017, with the last update of this effort presented in this edition (production XS for F to Si fluxes): forecasts showed that new nuclear data would drastically reduce the transport parameter and antiproton background flux uncertainties [10]. Measuring these high-priority reactions is a low-risk/high-benefit investment that would be transformative for GCR physics. It was also stressed that, while high-precision nuclear data for nuclei with atomic number $Z=1–15$ from hundreds of MeV/n to tens of GeV/n energies are already needed now, data for $Z>15$ will also be needed soon. Indeed, AMS-02 data is now releasing data for heavier species. Additionally, the TIGERISS project [11] targets $Z>30$ species. An illustration of the many XS needed for nuclei and their impact on the antiproton modelling is shown in Figure 2.

Several experiments and facilities can provide the desired nuclear data. We invited to this workshop experts on particle, nuclear, and medical physics experiments, who presented the following ongoing and future projects:

• NA61/SHINE at CERN SPS: This detector was designed for strong interaction, $\nu$, and ultra-high-energy CR physics, but a proposal for measuring the highly ranked XS for GCRs was made as a follow-up of XSCRC2017. A successful pilot run took place in 2018 (for 2.5 days), demonstrating its capability for GCR physics [12]: its high-performance superconducting magnet and high-resolution time projection chamber enables the separation of all the fragments of the reactions needed for GCRs. The measurement were made at ∼10 GeV/n. A second run (one week) was planned (at the time of the conference) for late 2024, with a 10-fold increase in the readout rate. There could also be plans for primary oxygen beams in 2025 for CR fragmentation studies. This is illustrated in Figure 3.
• CNAO (Italy): This facility [13] is dedicated to hadron-therapy studies, that is, the use of beams of protons or heavier ions (like carbon) to precisely target and destroy cancerous tumours. Some measurements in these fields overlap with those for GCRs and space radiation protection, and ongoing measurements with ⁴He, ¹²C, ¹⁶O, ⁵⁶Fe beams are carried out at 200–700 MeV/n by the FOOT collaboration [14]. These measurements are of great interest for the GCR community.
• Brookhaven (USA): This facility has been used in the last 30 years to perform sub-GeV/n production XS measurements. In the context of forthcoming high-precision sub-Fe fluxes in GCRs, some measurements are ongoing to improve the precision of existing XS.
• FAIR [15] (Germany) and HIAF [16] (China) in ∼2027: These future installations were identified as extremely promising nuclear facilities to carry out fragmentation measurements, for a variety of projectiles, up to a few GeV/n.

Pictures of the four above nuclear facilities are shown in Figure 4.

3.3. XS for Anti-Nuclei and CERN Experiments

Direct DM detection is carried out for antimatter CRs, but also for $\gamma$-rays and $\nu$. A few presentations highlighted the status of the XS needed to match the CR data precision (see Figure 5). Although improving the production XS of $\gamma$-rays, $e^{+}$, and $\nu$ is always useful, improving the production XS of anti-nuclei, especially antiproton, is the most urgent task. Indeed, the latter XS suffer from ∼20% uncertainties, compared to a few percent uncertainties in the GCR data in which an excess is sought.

More than 90% of the production of CR antiprotons involve p and He interactions (the rest involving heavier CRs on H and He). The dominant contribution is CR protons on hydrogen in the ISM, followed by pHe and Hep, and then HeHe. In practice, all production XS are rescaled from pp data. Also, the majority of the relevant kinematic region is poorly sampled in existing measurements [17]. There are almost no data on neutron-induced production, which contributes to half of the production. A small departure from isospin symmetry—which assumes an equal production of $\overline{p}$ and $\overline{n}$ in pp collisions—would have a direct and major impact on the predicted anti-nuclei fluxes [18].

Anti-deuterons have not yet been detected in GCRs, but they are one of the targets of AMS-02, GAPS [19], and other experiments. Their production uncertainties result from folding $\overline{p}$- and $\overline{n}$-invariant production XS uncertainties and those from the so-called coalescence mechanism. The latter are dominant in the calculation and need to be further improved on. This is especially important in the context of the few anti-helium-like events reported by the AMS-02 collaboration.

Several CERN experiments prove to be uniquely positioned to address the gaps in the data (see top panel of Figure 6). Following several discussions held during XSCRC217 and XSCRC2019, several important published or preliminary results were presented at XSCRC2024, and prospects for future measurements were also discussed. We very briefly highlight a few below:

• Experiments using the SPS beam [20] (secondary fragmentation beams from 10 to 158 GeV/n): AMBER will measure the level of isospin asymmetry in the antiproton production, while NA61/SHINE [21], in addition to the production of nuclei, is measuring antiprotons and the coalescence mechanisms, via pp, pC, and heavy species collisions.
• Experiments at LHC (collisions of p, Pb, and lighter ions up to 13.6 TeV): ALICE [22] has measured antiproton production in pp, pPb, PbPb, and XeXe collisions at several collision energies and particle multiplicities. It has also performed the first measurement of the inelastic XS of ³$\overline{\mathrm{He}}$ [23], which is another important ingredient for their transport in the Galaxy. LHCb [24], thanks to the SMOG device [25] (injection of gas in a cell on the beam passage), has already performed pHe antiproton production measurements, and demonstrated the feasibility to constrain anti-deuteron production in the same system. The SMOG2 upgrade [26] will allow testing the scaling violation in the forward hemisphere of the antiproton XS, as well as to test isospin effects, other than to repeat and improve the antiproton production measurements in pp, pD, and pHe collisions. Finally, LHCf [27] has acquired pp data for high-precision measurements on forward ${\pi }^0$, $\eta$ production, as well as the first ever measurement of $K_s^0$ production in the forward region; these data will be useful to improve the $\gamma$-ray flux modelling.

These few examples (see some illustrations in the bottom panel of Figure 6) show that CERN is a unique facility to provide insight into the XS needed for DM searches.

3.4. Forthcoming GCR Experiments

High-precision nuclear data are now needed to interpret CR data from ongoing experiments. As presented at this workshop, this need for better XS will further increase, owing to the next generation of experiments pushing several frontiers (see Figure 7): the isotopic frontier, with the HELIX experiment [28] designed to measure the ¹⁰Be/⁹Be ratio (to determine the halo size of the Galaxy), and the anti-nuclei frontier with GAPS [29]; these two experiments are balloon-borne and are planning to fly several times in the coming years. The precision, energy, and mass frontiers will be pushed thanks to several ongoing and planned space experiments: the AMS upgrade [30] allows us to push, for instance, the electron and positron measurements to a few TeV; TIGERISS [11] on the ISS for the measurement of heavy nuclei (Z > 30); HERD [31] on the Chinese Space Station aiming for higher energies (owing to a 55 radiation lengths calorimeter).

In the longer term, ideas for the next generation of space detectors were also presented, with the ALADIno [32] and AMS-100 [33] concepts, where the sub-percent precision is one of the sought-after frontiers. These experiments will make even more acute the need for high-precision XS nuclear data.

3.5. Overlapping Interests, Codes, and Other Synergies

One of the goals of the XSCRC series was also to bring together adjacent fields and scientists with overlapping interests or similar concerns (about XS). In this edition, we had several talks highlighting these existing synergies and issues (see Figure 8).

3.5.1. Space Radiation Protection, Hadron-Therapy, and Cosmogenic Studies

In the context of space faring, the impact of fragmentation on the dose received by astronauts during their journey is one of the major concerns [34]. Both the GCR fluxes (peaking at GeV/n energies) and the transient Solar flares (peaking at lower energies) contribute to this dose. The total and the differential production XS are needed for the most abundant species (H, He, C, O, etc.), overlapping with some needs of GCR physics. The impact of fragmentation on the dose delivered in hadron-therapy treatments [35] also requires differential production XS for p, He, C, as well as sub-GeV/n energies. There are also synergies with cosmogenic studies [36]. The latter analyse rare isotopes produced in Earth’s surface materials by CR interactions to determine exposure ages, erosion rates, and geological processes over thousands to millions of years. This last topic was not covered in this edition, but it was in the previous ones.

3.5.2. XS Codes

The central piece of all the above studies (CR data analysis and interpretation, space radiation and hadron-therapy studies) are the XS codes. Indeed, the scarcity and low coverage of existing nuclear data make them insufficient for practical uses and calculations. This is why multipurpose or specific XS codes are developed. In this workshop, the latest developments of the INCL code [37] were presented for antimatter production. This code is actually widely used as one of the reference models in the GEANT framework. The application of the FLUKA code for GCR studies [38], as well as the recent developments in the EPOS code, were also presented [39]. Statistical hadronisation of hot quark matter to form light systems could actually be an alternative or co-existing process to coalescence, currently used to describe the formation of anti-deuterons and heavier anti-nuclei. Stand-alone codes were presented on this topic: ToMCCA [40] (Toy Monte Carlo Coalescence Afterburner) for the coalescence of anti-nuclei, based on the quantum–mechanical Wigner function formalism (the latter models the formation, for instance, of an anti-deuteron by evaluating the overlap of the proton and neutron phase-space distributions with the deuteron’s internal wave function); CosmiX [41], for DM-induced production.

There was no presentation on the latest updates on XS in GEANT at this workshop, but there were in the previous editions. Nonetheless, many speakers presented their measurements compared to GEANT4 predictions (with various physics lists), including interactions of GCRs in the materials of the AMS-02 and DAMPE detectors, hadron-therapy measurements, measurements of inelastic XS, and production XS of anti-nuclei in LHC experiments. The differences between the model predictions and data—where no measurements were made before—further highlighted the need for dedicated studies to fill these gaps. It also stresses that further efforts and synergies with the XS code community are necessary.

3.5.3. Ultra-High Energy CRs (UHECR)

CRs at the highest energies are of extragalactic origin. Understanding the origin and acceleration mechanisms of these particles is still an open issue; and nuclear physics uncertainties are also of concern here [42]. First, hadronic XS in the atmosphere are fundamental to understanding the physics of air showers. Precise measurements of these XS are essential for analysing data taken by facilities like the Pierre Auger Observatory and the Telescope Array. The energy range of interest surpasses by far that of LHC. Reducing uncertainties in these measurements enhances our ability to distinguish between different CR composition models. Furthermore, UHECRs exhibit a predominantly heavy composition, suggesting that photo-disintegration processes—excitation of the giant dipole resonance via photon energies above ∼8 MeV in the nucleus’ rest frame—play a crucial role in modifying their nuclear species as they travel from their sources to Earth. More generally, photo–nuclear interactions contribute significantly to the evolution of the UHECR composition during propagation and in the sources.

The overall status of XS for UHECRs was presented at this workshop, with a focus on the PANDORA project [43] (Photo-Absorption of Nuclei and Decay Observation for Reactions in Astrophysics). These presentations illustrated that XS are needed for all types of CRs, with a variety of reactions and processes, albeit not with the same urgency.

4. Summary, Outcomes, and Next Steps

4.1. XSCRC2024 and Next Edition

The XSCRC workshop series was initiated because GCR studies have reached a critical point: we cannot fully exploit current high-precision data or expect significant discoveries without substantially improved nuclear XS measurements. Doing so requires coordinated effort across disciplines (CR, nuclear and particle physics, among others). As illustrated in this proceeding, the XSCRC series has already achieved some of its goals by establishing fruitful and successful collaborations (across communities), growing in number since the first edition. The 2024 edition reported many exciting and puzzling new GCR data, as well as preliminary exciting XS measurements. This confirmed the growing interest for further involvements and coordinated efforts to obtain new high-precision XS measurements. We also devoted a lot of time to the discussions, with the unanimous conclusion that the time was ripe for a white paper (see below), in order to draw more attention outside our community.

The XSCRC series has still a lot to offer, firstly to follow up and report on the recent and ongoing measurements, and also to further foster collaborations. With numerous research initiatives currently underway on these topics, the next edition is anticipated to occur in 2026.

4.2. Beyond XSCRC: Ensuring XS Measurements

Surfing on the wealth of excellent and exciting results (and discussions) at XSCRC2024, the following concrete outcomes have already been produced by its very motivated and talented participants:

• Our community turned the envisioned white paper into a comprehensive review paper for Physics Report: Precision cross-sections for advancing cosmic-ray physics and other applications: a comprehensive programme for the next decade [44].
• An abridged version, more focused on CERN experiments, was submitted as a contribution of the CR community to the ESPPU (European Strategy for Particle Physics Update): Precision cross-sections for advancing cosmic-ray physics. Input to the 2026 ESPPU from the XSCRC community [45].
• In response to CERN’s latest call for proposals for experiments at the AD (Antiproton Decelerator) and at ELENA (Extra Low Energy Antiproton ring), a LoI (Letter of Intent) was written to construct a new experiment for investigating antiproton and anti-deuteron interactions over a broad range of energies: Precision Measurement of the Cross-Sections for Inelastic Interactions of Antiprotons and Antideuterons with Nuclei for Cosmic-Ray Research [46].

All the above contributions should help to increase the odds of securing dedicated beam time for our projects or obtaining more support from our respective funding agencies. The successful execution of the XS programme depends on several critical actions: (i) to actively pursue the discussions between our communities; (ii) to propose measurements at nuclear and particle physics facilities; (iii) to advocate for beam time and funding through relevant committees; (iv) to maintain the collaborative XSCRC spirit. The items (i) and (iv) should be easily addressed by continuing the XSCRC series. In the last few years, (iii) has often been challenging. However, participation in collaboration meetings of the targeted experiments has been highly beneficial, helping all parties develop a shared understanding of the scientific needs and sometimes to articulate a more compelling case for the measurements. While (ii) is now well engaged at CERN facilities, more outreach is needed to spur proposals from nuclear physicists for dedicated measurements at their facilities.

To conclude, we reiterate that the community-devised XS programme represents a game-changing investment, while using a small fraction of fundamental physics resources, presenting large benefits across multiple domains.