Abstract The precise measurement of the cosmic ray composition is a key objective of ground-based cosmic ray experiments. The primary challenge arises due to the significant uncertainties in high-energy hadronic interaction models. These models not only affect the theoretical description of the propagation and evolution of cosmic rays in the atmosphere, but also directly determine the physical interpretation of experimental observations. As one of the principal secondary particles produced in hadronic cascades, muons retain substantial information from the primary interactions owing to their strong penetrating power and small interaction cross-section with matter. This makes them an effective probe for validating hadronic interaction models. In this study, based on the air shower data acquired by Yangbajing hybrid array (YBJ-HA), a high-statistics measurement of the muon component in cosmic-ray-induced events was performed. Subsequent systematic comparison between the experimental observations and predictions of major existing hadronic interaction models revealed overall consistency within the “knee” of the cosmic ray energy spectrum, thereby supporting the basic validity of existing models in this range. Additionally, the results of combined spectral and compositional analyses indicated a transition in cosmic ray mass composition around the “knee” shifting from light-nuclei dominance to heavy-nuclei dominance. The findings of our study provide important insights into the applicability of hadronic interaction models in TeV–PeV energy range and offer observational evidence for understanding not only the physical origin of the knee in the cosmic ray energy spectrum but also its compositional evolution mechanisms.

We investigate the decay modes of a CP-even scalar boson ϕ that mixes with the Standard Model Higgs boson, focusing on the mass range between 2 GeV and 2 m τ . Starting from a higher-order perturbative calculation of the inclusive decays ϕ → gg and ϕ → s s ¯ , we employ a hadronisation model to obtain predictions for individual hadronic final states. Our hadronisation model is based on the Herwig cluster model, but incorporates various conservation laws to determine the allowed final states and their respective weights. The model includes two tunable parameters, which we determine using dispersion relation results at m ϕ = 2 GeV, enabling extrapolation to higher masses. Our predictions show that two-particle hadronic final states like π + π − and K + K − dominate over μ + μ − for m ϕ near 2 GeV, suggesting promising targets for future experimental searches.

This paper reviews the development of theoretical and experimental studies of low-energy QCD parameters starting from early investigations at the JINR Laboratory of Theoretical Physics and ending with modern measurements at CERN. We summarize the historical background and the pioneering theoretical approaches used at JINR to calculate meson parameters in various hadronic models which have laid the foundation for the experimental proposal to investigate the pion polarizability via radiative scattering off nuclei. The first observation of the Compton effect on the pion and the first measurements of the charged pion polarizability and the γ → 3π constant performed with the U-70 accelerator are discussed as key milestones enabling quantitative studies of the meson structure and highlighting their impact on the low-energy QCD phenomenology. Continued advances in theoretical predictions have underscored the need for higher-precision experimental data and motivated new measurements carried out with pion beams in the COMPASS experiment at CERN. Finally, we outline the prospects for future studies within the AMBER experiment where kaon beams will enable a precision determination of kaon polarizabilities and related low-energy constants further advancing our understanding of dynamics of the strong interaction.

The energy-momentum tensor form factor <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>D</a:mi> <a:mo stretchy="false">(</a:mo> <a:mi>t</a:mi> <a:mo stretchy="false">)</a:mo> </a:math> is finite and negative in hadronic models and lattice QCD when only strong forces are included. However, when electromagnetic forces are considered, the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>D</e:mi> <e:mo stretchy="false">(</e:mo> <e:mi>t</e:mi> <e:mo stretchy="false">)</e:mo> </e:math> of charged hadrons undergoes a dramatic change: at small <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>t</i:mi> </i:math> , it changes sign and diverges like <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mn>1</k:mn> <k:mo>/</k:mo> <k:msqrt> <k:mrow> <k:mo>−</k:mo> <k:mi>t</k:mi> </k:mrow> </k:msqrt> </k:math> as shown for the proton in the classical model by Białynicki-Birula based on residual nuclear forces which can be understood as a mean field approach. We construct an analogous neutron model and show that this framework accurately explains the electromagnetic proton-neutron mass difference. We demonstrate that, after appropriately rescaling the residual nuclear forces, the model can reproduce lattice data on the nucleon <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mi>D</m:mi> <m:mo stretchy="false">(</m:mo> <m:mi>t</m:mi> <m:mo stretchy="false">)</m:mo> </m:math> up to <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mrow> <q:mo stretchy="false">(</q:mo> <q:mo>−</q:mo> <q:mi>t</q:mi> <q:mo stretchy="false">)</q:mo> <q:mo>≲</q:mo> <q:mn>1</q:mn> <q:mtext> </q:mtext> <q:mtext> </q:mtext> <q:msup> <q:mi>GeV</q:mi> <q:mn>2</q:mn> </q:msup> </q:mrow> </q:math> as well as QED effects. Based on this realistic model description, we show that the proton and neutron <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:mi>D</u:mi> <u:mo stretchy="false">(</u:mo> <u:mi>t</u:mi> <u:mo stretchy="false">)</u:mo> </u:math> form factors are practically indistinguishable down to <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:mrow> <y:mo stretchy="false">(</y:mo> <y:mo>−</y:mo> <y:mi>t</y:mi> <y:mo stretchy="false">)</y:mo> <y:mo>≈</y:mo> <y:msup> <y:mn>10</y:mn> <y:mrow> <y:mo>−</y:mo> <y:mn>4</y:mn> </y:mrow> </y:msup> <y:mtext> </y:mtext> <y:mtext> </y:mtext> <y:msup> <y:mi>GeV</y:mi> <y:mn>2</y:mn> </y:msup> </y:mrow> </y:math> , far below what can currently be accessed experimentally. We conclude that in the foreseeable future the <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"> <cb:mi>D</cb:mi> <cb:mo stretchy="false">(</cb:mo> <cb:mi>t</cb:mi> <cb:mo stretchy="false">)</cb:mo> </cb:math> form factors of the proton and neutron will practically look the same in experiments and phenomenology.

Context. PKS 0346-27 is a low synchrotron peaked blazar at redshift 0.991. The very high energy (VHE; E &gt; 100 GeV) spectra of blazars are always affected by γγ absorption by the extragalactic background light (EBL), and subsequently no blazars have been detected in VHE γ -rays at redshifts exceeding 1. Aims. This is the goal of a target-of-opportunity (ToO) programme by H.E.S.S.: to observe flaring high-redshift ( z ≳ 1) blazars. Importantly, extending the redshift range of VHE-detected blazars to z ≳ 1 will yield insights into the cosmological evolution of both the VHE blazar population and the EBL. Methods. We report H.E.S.S. ToO and multi-wavelength observations of the blazar PKS 0346−27. We analysed and modelled the H.E.S.S. data together with simultaneous data from Fermi -LAT, Swift (XRT and UVOT), using single-zone leptonic and hadronic models. Results. PKS 0346-27 was detected by H.E.S.S. at a significance of 6.3 σ during one night on 3 November 2021, while for other nights before and after this day, upper limits on the VHE flux have been determined. No evidence for intra-night γ -ray variability has been found. A flare in high-energy ( E &gt; 100 MeV) γ -rays detected by Fermi -LAT preceded the H.E.S.S. detection by 2 days. A fit with a single-zone emission model to the contemporaneous spectral energy distribution during the detection night was possible with a proton-synchrotron-dominated hadronic model, requiring a proton-kinetic-energy-dominated jet power temporarily exceeding the source’s Eddington limit, although alternative (e.g. multi-zone) models cannot be ruled out. A one-zone leptonic model is, in principle, also able to fit the flare-state spectral energy distribution. However, it requires implausible parameter choices, in particular, extreme Doppler and bulk Lorentz factors of ≳80.

The accurate simulation of sub-GeV particle detectors is essential for interpreting experimental data and optimizing detector design. This work identifies and addresses several critical aspects in modeling such detectors, taking as a case study the High-Energy Particle Detector (HEPD-02), a space-borne instrument developed within the CSES-02 mission to measure electrons in the ∼3–100 MeV range, protons and light nuclei in the ∼30–200 MeV/n. The HEPD-02 instrument consists of a silicon tracker, plastic and LYSO scintillator calorimeters, and anticoincidence systems, making it a representative example of a complex low-energy particle detector operating in Low Earth Orbit. Key challenges arise from replicating intricate detector geometries derived from CAD models, selecting appropriate hadronic physics lists for low-energy interactions, and accurately describing the detector response—particularly quenching effects in scintillators and digitization in solid-state tracking planes. Particular attention is given to three critical aspects: the precise CAD-level geometry implementation, the impact of hadronic physics models on the detector response, and the parameterization of scintillation quenching. In this study, we present original solutions to these challenges and provide data–MC comparisons using data from HEPD-02 beam tests.

Abstract The modelling of the formation of colour-singlet hadrons from coloured partons, known as Hadronization, is crucial for generating realistic events in Monte Carlo Event Generators. Due to limited understanding of the non-perturbative regime, physically motivated phenomenological hadronization models with tunable parameters are used and later tuned to the experimental data. Modern Monte Carlo generators primarily employ one of two hadronization models: the Lund string model, which is the default in , and the cluster model, which is the default in and . In this work, we combine the Lund string hadronization model, as implemented in , with using interface. We tune the string model with ’s Angular Ordered Parton Shower (AOPS) to lepton and hadron collision data, resulting in the Les Houches Tune ( LH Tune ), which shows good performance across a wide range of observables. The LH Tune will be included in the release. (It can also be used with , provided that the relevant patch is applied to the installation script which can be provided by the authors.) This development enables a direct comparative study of the two hadronization models within , both interfaced with the Angular Ordered Parton Shower, which serves as the main motivation behind this work.

This work investigates the properties of the Lateral Distribution Function (LDF) of gamma-ray-induced Extensive Air Showers (EAS) across a large energy range from (1015 to 1020) eV, which includes the knee and ankle energy regions. The AIRES (AIR-shower Extended Simulations) system was used in simulations to generate secondary gamma rays, with primary protons serving as initiating particles. Hadronic interaction models, particularly QGSJET-04-II and EPOS-LHC, were used to explore the impact of alternative physical assumptions on shower development. The lateral distribution of secondary gamma rays was studied systematically at various primary energy and zenith angles. The findings show that the LDF is clearly dependent on primary energy, with considerable differences between the knee and ankle regions. Furthermore, zenith angles have a major influence on the lateral dispersion of gamma rays, emphasizing differences in particle interactions and shower dynamics. The sigmoidal function was used to set the lateral distribution coefficient curves of EAS, generating new coefficients as a function of primary energy. These findings provide vital insights into the behavior and detection of gamma-ray-induced EAS, increasing our knowledge of high-energy astrophysics and cosmic-ray studies.

Objective. This study aims to validate a Monte Carlo model for fetal dose estimation in the complex secondary field of pencil beam scanning (PBS) proton therapy for breast cancer, one of the most common cancers occurring during pregnancy.Approach. A TOPAS/GEANT4 Monte Carlo simulation environment based on an IBA ProteusOne beam model was developed, reflecting the experimental setup of a breast irradiation using a pregnant anthropomorphic phantom. Experimental doses were acquired with thermoluminescent dosimeters for protons and gammas, and bubble detectors (BDs) for neutrons. Simulated doses were scored at the same positions using three hadronic physics models: BIC_HP, BIC_AllHP, and BERT_HP. Experimental doses were corrected for detector energy response using simulation-derived energy spectra.Main results. Agreement between simulation and measurement varied depending on hadronic model, scoring volume size, and correcting for BD energy response. Two physics models conservatively estimated fetal neutron doses within the combined measurement and simulation uncertainties, with BIC_AllHP showing the closest agreement. Combined proton and gamma doses were accurately reproduced for all models for inserts 2-6, but were underestimated for insert 1, likely due to dose gradients and modeling limitations near the treatment field. The total simulated fetal dose equivalent at the fundus height was 5.17 mSv. This value is substantially lower than doses reported for photon-based therapies, remains well below the 100 mSv threshold for deterministic effects, and is within range of the public 1 mSv dose limit.Significance. The results demonstrate that, within the tested experimental framework, the TOPAS/GEANT4 Monte Carlo model is suitable for fetal dose estimation in PBS proton therapy for breast cancer. In this setting, calculated fetal doses were substantially lower than those reported for photon-based radiotherapy. The validated framework provides a practical basis for treatment planning optimization and risk assessment and can be extended to other clinical scenarios following similar validation.

This paper presents a systematic study of charged pion and proton production in inelastic $p^{12}\text{C}$ and $d^{12}\text{C}$ collisions at a beam momentum of 4.2~GeV/$c$ per nucleon as a function of collision centrality, which is characterized by the net charge $Q$ of secondary particles serving as an experimental estimator of the number of participating nucleons. We analyze the average multiplicities and kinematic characteristics of $\pi^{+}$, $\pi^{-}$, and protons, including the mean momentum $\langle p \rangle$, transverse momentum $\langle p_{T} \rangle$, emission angle $\langle \theta \rangle$, and rapidity $\langle y \rangle$. The experimental results are compared in detail with predictions of the FRITIOF model, which provides a satisfactory overall description of the particle multiplicities. A clear centrality dependence is observed: with increasing $Q$, the average momentum of pions decreases while their mean emission angle increases, indicating an enhanced role of secondary intranuclear interactions. These effects are more pronounced in $p\text{C}$ than in $d\text{C}$ collisions. The data presented in this work provide a quantitative benchmark for hadronic transport models in the few-GeV energy range.

We present a novel approach for assessing the muon content of air showers with large zenith angles on a combined analysis of their radio emission and particle footprint. We use the radiation energy reconstructed by the Auger engineering radio array (AERA) as an energy estimator and determine the muon number independently with the water-Cherenkov detector array of the Pierre Auger Observatory, deployed on a 1500 m grid. We focus our analysis on air showers with primary energy above 4 EeV to ensure full detection efficiency. Over approximately ten years of accumulated data, we identify a set of 40 high-quality events that are used in the analysis. The estimated muon contents in data are compatible with those for iron primaries as predicted by current-generation hadronic interaction models. This result can be interpreted as a deficit of muons in simulations as a lighter mass composition has been established from X max measurements. This muon deficit was already observed in previous analyses of the Auger Collaboration and is confirmed using hybrid events that include radio measurements for the first time.

Global tuning of hadronic interaction models with accelerator-based and astroparticle data

Abstract We investigate the origin of the very-high-energy (VHE; ≥ 100 GeV) γ -ray emission from the low-synchrotron-peaked BL Lac object Ap Librae within the framework of a one-zone hadronuclear ( pp ) interaction model. Conventional leptonic and hadronic scenarios (including photohadronic processes and proton synchrotron emission), have encountered difficulties in reproducing the unusually broad GeV-TeV spectrum of this source without invoking extreme physical conditions. In this work, we construct a one-zone pp model that incorporates both leptonic and hadronuclear components, and apply it to fit the multiwavelength spectral energy distribution of Ap Librae. Our results show that the optical-GeV emission can be well explained by leptonic emission from primary electrons, while the TeV emission is naturally accounted for by γ -rays from neutral pion decay in pp interactions. The required total jet power is found to be ~1.8 × 10 46 erg s -1 , which corresponds to half of the Eddington luminosity of the central supermassive black hole. Compared with previous hadronic models that demand super-Eddington energetics, our approach provides a more physically reasonable explanation for the VHE spectrum of Ap Librae.

In this article, we study prompt unpolarised J/ψ production in protonproton collisions within the TMD factorisation (via the Soft Gluon Resummation approach) and the Improved Color Evaporation model as a hadronisation model. We fit nonberturbative hadronisation parameter of the ICEM to the set of J/ψ production experimental data at the wide range of center-of-mass energies √s from 15 GeV up to 13 TeV. Based on the obtained fit, we predict the unpolarised J/ψ production for kinematics of the SPD NICA experiment.

Abstract The Large High Altitude Air Shower Observatory has detected very high-energy (VHE) gamma-rays from NGC 4278, which is known to host a low-luminosity active galactic nucleus (AGN). Having only very weak radio jets, the origin of its VHE gamma-rays is unclear. In this paper we first show that NGC 4278 has a massive molecular cloud surrounding the nucleus by analyzing data taken with the Atacama Large Millimeter/submillimeter Array. We then assume that cosmic ray protons are accelerated in a radiatively inefficient accretion flow around the supermassive black hole, diffusing into the molecular cloud and producing gamma-rays and neutrinos via $pp$ interactions. We model the gamma-ray spectra and find that the observations can be explained by such hadronic processes if the AGN activity was higher in the past than at present, and the diffusion coefficient in the molecular cloud is appreciably smaller than in the Milky Way interstellar medium. We also show that although the high-energy neutrinos co-produced with the gamma-rays are unlikely to be detectable even with IceCube-Gen2, the accompanying synchrotron X-ray emission due to pion-decay secondary electrons and positrons may be detectable in the future, providing a valuable test of our hadronic model.

Active particles are nonequilibrium entities that uptake energy and convert it into self-propulsion. A dynamically rich class of inertial active particles having features of wave-particle coupling and wave memory are walking/superwalking droplets. Such classical, active wave-particle entities (WPEs) have previously been shown to exhibit hydrodynamic analogs of many single-particle quantum systems. Inspired by the rich dynamics of strongly interacting superwalking droplets in experiments, we numerically investigate the dynamics of WPE clusters using a stroboscopic model. We find that several interacting WPEs self-organize into a stable bound cluster, reminiscent of an atomic nucleus. This active cluster exhibits a rich spectrum of collective excitations, including shape oscillations and chiral rotating modes, akin to vibrational and rotational modes of nuclear excitations, as the spatial extent of the waves and their temporal decay rate (memory) are varied. Dynamically distinct excitation modes create a common time-averaged collective wave field potential, bearing qualitative similarities with the nuclear shell model and the bag model of hadrons. For high memory and rapid spatial decay of waves, the active cluster becomes unstable and disintegrates; however, within a narrow regime of the parameter space, the cluster ejects single particles whose decay statistics follow exponential laws, reminiscent of radioactive nuclear decay. Our study uncovers a rich spectrum of dynamical behaviors in clusters of active particles, opening new avenues for exploring hydrodynamic quantum analogs in active matter systems.

Statistical hadronization model for low-energy heavy-ion collisions

The recent observation of multiple near-threshold structures in e + e − annihilation—including ψ ( 3770 ) , G ( 3900 ) , R ( 3760 ) , R ( 3780 ) , and R ( 3810 ) —reveals limitations in existing models of charmonium and exotic hadrons. In this paper, we propose a unified coupled-channel description that simultaneously incorporates all five near-threshold structures using parameters constrained by hadron spectroscopy. Our model accurately reproduces the line shapes in both D D ¯ and nonopen-charm hadron (nOCH) channels, resolves the asymmetric profile of ψ ( 3770 ) , and produces the G ( 3900 ) bump. We identify the R ( 3780 ) as the dominant manifestation of ψ ( 3770 ) , attribute R ( 3760 ) to D D ¯ → nOCH rescattering and suggest that R ( 3810 ) arises from coupling between the ψ ( 1 D ) state and the h c π π channel. The significant non- D D ¯ decay of ψ ( 3770 ) is explained by its near-threshold position. This analysis provides a coherent, unquenched framework centered on a charmonium ψ ( 1 D ) core for near-threshold phenomena and offers a predictive approach extendable to bottomonium systems and future data from Belle II.

A search for cosmological axions has been performed by scanning a frequency region of 38MHz centered at about 10.2GHz, corresponding to an axion mass m_{a}≃42 μeV. The QUAX experimental apparatus, a haloscope comprised of a 1-liter volume tunable cavity immersed in an 8T magnetic field and a quantum-limited detection chain, set limits on the axion-photon coupling at the 10^{-14} GeV^{-1} level. As no signal candidate has been observed, viable hadronic axion models are ruled out in a currently preferred postinflationary region m_{a}>40 μeV.

The nucleon exhibits a rich internal structure governed by quantum chromodynamics (QCD), where its electric charge arises from valence quarks, while its spin and mass emerge from complex interactions among valence quarks, sea (anti)quarks, and gluons. At the advent of QCD, an alternative hypothesis emerged suggesting, at high energies, the transport of a nucleon's baryon number could be traced by a nonperturbative configuration of gluon fields connecting its three valence quarks, forming a Y -shaped topology known as the gluon junction. Recent measurements by the STAR experiment are compatible with this scenario. In light of these measurements, this study aims to explore the mechanisms of baryon transport in high-energy nuclear collisions using the -8 framework, which incorporates a state-of-the-art hadronization model with advanced color flow (CF) and color reconnection (CR) mechanisms that mimic signatures of a baryon junction. Within this model setup, we investigate (i) the rapidity slope of the net-baryon distributions in photon-included processes ( γ + p ) and (ii) baryon over charge transport in the isobaric ( Ru + Ru and Zr + Zr ) collisions. Our study highlights the importance of the CF and CR mechanisms in -8, which play a crucial role in baryon transport. The results show that the CF and CR schemes significantly affect the isobaric baryon-to-charge ratio, leading to different predictions for baryon stopping and underscoring the need to account for CF and CR effects in comparisons with experimental measurements.