Learning pole structures of hadronic states using predictive uncertainty estimation

We investigate the quantum properties of the truly gauge-invariant and conserved charges of two-dimensional Yang-Mills theories, focusing on lattice QCD in the strong coupling regime. The construction of those charges uses the integral version of the ( 1 + 1 )-dimensional Yang-Mills equations, and they correspond to the eigenvalues of a charge operator. The gauge invariance of the charges suggests that they are not confined, hence hadronic states may carry them. Using the path integral formalism with imaginary time (Euclidean), we evaluate the correlation functions of those charges on baryon and meson states through functional integrals over the gauge group S U ( N ) ( N = 2 , 3) and Grassmannian variables—the fermionic fields. Our results show that the expectation values of the lowest nontrivial charges are nonzero for baryon and meson states but vanish for non-gauge-invariant states, supporting the interpretation that hadrons indeed carry these charges. While renormalization effects and higher-order contributions remain to be analyzed, these findings point toward a potential link between gauge-invariant charges and confinement.

Abstract Color multiplets of the gauge fields and fermions on mass shell in SU (N ) Yang-Mills theory are classified according to representations of the Weyl group W (SU (N )). The multiplet structure of quark and gluon multiplets has been studied in the framework of a non-perturbative approach by considering complete exact equations of motion of the SU (N ) Yang-Mills theory with matter fields. An important case of singlet non-Abelian gluon solutions corresponding to one-dimensional singlet representations of the Weyl group is revised on a rigorous mathematical basis. We demonstrate that Weyl group as a finite color subgroup of SU (N ) reveals an inherent color symmetry of quarks and gluons on mass shell which determines a universal color multiplet structure of quark-gluon solutions in a pure SU (N ) Yang-Mills theory and in Abelian projected Yang-Mills theories with quarks. The obtained results allow to introduce strict concepts of fundamental particles, quarks and gluons, which differ drastically from the particle definitions in the conventional perturbative Yang-Mills theory. Possible applications of our results in non-perturbative quantum chromodynamics and hadron physics are discussed.

Abstract In this work, the mass spectra of charm-strange hadrons are studied using a non-relativistic screened potential model. The four-body problem is reduced to two-body problem using the diquark-antidiquark approach. Mass and decay properties are studied and compared with available experimental and other theoretical studies. The Schrödinger equation is solved numerically with the help of the Mathematica package. Spin-dependent terms are also added to the potential perturbatively.

Hadronic physics has gradually emerged as one of the growing research frontiers in Indonesia, driven by efforts to better understand the properties of the strong interaction and the internal structure of hadrons from the fundamental principles of Quantum Chromodynamics. In the last few decades, Indonesian researchers have made significant contributions to developing various theoretical and phenomenological aspects of hadrons. In addition, on the experimental side, Indonesian scientists have participated in hadron experiment facilities overseas, such as the ALICE collaboration at CERN, which has strengthened the scientific activities and networks and has supported the training of young Indonesian researchers. In the present paper, we review Indonesian scientists’ contributions to hadronic physics, highlight ongoing research directions in both experimental and theoretical, and outline strategies for future development toward integration into the international hadronic physics community.

The observation of the [Formula: see text] state by Belle II Collaboration has sparked significant interest in the theoretical understanding of such states within the context of hadron physics. Considering the similar mass and the decay with, as well as the same quantum numbers [Formula: see text] with the [Formula: see text] state, which is referred to be the [Formula: see text] in PDG, in this work, we try to calculate the mass of the [Formula: see text] state. The model used to predict the high-energy spectrum of these states generally involves a constituent quark model, which can describe a variety of properties of hadrons containing heavy quarks. In the framework of the unquenched quark model, a coupled-channel calculation is employed to explore the effect of open-bottom meson–meson thresholds on the [Formula: see text] state. The hypothesis is that coupled-channel effects could be large enough to create new dynamically generated states, thus potentially explaining the nature of the [Formula: see text] state, as well as whether [Formula: see text] and [Formula: see text] is the same state. The results indicate that unquenched effects play a crucial role in explaining [Formula: see text] state, providing a plausible mechanism for its formation. Besides in our calculations, [Formula: see text] and [Formula: see text] may be two different states.

Quantum computers are coming online and will quickly impact hadron physics once certain fidelity, decoherence and memory thresholds are met, quite possibly within a decade. We review a selected number of topics where ab-initio quantum chromodynamics-level information about hadrons can be obtained with this computational tool that is hard to come by from other methods. This includes high baryon-density systems such as neutron-star matter (with a sign problem in lattice gauge theory); fragmentation functions; Monte Carlo generation of particles which accounts for quantum correlations in the final state; entropy production in jets; and generally, any application where time evolution in Minkowski space (as opposed to a Euclidean formulation) or where large chemical potentials play an important dynamical role. For other problems, such as the prediction of very highly excited hadron spectroscopy, they will not be a unique, but a complementary tool.

This Letter reports the first calculation of the gravitational form factors (GFFs) of the scalar glueball, performed via lattice field theory in Yang-Mills theory at a single lattice spacing. The glueball GFFs are compared with those of other hadrons as determined in previous lattice calculations, providing strong indications that glueballs have a different gluonic structure than typical hadronic states. A mass radius of 0.263(31)fm is predicted, supporting previous suggestions that the scalar glueball is significantly smaller than other hadrons.

Symmetry is a key with which it is possible to unlock the doors that nature keeps hidden [...]

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.

We perform a theoretical study of the decay process ϒ → D − B ¯ 0 D s + in search of the doubly heavy tetraquark states T b c s ¯ with quark content b c s ¯ d ¯ . These T b c s ¯ states are assumed to be dynamically generated molecular states from the S-wave interactions between B ¯ s ( * ) 0 D ( * ) + and B ¯ ( * ) 0 D s ( * ) + meson pairs. Based on the total angular momentum and the type of the constituent mesons (pseudoscalars P or vectors V ), they are labeled as T b c s ¯ 0 , P P , T b c s ¯ 0 , V V , and T b c s ¯ 2 , V V , respectively. The B ¯ 0 D s + invariant mass distribution for this decay is calculated using current algebra, incorporating contributions from T b c s ¯ states arising from final-state interactions. Our results reveal a clear peak structure in the 7415–7425 MeV region, which is attributed to the T b c s ¯ 2 , V V state. Additionally, a distinct dip structure appears near the B ¯ * 0 D s * + threshold, characteristic of the T b c s ¯ 2 , V V as a hadronic molecular state. A near-threshold enhancement associated with the T b c s ¯ 0 , P P state and a dip arising from the T b c s ¯ 0 , V V state are also identified, though the manifestation of these features depends sensitively on model parameter fine-tuning. Therefore, with increased experimental statistics, the decay channel ϒ → D − B ¯ 0 D s + offers a promising avenue for discovering and characterizing the T b c s ¯ states.

Abstract Understanding the spectrum and dynamics of excited nucleon states (N* resonances) remains a central challenge in hadron physics, as these resonances emerge in intermediate states of πN and γN interactions. The dynamical coupled-channel (DCC) models addressing this problem rely critically on experimental inputs for partial wave analyses (PWA). However, polarization observables of hyperons, which serve as sensitive probes of reaction mechanisms, have so far been limited in precision. To end this, we aim to provide high-precision measurements of the polarization of the Λ hyperon produced in the π−p → K0Λ reaction. The data were obtained with the J-PARC E40 experiment at the K1.8 beamline of the J-PARC Hadron Experimental Facility. The polarization of the Λ was precisely measured in the angular range $0.6 < \cos {\theta ^{K0}_{CM}}< 1.0$ with a fine bin width of $d\cos {\theta ^{K0}_{CM}}= 0.05$. The observed average polarization in the region $0.60 < \cos {\theta ^{K0}_{CM}}< 0.85$ was 0.932 ± 0.058(stat) ± 0.028(syst). These results provide essential input for PWAs of DCC models, contributing to a deeper understanding of N* resonance dynamics. Furthermore, the strong Λ polarization observed indicates the feasibility of developing a highly polarized Λ beam, opening prospects for future Λp scattering experiments such as J-PARC E86.

Statistical hadronization model for low-energy heavy-ion collisions

We simulate the heavy quarkonium equilibration through transport in a static and homogeneous quark-gluon plasma (QGP) box within the semiclassical Boltzmann approach, incorporating both the leading-order and next-to-leading-order dissociation and regeneration reactions. The scattering amplitudes involved are taken from perturbative computations based on effective color-electric dipole coupling of the heavy quarkonium with thermal gluons. By coupling the Langevin simulation of single heavy quark diffusion and the Boltzmann transport of the heavy quarkonium in a real-time fashion, we demonstrate how the kinetic and chemical equilibrium of heavy quarkonium with single heavy quarks in the medium is achieved in terms of both the bound state’s yields and momentum distributions. The pertinent equilibration time turns out to be comparable to the lifetime of the QGP created in the most central heavy-ion collisions at the LHC energies. The role of the intricate interplay between the open and hidden heavy sector in the process of equilibration is highlighted. This work provides a dynamical way of understanding the phenomenological success of the statistical hadronization model for charmonium production in relativistic heavy-ion collisions and also paves the way for realistic phenomenological applications to heavy quarkonium transport.

Simulation of nuclear relaxation in Geant4 hadronic physics

Theoretical modeling of 65Zn production via charged particle reactions on 66Zn.

Abstract We present track reconstruction algorithms based on deep learning, tailored to overcome specific central challenges in the field of hadron physics. Two approaches are used: (i) deep learning (DL) model known as fully-connected neural networks (FCNs), and (ii) a geometric deep learning (GDL) model known as graph neural networks (GNNs). The models have been implemented to reconstruct signals in the non-Euclidean detector geometry of the future antiproton experiment PANDA. In particular, the GDL model shows promising results for cases where other, more conventional track-finders fall short: (i) tracks from low-momentum particles that frequently occur in hadron physics experiments and (ii) tracks from long-lived particles such as hyperons, hence originating far from the beam-target interaction point. Benchmark studies using Monte Carlo simulated data from PANDA yield an average technical reconstruction efficiency of 92.6% for high-multiplicity muon events, and 97.1% for the $$\Lambda$$ Λ daughter particles in the reaction $$\bar{p}p \rightarrow \bar{\Lambda }\Lambda \rightarrow \bar{p}\pi ^+ p\pi ^-$$ p ¯ p → Λ ¯ Λ → p ¯ π + p π - . Furthermore, the technical tracking efficiency is found to be larger than 70% even for particles with transverse momenta $$p_\text {T}$$ p T below 100 MeV/c. For the long-lived $$\Lambda$$ Λ hyperons, the track reconstruction efficiency is fairly independent of the distance between the beam-target interaction point and the $$\Lambda$$ Λ decay vertex. This underlines the potential of machine-learning-based tracking, also for experiments at low- and intermediate-beam energies.

Abstract In this study, we utilize light-cone QCD sum rules at twist-3 accuracy to compute the coupling parameters of the $$\chi _{c1}(2P)$$ χ c 1 ( 2 P ) state with D and $$D^*$$ D ∗ mesons. The analysis reveals that the observed $$\chi _{c1}(3872)$$ χ c 1 ( 3872 ) meson incorporates significant amounts of both charmonium and molecular components. The interplay between these components highlights the exotic nature of $$\chi _{c1}(3872)$$ χ c 1 ( 3872 ) . Furthermore, implications for a possible mixing between the $$\chi _{b1}(2P)$$ χ b 1 ( 2 P ) state and a potential $$B\bar{B}^*$$ B B ¯ ∗ molecule is discussed. These findings contribute to the understanding of exotic hadron states and their intricate internal structures.

Abstract Solving the Dirac equation has played an important role in many areas of fundamental physics. In this work, we present the Dirac equation solver DiracSVT, which solves the Dirac equation with scalar, vector, and tensor nuclear potentials in spherical coordinate space. The shooting method was used with a Runge–Kutta 4 integration scheme. The potentials are parameterized in a Woods–Saxon form, which reproduce well the known single-particle states around all doubly magic nuclei and can be applied to study the shell evolution of exotic nuclei. The code can be easily extended to the study of other systems, including atomic, hadron, and molecular physics.

The properties of bound states are fundamental to hadronic spectroscopy and play a central role in the transition from hadronic matter to a quark-gluon plasma (QGP). In a strongly coupled QGP (sQGP), the interplay of temperature, binding energy, and large collisional widths of the partons poses formidable challenges in evaluating the in-medium properties of hadronic states and their eventual melting. In particular, the existence of heavy quarkonia in the QGP is a long-standing problem that is hard to solve by considering their spectral properties on the real-energy axis. We address this problem by analyzing in-medium thermodynamic quarkonium T matrices in the complex energy plane. We first validate this method in vacuum, where the T-matrix poles of observed states are readily identified. When deploying this approach to recent self-consistently calculated T matrices in the QGP, we find that poles in the complex energy plane can persist to surprisingly large temperatures, depending on the strength of the in-medium interactions. While the masses and widths of the pole positions are precisely defined, the notion of a binding energy is not due to the absence of thresholds caused by the (large) widths of the underlying quark or anti-quark spectral functions. Our method thus provides a new and definitive quantum-mechanical criterion to determine the melting temperature of hadronic states in the sQGP while increasing the accuracy in the theoretical determination of transport parameters.