Hadron Dynamics Research Articles

SMASH as an event generator for heavy-ion collisions

In this article we present an overview of the SMASH hadronic transport approach that is applied for non-equilibrium dynamics of hadrons in heavy-ion collisions. We will give an overview about the ingredients of the approach and the applications for the dynamical description of heavy-ion collisions and for calculations of fundamental properties of the hadron gas. The main emphasis of the article will be the infrastructure for sustainable software development that we have developed over the last 10 years including extensive unit tests and continuous integration. We will also provide one section about the performance of the code and how it can be analyzed and improved in the future.

Isospin sum rules for the nonleptonic B decays

Isospin symmetry, as the most precise flavor symmetry, can be used to extract information about hadronic dynamics. The effective Hamiltonian for bottom quark weak decay is zero under the isospin lowering operators I-n\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$I_-^n$$\\end{document}, which allows us to generate isospin sum rules through several master formulas. In this work, we derive the master formulas of isospin sum rules for the two- and three-body non-leptonic decays of B mesons. Numerous new isospin sum rules, especially those involving three or more decay channels, are proposed. The isospin sum rules can be used to test isospin symmetry and provide hints the isospin partners of exotic hadrons in B decays. It is found ten percent isospin breaking only in decay modes involving two vector mesons, indicating the complex dynamics of vector mesons. Besides, the isospin analysis suggests the charm tetraquark resonances might be observed in the B-→J/Ψπ-K¯0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ B^- \\rightarrow J/\\Psi \\pi ^-\\overline{K}^0$$\\end{document}, B¯0→J/ΨK¯0ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\overline{B}^0 \\rightarrow J/\\Psi \\overline{K}^0\\phi $$\\end{document}, and B¯0→D0D¯0K¯0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\overline{B}^0\\rightarrow D^0\\overline{D}^0\\overline{K}^0$$\\end{document} modes.

Thermodynamic signatures and phase transitions in high-energy Au–Au collision

In this study, we systematically investigate the dynamics of various hadrons namely π +, π −, K +, K −, p, p¯ , Λ, Λ¯ , Ξ− and Ξ¯+ produced in central Au–Au collisions. We analyze data of AGS and RHIC, which span a broad range of collision energies, ranging from sNN = 1.9 to 200 GeV. To analyze the transverse momentum (p T ) and transverse mass (m T ) distributions, we employ a two-component standard distribution function, achieving a very good representation of the experimental data across these energy regimes. We extract key thermodynamic parameters, including the effective temperature T, the mean transverse momentum 〈p T 〉, and the initial temperature T i , and analyze their dependence on the values of collision energy and particle mass. Our findings reveal a distinct transition behaviour around sNN=19.6GeV . Below sNN=19.6GeV , the values of T, 〈p T 〉, and T i increase monotonically for all hadrons due to higher energy transfer into the system. Above this energy threshold, these extracted parameters plateau, suggesting that the additional energy is utilized as latent heat for phase transition rather than increasing the system’s temperature. These observations delineate two distinct regions: a hadron-dominated region at lower energies and a parton-dominated region at higher energies, each potentially indicative of different phases of matter, with the latter possibly signalling the onset of a quark–gluon plasma. The study thus provides critical insights into the complex interplay of thermodynamics, phase transitions, and particle interactions in high-energy Au–Au collisions.

Dark sector glueballs at the LHC

We study confining dark sectors where the lightest hadrons are glueballs. Such models can provide viable dark matter candidates and appear in some neutral naturalness scenarios. In this work, we introduce a new phenomenological model of dark glueball hadronization inspired by the Lund string model. This enables us to make the most physically-motivated predictions for dark glueball phenomenology at the LHC to date. Our model approximately reproduces the expected thermal distribution of hadron species as an emergent consequence of hadronization dynamics. The ability to predict the production of glueball states heavier than the lightest species significantly expands the reach of long-lived glueball searches in MATHUSLA compared to previous simplified estimates. We also characterize regions of parameter space where emerging and/or semivisible jets could arise from pure-glue dark sectors, thereby providing new benchmark models that motivate searches for these signatures.

Unveiling the dynamics of little-bang nucleosynthesis

High-energy nuclear collisions provide a unique site for the synthesis of both nuclei and antinuclei at temperatures of kT ≈ 100 − 150 MeV. In these little bangs of transient collisions, a quark-gluon plasma (QGP) of nearly vanishing viscosity is created, which is believed to have existed in the early universe within the first few microseconds after the Big Bang. Analyses of identified particles produced in these little bangs based on the statistical hadronization model for the QGP have suggested that light (anti)nuclei are produced from the QGP as other hadrons and their abundances are little affected by later hadronic dynamics. Here, we find a strong reduction of the triton yield by about a factor of 1.8 in high-energy heavy-ion collisions based on a kinetic approach that includes the effects of hadronic re-scatterings, particularly that due to pion-catalyzed multi-body reactions. This finding is supported by the latest experimental measurements and thus unveils the important role of hadronic dynamics in the little-bang nucleosynthesis.

Charming penguins and lepton universality violation in varvec{b rightarrow s ell ^+ ell ^-} decays

The LHCb experiment has recently presented new results on Lepton Universality Violation (LUV) in B rightarrow K^{(*)} ell ^+ ell ^- decays involving K_S in the final state, which strengthen the recent evidence of LUV obtained in B^+ rightarrow K^{+} ell ^+ ell ^- decays and the previous measurements of B rightarrow K^{*0} ell ^+ ell ^-. While LUV observables in the Standard Model are theoretically clean, their predictions in New Physics scenarios are sensitive to the details of the hadronic dynamics, and in particular of the charming penguin contribution. In this work, we show how a conservative treatment of hadronic uncertainties is crucial not only to assess the significance of deviations from the Standard Model but also to obtain a conservative picture of the New Physics responsible for LUV. Adopting a very general parameterization of charming penguins, we find that: (i) current data hint at a sizable q^2 and helicity dependence of charm loop amplitudes; (ii) conservative NP solutions to B anomalies favour a left-handed or an axial lepton coupling rather than a vector one.

Heavy quark contribution to the electromagnetic properties of the nucleon

Quantum chromodynamics (QCD) predicts the existence of both nonperturbative intrinsic and perturbative extrinsic heavy quark contributions to the fundamental structure of hadrons. The existence of intrinsic charm at the 3-standard-deviation level in the proton has recently been established from structure function measurements by the NNPDF Collaboration. Here we revisit the physics of intrinsic heavy quarks using light-front holographic QCD (LFHQCD) - a novel comprehensive approach to hadron structure which provides detailed predictions for dynamical properties of the hadrons, such as form factors, distribution amplitudes, structure functions, etc. We will extend this nonperturbative light-front QCD approach to study the heavy quark-antiquark contribution to the electromagnetic properties of nucleon. Our framework is based on a study of the eigenfunctions of the QCD light-front Hamiltonian, the frame-independent light-front wave functions (LFWFs) underlying hadron dynamics. We analyze the heavy quark content in the proton, induced either directly by the nonperturbative $|uud+Q\bar Q\rangle$ Fock state or by the $|uud+g\rangle$ Fock state, where the gluon splits into a heavy quark-antiquark pair. The specific form of these LFWFs are derived from LFHQCD. Using these LFWFs, we construct light-front representations for the heavy quark-antiquark asymmetry, the electromagnetic form factors of nucleons induced by heavy quarks, including their magnetic moments and radii.

Low energy protons as probes of hadronization dynamics

Energetic quarks liberated from hadrons in nuclear deep-inelastic scattering propagate through the nuclear medium, interacting with it via several processes. These include quark energy loss and nuclear interactions of forming hadrons. One manifestation of these interactions is the enhanced emission of low-energy charged particles, referred to as grey tracks. We use the theoretical components of the BeAGLE event generator to interpret grey track signatures of parton transport and hadron formation by comparing its predictions to E665 data. We extend the base version of BeAGLE by adding four different options for describing parton energy loss. The E665 data we used consists of multiplicity ratios for fixed-target scattering of 490 GeV muons on Xe normalized to deuterium as a function of the number of grey tracks. We compare multiplicity ratios for E665 grey tracks to the predictions of BeAGLE, varying the options and parameters to determine which physics phenomena can be identified by these data. We find that grey tracks are unaffected by modifications of the forward production. Thus their production must be dominated by interactions with hadrons in the backward region. This offers the advantage that selecting certain particles in the forward region is unlikely to bias a centrality selection. We see a strong correlation between the number of grey tracks and the in-medium path length. Our energy loss model does not reproduce the suppression observed in the projectile region. We see an underprediction of the proton production rate in backward kinematics, suggesting that a stronger source of interaction with the nuclear medium is needed for accurate modeling. These results lay an important foundation for future spectator tagging studies at both Jefferson Lab and at the Electron-Ion Collider, where neutron and proton grey track studies will be feasible down to very small momenta.

Explaining mass and spin in the visible matter: the next challenge

Understanding in depth …the origin of the nucleon mass, the nucleon spin, and the emergent properties of a dense gluon system… (Electron-ion collider Yellow Report, arXiv:2103.05419v) represents the frontier of modern hadron physics, both on the experimental and theoretical side. In this contribution, after briefly outlining the above challenges in view of the various experimental facilities planned in the near future, some insights into the non-perturbative regime of QCD will be provided. In particular, the most recent achievements in the description of the pion, playing a fundamental role in the hadron dynamics, will be illustrated within a genuinely relativistic quantum-field theoretical framework, based on actual solutions of the homogeneous Bethe-Salpeter equation.

Predictions for the Sivers single-spin asymmetry from holographic QCD

A new approach to nonperturbative QCD, holographic light-front QCD, provides a comprehensive model for hadron dynamics and spectroscopy, incorporating color confinement, a universal hadron mass scale, the prediction of a massless pion in the chiral limit, and connections between the spectroscopy of mesons, baryons and tetraquarks across the full hadron spectrum. In this article we present predictions for the Sivers asymmetry and related transverse momentum distributions for the proton based on the light-front wavefunctions of the baryon eigenstate predicted by holographic QCD.

Harmonic flow correlations in Au+Au reactions at 1.23 AGeV: a new testing ground for the equation-of-state and expansion geometry

Correlations between the harmonic flow coefficients v_1, v_2, v_3 and v_4 of nucleons in semi-peripheral Au+Au collisions at a beam energy of 1.23 AGeV are investigated within the hadronic transport approach ultra-relativistic quantum molecular dynamics (UrQMD). In contrast to ultra-relativistic collision energies (where the flow coefficients are evaluated with respect to the respective event plane), we predict strong correlations between the flow harmonics with respect to the reaction plane. Based on an event-by-event selection of the midrapidity final state elliptic flow of nucleons we show that as a function of rapidity, (I) the sign of the triangular flow changes, (II) that the shape of v_4 changes from convex to concave, and (III) that v_3propto v_1v_2 and v_4propto v_2^2 for all different event classes, indicating strong correlations between all investigated harmonic flow coefficients.

Event-by-Event Investigation of the Two-Particle Source Function in Heavy-Ion Collisions with EPOS.

Exploring the shape of the pair-source function for particles such as pions or kaons has been an important goal of heavy-ion physics, and substantial effort has been made in order to understand the underlying physics behind the experimental observations of non-Gaussian behavior. In experiments, since no direct measurement of the source function is possible, quantum-statistical momentum correlations are utilized to gain information about the space-time geometry of the particle emitting source. Event generators, such as EPOS, however, provide direct access to the freeze-out coordinates of final state particles, and thus the source function can be constructed and investigated. The EPOS model is a sophisticated hybrid model where the initial stage evolution of the system is governed by Parton-Based Gribov–Regge theory, and subsequently a hydrodynamic evolution is utilized, followed by hadronization and hadron dynamics. EPOS has already proven to be successful in describing several different experimental observations for systems characterized by baryon chemical potential close to zero, but so far the source shape has not been explored in detail. In this paper we discuss an event-by-event analysis of the two-particle source function in = 200 GeV Au+Au collisions generated by the EPOS model. We find that when utilizing all stages of the model, Lévy-shaped distributions (unlike Gaussian distributions) provide a good description of the source shape in the individual events. Hence it is clear that it is not the event averaging that creates the non-Gaussian features in the pair distributions. Based on this observation, we determine Lévy-parameters of the source as a function of event centrality and particle momentum.

Cold-atom quantum simulator for string and hadron dynamics in non-Abelian lattice gauge theory

We propose an analog quantum simulator for simulating real-time dynamics of $(1+1)$-dimensional non-Abelian gauge theory well within the existing capacity of ultracold-atom experiments. The scheme calls for the realization of a two-state ultracold fermionic system in a one-dimensional bipartite lattice, and the observation of subsequent tunneling dynamics. Being based on the loop string hadron formalism of $SU(2)$ lattice gauge theory, this simulation technique is completely $SU(2)$ invariant and simulates accurate dynamics of physical phenomena such as string breaking and/or pair production. The scheme is scalable and particularly effective in simulating the theory in the weak-coupling regime, and also a bulk limit of the theory in the strong-coupling regime up to certain approximations. This paper also presents a numerical benchmark comparison of the exact spectrum and real-time dynamics of lattice gauge theory to that of the atomic Hamiltonian with an experimentally realizable range of parameters.

Zcs states from the Ds*D¯* and J/ψK* coupled channels: Signal in B+→J/ψϕK+ decay

We study the ${D}_{s}^{*}{\overline{D}}^{*}$ system in connection with the $J/\ensuremath{\psi}{K}^{*}$ in coupled channels and observe that, within reasonable values of the cutoff used to regularize the loops, the system does not develop a bound state. However, the ${J}^{P}={2}^{+}$ channel has enough attraction to create a strong cusp structure that shows up in the $J/\ensuremath{\psi}{K}^{+}$ invariant mass distribution in the ${B}^{+}\ensuremath{\rightarrow}J/\ensuremath{\psi}\ensuremath{\phi}{K}^{+}$ decay at the ${D}_{s}^{*}{\overline{D}}^{*}$ threshold. Such structure is visible in the experimental ${B}^{+}\ensuremath{\rightarrow}J/\ensuremath{\psi}\ensuremath{\phi}{K}^{+}$ and ${\overline{B}}^{0}\ensuremath{\rightarrow}J/\ensuremath{\psi}{K}^{+}{K}^{\ensuremath{-}}$ decays, with small statistics, and our results should stimulate further measurements around this region, given the fact that cusp effects provide as valuable information on hadron dynamics as resonances themselves.

Resonance production in Pb+Pb collisions at 5.02 TeV

The yields, mean transverse momenta, and flow of K*0, ρ0, Λ(1520) resonances provide an evidence of a late stage hadronic rescattering in ultrarelativistic central heavy ion collisions [1]. Using hydrodynamic + hadronic afterburner simulations of Pb+Pb collisions at 5.02 TeV we achieve a reasonable description of resonance yields and spectra as a function of collision centrality. We demonstrate that the measurements of Λ(1520)’s mean transverse momentum allow to constrain the unknown branching ratios of Σ* → Λ(1520)π decays. Hadronic dynamics leads to an enhanced ∆(1232) production in central collisions.

New insight on the quark condensate beyond the chiral limit

With analyzing the mass function obtained by solving Dyson-Schwinger Equations, we propose a cut-off independent definition of quark condensate beyond chiral limit. With this well-defined condensate, we then analyze the evolution of the condensate and its susceptibility with the current quark mass. The susceptibility shows a critical mass in the neighborhood of the s-quark current mass, which defines a transition boundary for internal hadron dynamics.

Study of freeze-out dynamics of strange hadrons

We study the dynamics of chemical freeze-out of single strange hadrons---$K$, $\mathrm{\ensuremath{\Lambda}}$, $\mathrm{\ensuremath{\Sigma}}$, from a homogeneous and isotropically expanding system consisting of $\ensuremath{\pi}$, $K$, $\ensuremath{\rho}$, $N$, $\mathrm{\ensuremath{\Lambda}}$, and $\mathrm{\ensuremath{\Sigma}}$ hadrons with zero net baryon density. We use the momentum-integrated Boltzmann equation or rate equation to study the evolution of strange hadrons considering Bjorken and Hubble-like expansions. We calculate the scattering rates of $K$, $\mathrm{\ensuremath{\Lambda}}$, $\mathrm{\ensuremath{\Sigma}}$ and compare with the expansion rate to analyze the chemical freeze-out of these species. In this microscopic calculation the cross sections, which are input to the rate equation, are taken either from phenomenological models or are parametrized by comparing against experimental data. From this calculation it is found that these strange hadrons freeze out early near transition temperature ${T}_{c}$ when the system follows a Hubble-like fast expansion. But, for a slower Bjorken-like expansion, strange hadrons take a longer time to decouple following a sequential behavior. The present calculation may set a guideline to understand the common freeze-out behavior of strange hadron species at Relativistic Heavy Ion Collider(RHIC) and Large Hadron Collider(LHC), which is mostly predicted by thermal models while explaining the yields of identified particles.

Probing QCD dynamics and the standard model with {D}_{(s)}^{+}to {P}_1^{+}{P}_2^0gamma decays

We compute 10 radiative three-body decays of charged charmed mesons {D}^{+}to {P}_1^{+}{P}_2^0gamma and {D}_sto {P}_1^{+}{P}_2^0gamma , P1,2 = π, K, in leading order QCDF, HHχPT and the soft photon approximation. We work out decay distributions and asymmetries in the standard model and with new physics in the electromagnetic dipole operators. The forward-backward asymmetry is suitable to probe the QCD frameworks, in particular the s-channel dependent weak annihilation contributions in QCDF against the markedly different resonance structure in HHχPT. These studies can be performed with Cabibbo-favored modes Ds → π+π0γ, {D}^{+}to {pi}^{+}{overline{K}}^0gamma and {D}_sto {K}^{+}{overline{K}}^0gamma with mathcal{O}left({10}^{-4}-{10}^{-3}right)hbox{-} mathrm{level} branching ratio, which are standard model-like and induced by different hadronic dynamics. Understanding of the latter can therefore be improved in a data-driven way and sharpens the interpretation of standard model tests. Singly Cabibbo-suppressed modes such as D+ → π+π0γ, Ds → π+K0γ, Ds → K+π0γ with branching ratios within ∼ 10−5–10−4 are sensitive to new physics that can be signalled in the forward-backward asymmetry and in the CP-asymmetry of the rate, ideally in the Dalitz region but also in single differential distributions. Results complement those with neutral D0→ P1P2γ decays.

Review of the $${\Lambda }$$(1405) A curious case of a strangeness resonance

During its long-lasting history, the $\Lambda(1405)$ has become a benchmark for our understanding of the $\rm SU(3)$ hadron dynamics. Starting with its theoretical prediction and later experimental verification, until the most recent debates on the existence of the second broad pole, it emerged as a fruitful research area sparking many theoretical and experimental developments. This review intends to provide the reader with the current status of research on the $\Lambda(1405)$-resonance, reflecting on historical, experimental and theoretical developments. A common database for experimental results and a comparison of most recent theoretical approaches will be provided in the last two parts of this manuscript.

Decay properties of N*(1895)

The nature of nucleon resonances is still being debated, while much experimental data are accumulated. In this work, we focus on the negative parity resonance ${N}^{*}(1895)$ which is located in the scattering region of various meson-baryon coupled channels, and such dynamics can be crucial in understanding its properties. To test the relevance of such hadron dynamics, we investigate the decay properties of ${N}^{*}(1895)$ in detail. We examine how a two pole nature of ${N}^{*}(1895)$ is compatible with its observed decay properties. Moreover, we find that the resonance decays into final states involving $\mathrm{\ensuremath{\Lambda}}(1405)$ and $\mathrm{\ensuremath{\Sigma}}(1400)$, where the latter is not yet observed experimentally. Such decay processes can be useful to study the properties of the aforementioned hyperon resonances.