Properties of hadron matter. I - The equation of state
Hadron matter thermodynamical properties at high temperatures, developing dual resonance dynamic model of high energy particle interactions
Lee, H.↗
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Charm and bottom hadrons in hot hadronic matter
Heavy quarks, and the hadrons containing them, are excellent probes of the QCD medium formed in high-energy heavy-ion collisions, as they provide essential information on the transport properties of the medium and how quarks color-neutralize into hadrons. Large theoretical and phenomenological efforts have been dedicated thus far to assess the diffusion of charm and bottom quarks in the quark–gluon plasma and their subsequent hadronization into heavy-flavor (HF) hadrons. However, the fireball formed in heavy-ion collisions also features an extended hadronic phase, and therefore any quantitative analysis of experimental observables needs to account for the rescattering of charm and bottom hadrons. This is further reinforced by the presence of a QCD cross-over transition and the notion that the interaction strength is maximal in the vicinity of the pseudo-critical temperature. We review existing approaches for evaluating the interactions of open HF hadrons in a hadronic heat bath and the pertinent results for scattering amplitudes, spectral functions and transport coefficients. While most of the work to date has focused on D -mesons, we also discuss excited states as well as HF baryons and the bottom sector. Both the HF hadro-chemistry and bottom observables will play a key role in future experimental measurements. We also conduct a survey of transport calculations in heavy-ion collisions that have included effects of hadronic HF diffusion and assess its impact on various observables.
effective field theories↗
Properties of hadron matter. II - Dense baryon matter and neutron stars.
In this article we have provided certain details of a nuclear-matter computation, based on the Brueckner-Bethe-Goldstone theory of nuclear reaction, which leads to an equation of state for matter in the density region of 10 to 500 trillion g/cu cm. We also explore the possibilities that at very high baryon densities or for very short baryon separations, the net baryon-baryon interaction may be negligible so that the results of dynamical models, like the statistical bootstrap model and the dual-resonance model, may be applicable to the study of dense baryon matter. Several plausible equations of state are constructed, and their effect on the limiting mass of the neutron star is examined.
Leung, Y. C.↗
Study of the doubly charmed tetraquark $\mathrm{T}$ $^+_{cc}$
Quantum chromodynamics, the theory of the strong force, describes interactions of coloured quarks and gluons and the formation of hadronic matter. Conventional hadronic matter consists of baryons and mesons made of three quarks and quark-antiquark pairs, respectively. Particles with an alternative quark content are known as exotic states. Here a study is reported of an exotic narrow state in the D 0 D 0 π + mass spectrum just below the D *+ D 0 mass threshold produced in proton-proton collisions collected with the LHCb detector at the Large Hadron Collider. The state is consistent with the ground isoscalar T$^{+}_{cc}$ tetraquark with a quark content of cc$\bar{u}\bar{d}$ and spin-parity quantum numbers J P = 1 + . Study of the DD mass spectra disfavours interpretation of the resonance as the isovector state. The decay structure via intermediate off-shell D *+ mesons is consistent with the observed D 0 π+ mass distribution. To analyse the mass of the resonance and its coupling to the D*D system, a dedicated model is developed under the assumption of an isoscalar axial-vector T$^{+}_{cc}$ state decaying to the D*D channel. Using this model, resonance parameters including the pole position, scattering length, effective range and compositeness are determined to reveal important information about the nature of the T$^{+}_{cc}$ state. In addition, an unexpected dependence of the production rate on track multiplicity is observed.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Light nuclei production in a multiphase transport model for relativistic heavy ion collisions
Based on an enhanced multiphase transport (AMPT) model, which gives a good description of proton production with a smooth quark matter to hadronic matter transition in relativistic heavy ion collisions, we study deuteron and triton productions from the coalescence of nucleons at the kinetic freezeout of these collisions. For central Au + Au collisions at center-of-mass energies √s NN from 7.7 GeV to 200 GeV available at the Relativistic Heavy Ion Collider (RHIC), we find that the yield ratio N t N p /N$^2_d$ of proton, deuteron, and triton is a monotonic function of collision energy. Our study confirms the results from similar studies based on different dynamic model, which have either no phase transition or a crossover transition between the quark-gluon plasma and the hadronic matter, that this yield ratio does not show any nonmonotonic behavior in its collision-energy dependence.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
QCD Constraints on Isospin-Dense Matter and the Nuclear Equation of State
Understanding the behavior of dense hadronic matter is a central goal in nuclear physics as it governs the nature and dynamics of astrophysical objects such as supernovae and neutron stars. Because of the nonperturbative nature of quantum chromodynamics (QCD), little is known rigorously about hadronic matter in these extreme conditions. Here, lattice QCD calculations are used to compute thermodynamic quantities and the equation of state of QCD over a wide range of isospin chemical potentials with controlled systematic uncertainties. Agreement is seen with chiral perturbation theory when the chemical potential is small. Comparison to perturbative QCD at large chemical potential allows for an estimate of the gap in the superconducting phase, and this quantity is seen to agree with perturbative determinations. Since the partition function for an isospin chemical potential μ I bounds the partition function for a baryon chemical potential μ B = 3 μ I / 2 , these calculations also provide rigorous nonperturbative QCD bounds on the symmetric nuclear matter equation of state over a wide range of baryon densities for the first time. Published by the American Physical Society 2025
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Bayesian Exploration of Phenomenological EoS of Neutron/Hybrid Stars with Recent Observations
The description of the stellar interior of compact stars remains as a big challenge for the nuclear astrophysics community. The consolidated knowledge is restricted to density regions around the saturation of hadronic matter ρ 0 =2.8 × 10 14 g cm -3 , regimes where our nuclear models are successfully applied. As one moves towards higher densities and extreme conditions up to the quark/gluons deconfinement, little can be said about the microphysics of the equation of state (EoS). Here, we employ a Markov Chain Monte Carlo (MCMC) strategy to access the variability at high density regions of polytropic piecewise models for neutron star (NS) EoS or possible hybrid stars, i.e., a NS with a small quark-matter core. With a fixed description of the hadronic matter for low density, below the nuclear saturation density, we explore a variety of models for the high density regimes leading to stellar masses near to 2.5 M ⊙ , in accordance with the observations of massive pulsars. The models are constrained, including the observation of the merger of neutrons stars from VIRGO-LIGO and with the pulsar observed by NICER. In addition, we also discuss the possibility of the use of a Bayesian power regression model with heteroscedastic error. The set of EoS from the Laser Interferometer Gravitational-Wave Observatory (LIGO) was used as input and treated as the data set for the testing case.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
On the Minimum Radius of Very Massive Neutron Stars
Prospects of establishing the radii of massive neutron stars in PSR J1614 – 2230 and PSR J0740 + 6620 from Neutron Star Interior Composition ExploreR and Chandra observatories hold the potential to constrain the equation of state (EoS) of matter to densities well beyond those encountered in canonical stars of mass $\sim 1.4\,{M}_{\odot }$. In this work, we investigate the relation between the radii of very massive neutron stars up to the maximum mass, ${M}_{\max }$, supported by dense matter EoSs. Results from models with hadronic matter are contrasted with those that include a first-order hadron-to-quark phase transition. We find that a lower bound on ${M}_{\max }$ with an upper bound on the radius of massive pulsars serves to rule out quark matter that is too soft, and an upper bound on ${M}_{\max }$ with a lower bound on the radius of massive pulsars strongly disfavors a transition into quark matter that is too stiff appearing at low densities. In conclusion, the complementary role played by radius inferences from future gravitational-wave events of inspiraling binary neutron stars is also briefly discussed.
79 ASTRONOMY AND ASTROPHYSICS↗
Energy-range relations for hadrons in nuclear matter
Range-energy relations for hadrons in nuclear matter exist similarly to the range-energy relations for charged particles in materials. When hadrons of GeV kinetic energies collide with atomic nuclei massive enough, events occur in which incident hadron is stopped completely inside the target nucleus without causing particle production - without pion production in particular. The stoppings are always accompanied by intensive emission of nucleons with kinetic energy from about 20 up to about 400 MeV. It was shown experimentally that the mean number of the emitted nucleons is a measure of the mean path in nuclear matter in nucleons on which the incident hadrons are stopped.
Strugalski, Z.↗
Dynamics of hot QCD matter 2024 — Bulk properties
The second Hot QCD Matter 2024 conference at IIT Mandi focused on various ongoing topics in high-energy heavy-ion collisions, encompassing theoretical and experimental perspectives. This proceedings volume includes 19 contributions that collectively explore diverse aspects of the bulk properties of hot QCD matter. The topics encompass the dynamics of electromagnetic fields, transport properties, hadronic matter, spin hydrodynamics, and the role of conserved charges in high-energy environments. These studies significantly enhance our understanding of the complex dynamics of hot QCD matter, the quark–gluon plasma (QGP) formed in high-energy nuclear collisions. Advances in theoretical frameworks, including hydrodynamics, spin dynamics and fluctuation studies, aim to improve theoretical calculations and refine our knowledge of the thermodynamic properties of strongly interacting matter. Experimental efforts, such as those conducted by the ALICE and STAR collaborations, play a vital role in validating these theoretical predictions and deepening our insight into the QCD phase diagram, collectivity in small systems, and the early-stage behavior of strongly interacting matter. In conclusion, combining theoretical models with experimental observations offers a comprehensive understanding of the extreme conditions encountered in relativistic heavy-ion and proton-proton collisions.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Reverse phase transitions in binary neutron-star systems with exotic-matter cores
Multimessenger observations of binary neutron-star mergers provide a unique opportunity to constrain the dense-matter equation of state. Although it is known from quantum chromodynamics that hadronic matter will undergo a phase transition to exotic forms of matter—e.g., quark matter—the onset density of such a phase transition cannot be computed from first principles. Hence, it remains an open question if such phase transitions occur inside isolated neutron stars or during binary neutron-star mergers, or if they appear at even higher densities that are not realized in the cosmos. Here, in this article, we perform numerical relativity simulations of neutron-star mergers and investigate scenarios in which the onset density of such a phase transition is exceeded in at least one inspiraling binary component. Our simulations reveal that shortly before the merger, it is possible that such stars undergo a “reverse phase transition”—i.e., densities decrease and the quark core inside the star disappears, leaving a purely hadronic star at merger. After the merger, when densities increase once more, the phase transition occurs again and leads, in the cases considered in this work, to the rapid formation of a black hole. We compute the gravitational-wave signal and the mass ejection for our simulations of such scenarios and find clear signatures that are related to the postmerger phase transition—e.g., smaller ejecta masses due to the softening of the equation of state through the quark core formation. Unfortunately, we do not find measurable imprints of the reverse phase transition.
79 ASTRONOMY AND ASTROPHYSICS↗
Lattice QCD for Neutrino Physics
Neutrinos are the most poorly understood particles in the Standard Model but may be key to understanding fundamental mysteries of the universe, including matter-antimatter asymmetry. Most experiments to improve our knowledge of neutrinos depend on neutrino interactions with hadronic matter and therefore rely on a solid theoretical understanding of these interactions. Lattice QCD offers a first-principles, model-independent method of analyzing hadronic systems and their responses to external currents, including the electroweak currents induced by neutrino interactions. In this talk, I will discuss my work on using lattice QCD to understand the hadronic systems needed for both neutrino oscillation and neutrinoless double-beta decay experiments and the impact of this work on neutrino physics.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Evolution of Λ polarization in the hadronic phase of heavy-ion collisions
Using the AMPT+MUSIC+URQMD hybrid model, we study the global and local spin polarizations of Λ hyperons as functions of the freeze-out temperature of the spin degree of freedom in the hadronic phase of Au+Au collisions at $\sqrt{s_{NN}}$ = 19.6 GeV. Including contributions from both the thermal vorticity and thermal shear of the hadronic matter, we find that with the spin freeze-out temperature dropping from the hadronization temperature of 160 MeV to 110 MeV at the kinetic freeze-out, both the global and local spin polarizations of Λ hyperons due to the thermal vorticity decrease by a factor of 2, while those due to the thermal shear decrease quickly and become negligibly small at 140 MeV. Here our results thus suggest that it is important to take into account the evolution of the spin degree of freedom in the hadronic stage of relativistic heavy-ion collisions when theoretically predicted global and local Λ spin polarizations are compared with the experimental measurements.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Interacting mesons as degrees of freedom in a chiral model
Here, we study the equation of state of hot and dense hadronic matter using an extended chiral mean field (CMF) model framework where the addition is the inclusion of interactions of thermally excited mesons. This is implemented by calculating the in-medium masses of pseudoscalar and vector mesons, obtained through the explicit chiral symmetry-breaking and vector-interaction terms in the Lagrangian, respectively, prior to applying the mean-field approximation. As a result, the in-medium meson contributions generate a feedback term to the CMF’s equations of motion, which then modifies the equation of state. With this improvement, we quantify the effect on the equation of state of strongly interacting matter through comparisons with state-of-the-art lattice QCD results and other hadronic models like the hadron resonance gas model. We find that the results of the updated hadronic CMF model with an improved meson description (mCMF) provide a better agreement with lattice-QCD data for thermodynamic state variables across a wide range of temperatures and baryon chemical potentials.
phenomenology↗
Observation of partonic flow in proton—proton and proton—nucleus collisions
Quantum Chromodynamics predicts a phase transition from hadronic matter to quark–gluon plasma (QGP) at high temperatures and energy densities, where quarks and gluons (partons) are no longer confined within hadrons. The QGP forms in ultrarelativistic heavy-ion collisions. Anisotropic flow coefficients, quantifying the azimuthal expansion of produced matter, probe QGP properties. Flow measurements in high-energy heavy-ion collisions show a distinctive grouping of anisotropic flow for baryons and mesons at intermediate transverse momentum – a feature associated with flow imparted at the quark level, confirming QGP existence. The observation of QGP-like features in proton–proton and proton–ion collisions has sparked debate about QGP formation in smaller systems. For the first time, we demonstrate the distinctive grouping of anisotropic flow for baryons and mesons in high-multiplicity proton–lead and proton–proton collisions at the Large Hadron Collider (LHC). These results are described by a model including hydrodynamic flow followed by hadron formation via quark coalescence, consistent with the formation of partonic flowing systems in these collisions.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Heavy nucleus collisions between 20 and 60 GeV/nucleon
Interest in studying relativistic nucleus-nucleus interations arises from the fact that they offer an opportunity to probe nuclear matter at high density and temperature. It is expected that under such extreme conditions a transition from hadronic matter into quark-gluon plasma occurs and that in the interactions of highly relativistic nuclei such conditions are created. Cosmic rays remain a unique source of high energy heavy nuclei. The Japanese-American Cooperative Emulsion Experiment (JACEE-3) was designed to study the collisions of heavy cosmic ray nuclei with different nuclear targets at energies beyond 20 GeV/nucleon. JACEE-3 experiment was carried out using a combined electronic counters and an emulsion chamber detector, which was exposed to the cosmic rays on a balloon at an altitude of 5 g/sq cm.
Burnett, T. H.↗
Observation of an exotic narrow doubly charmed tetraquark
Conventional, hadronic matter consists of baryons and mesons made of three quarks and a quark–antiquark pair, respectively. Here, we report the observation of a hadronic state containing four quarks in the Large Hadron Collider beauty experiment. This so-called tetraquark contains two charm quarks, a \(\overline{{{{{u}}}}}\) and a \(\overline{{{{{d}}}}}\) quark. This exotic state has a mass of approximately 3,875 MeV and manifests as a narrow peak in the mass spectrum of D 0 D 0 π + mesons just below the D *+ D 0 mass threshold. The near-threshold mass together with the narrow width reveals the resonance nature of the state.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Parity-Doubled Nucleons Can Rapidly Cool Neutron Stars
In confined hadronic matter, the spontaneous breaking and restoration of chiral symmetry can be described by considering nucleons, 𝑁 + (939), and excited states of opposite parity, 𝑁 − (1535). In a cold, dense hadronic phase where chiral symmetry remains spontaneously broken, direct Urca decay processes involving the 𝑁 − are possible, e.g., 𝑁 − → 𝑁 + + 𝑒 − + $\bar{𝜈}_𝑒$. Here, we show that at low temperature and moderate densities, because the 𝑁 − are much heavier than the 𝑁 + , such cooling dominates over standard 𝑁 + direct Urca processes. This provides a strong astrophysical signature of the pattern of chiral symmetry restoration in neutron stars.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗