Hadronic Matter Research Articles

Merger and Postmerger of Binary Neutron Stars with a Quark-Hadron Crossover Equation of State.

Fully general-relativistic binary-neutron-star (BNS) merger simulations with quark-hadron crossover (QHC) equations of state (EOS) are studied for the first time. In contrast to EOS with purely hadronic matter or with a first-order quark-hadron phase transition (1PT), in the transition region QHC EOS show a peak in sound speed and thus a stiffening. We study the effects of such stiffening in the merger and postmerger gravitational (GW) signals. Through simulations in the binary-mass range 2.5<M/M_{⊙}<2.75, characteristic differences due to different EOS appear in the frequency of the main peak of the postmerger GW spectrum (f_{2}), extracted through Bayesian inference. In particular, we found that (i)for lower-mass binaries, since the maximum baryon number density (n_{max}) after the merger stays below 3-4 times the nuclear-matter density (n_{0}), the characteristic stiffening of the QHC models in that density range results in a lower f_{2} than that computed for the underlying hadronic EOS and thus also than that for EOS with a 1PT; (ii)for higher-mass binaries, where n_{max} may exceed 4-5n_{0} depending on the EOS model, whether f_{2} in QHC models is higher or lower than that in the underlying hadronic model depends on the height of the sound-speed peak. Comparing the values of f_{2} for different EOS and BNS masses gives important clues on how to discriminate different types of quark dynamics in the high-density end of EOS and is relevant to future kilohertz GW observations with third-generation GW detectors.

Analyses of the collective properties of hadronic matter in Au-Au collisions at 54.4 GeV

We investigated the strange hadrons transverse momentum (${p}_{T}$) spectra in Au-Au collision at $\sqrt{{s}_{NN}}=54.4\text{ }\text{ }\mathrm{GeV}$ in the framework of modified Hagedorn function with embedded flow. It is found that the model can describe the particle spectra well. We extracted the kinetic freeze-out temperature ${T}_{0}$, transverse flow velocity ${\ensuremath{\beta}}_{T}$, kinetic freeze-out volume $V$, mean transverse momentum $⟨{p}_{T}⟩$, the entropy parameter $n$, and the multiplicity parameter ${N}_{0}$. We reported that all these parameters increase towards the central collisions. The larger kinetic freeze-out temperature, transverse flow velocity, kinetic freeze-out volume, and the entropy parameter ($n$) in central collisions compared to peripheral collisions show the early decoupling of the particles in central collisions. In addition, all the above parameters are mass dependent. The kinetic freeze-out temperature (${T}_{0}$), the entropy parameter $n$, and mean transverse momentum ($⟨{p}_{T}⟩$) are larger for massive particles, while the transverse flow velocity (${\ensuremath{\beta}}_{T}$), kinetic freeze-out volume ($V$), and the multiplicity parameter (${N}_{0}$) show the opposite behavior. Larger ${T}_{0}$, $n$, and smaller ${\ensuremath{\beta}}_{T}$ as well as $V$ of the heavier particles indicate the early freeze-out of the heavier particles, while larger $⟨{p}_{T}⟩$ for the heavier particles evince that the effect of radial flow is stronger in heavier particles. The separate set of parameters for each particle shows the multiple kinetic freeze-out scenario, where the mass-dependent kinetic freeze-out volume shows the volume differential freeze-out scenario. We also checked the correlation among different parameters, which include the correlation of ${T}_{0}$ and ${\ensuremath{\beta}}_{T}$, ${T}_{0}$ and $V$, ${\ensuremath{\beta}}_{T}$ and $V$, $⟨{p}_{T}⟩$ and ${T}_{0}$, $⟨{p}_{T}⟩$ and ${\ensuremath{\beta}}_{T}$, $⟨{p}_{T}⟩$, and $V$, $n$ and ${T}_{0}$, $n$ and ${\ensuremath{\beta}}_{T}$, and $n$ and $V$, and they all are observed to have positive correlations with each other which validates our results.

Anisotropic Strange Star Model Beyond Standard Maximum Mass Limit by Gravitational Decoupling in f(Q)$f(Q)$ Gravity

AbstractThe current theoretical development identified as the gravitational decoupling via Complete Geometric Deformation (CGD) method that has been introduced to explore the nonmetricity Q effects in relativistic astrophysics. In the present work, we have investigated the gravitationally decoupled anisotropic solutions for the strange stars in the framework of gravity by utilizing the CGD technique. To do this, we started with Tolman metric ansatz along with the MIT Bag model equation of state related to the hadronic matter. The solutions of the governing equations of motions are obtained by using two approaches, namely the mimicking of the θ sector to the seed radial pressure and energy density of the fluid model. The obtained models describe the self‐gravitating static, compact objects whose exterior solution can be given by the vacuum Schwarzschild Anti‐de Sitter spacetime. In particular, we modeled five stellar candidates, viz., LMC X‐4, PSR J1614‐2230, PSR J0740+6620, GW190814, and GW 170817 by using observational data. The rigorous viability tests of the solutions have been performed through regularity and stability conditions. We observed that the nonmetricity parameter and decoupling constant show a significant effect on stabilizing to ensure the physically realizable stellar models. The innovative feature of this work is to present the stable compact objects with masses beyond the without engaging of exotic matter. Therefore, the present study shows a new perception and physical significance about the exploration of ultra‐compact astrophysical objects.

Bayesian inference of signatures of hyperons inside neutron stars

The possible signatures of the presence of hyperons inside neutron stars are discussed within a Bayesian inference framework applied to a set of models based on a density-dependent relativistic mean-field description of hadronic matter. Nuclear matter properties, hypernuclei properties, and observational information are used to constrain the models. General properties of neutron stars such as the maximum mass, radius, tidal deformability, proton fraction, hyperon fraction, and speed of sound are discussed. It is shown that the two solar mass constraint imposes that neutron stars described by equations of state that include hyperons have on average a larger radius, $\gtrsim 0.5$km, and a larger tidal deformability, $\gtrsim 150$, than the stars determined from a nucleonic equation of state, while the speed of sound at the center of the star is more than 25\% smaller. If a 1.4 M$_\odot$ star with a radius $\lesssim 12.5$ km is measured it is quite improbable that a massive star described by the same model contains hyperons. A similar conclusion is drawn if a two solar mass star with a radius $\lesssim 11.5$ km or a neutron star with a mass above 2.2 M$_\odot$ is observed: the possible hyperon content of these stars is ruled out or very reduced. The hyperon presence inside neutron stars is compatible with the present NICER mass-radius observations of the pulsars PSR J0030+0451 and PSR J0740+6620 and the gravitational wave detection GW170817. {It is shown that if the polytropic index $\gamma=\partial\ln p/\partial\ln\epsilon$ takes values of the order of 1.75 at not too large densities, it may indicate the onset of some kind of exotic matter, but not necessarily of deconfined quark matter.

Interpretation of recent form factor data in terms of an advanced representation of baryons in space and time

Data on electromagnetic form factors of proton, neutron, and $\mathrm{\ensuremath{\Lambda}}$ from annihilation and scattering reactions are collected and interpreted in the frame of a generalized picture of the internal structure of baryons which holds in space-like and time-like regions. It is shown that these data give an insight into the spatial structure of the baryon for distances 100 times smaller than the baryon size and, in the time-like region, a vision of the time evolution of the hadronic matter for times up to ${10}^{\ensuremath{-}25}$ s, that is two orders of magnitude shorter than the time taken by the light to cross the volume of a proton. In the proposed interpretation, the electric form factor of the proton in the space-like region cannot cross zero, but vanishes or stays very small, as an extrapolation of the data seems to show. In the time-like region specific structures appearing in the data give evidence of the dominance of the quark-diquark underlying dynamics in a well-determined time interval during the evolution of the system.

Phase transitions and latent heat in magnetized matter

Based on the assumption that the QCD phase diagram gives a realistic picture of hadronic and quark matter under different regimes, it is possible to claim that a quark core may be present inside compact objects commonly named hybrid neutron stars or even that a pure strange star may exist. In this work we explore how the phase transition is modified by the presence of strong magnetic fields and how it is impacted by parameters of the quark phase, for which we use the MIT-model with vector interactions. The phase transition is assumed to conserve flavor when hadrons turn into deconfined quarks. The hadronic equation of state is calculated with the NL3$\omega\rho^\ast$ parametrization of quantum hadrodynamics. We find that the magnetic field slightly reduces the pressure and chemical potential of the phase transition and the latent heat, the latter being very model dependent.

Hunting Quantum Gravity with Analogs: The Case of High-Energy Particle Physics

In this review, we collect, for the first time, old and new research results, and present future perspectives on how hadron production, in high-energy scattering processes, can experimentally probe fundamental questions of quantum gravity. The key observations that ignited the link between the two arenas are the so-called “color-event horizon” of quantum chromodynamics, and the (de)accelerations involved in such scattering processes. Both phenomena point to the Unruh (and related Hawking)-type effects. After the first pioneering investigations, such research studies continued, including studies of the horizon entropy and other “black-hole thermodynamical” behaviors, which incidentally are also part of the frontier of the analog gravity research itself. It has been stressed that the trait d’union between the two phenomenologies is that in both hadron physics and black hole physics, “thermal” behaviors are more easily understood, not as due to real thermalization processes (sometimes just impossible, given the small number of particles involved), but rather to a stochastic/quantum entanglement nature of such temperatures. Finally, other aspects, such as the self-critical organizations of hadronic matter and of black holes, have been recently investigated. The results of those investigations are also summarized and commented upon here. As a general remark, this research line shows that we can probe quantum gravity theoretical constructions with analog systems that are not confined to only the condensed matter arena.

Open bottom mesons and upsilon states in hot magnetized strange hadronic matter

The masses of open bottom mesons ([Formula: see text]([Formula: see text],[Formula: see text]), [Formula: see text]([Formula: see text],[Formula: see text]), [Formula: see text]([Formula: see text], [Formula: see text])) and upsilon states ([Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]) are investigated in the isospin asymmetric strange hadronic medium at finite temperature in the presence of strong magnetic fields using a chiral effective Lagrangian approach. Here the chiral SU(3) Lagrangian is generalized to include the bottom sector to incorporate the interactions of the open bottom mesons with the magnetized medium. At finite temperature, the number density and scalar density of baryons are expressed in terms of thermal distribution functions. For charged baryons, the magnetic field introduces contribution from Landau energy levels. The masses of the open bottom mesons get modified through their interactions with the baryons and the scalar mesons, which undergo modifications in a magnetized medium. The charged [Formula: see text], [Formula: see text] mesons have additional positive mass shifts due to Landau quantization in the presence of the magnetic field. The medium mass shift of the upsilon states originates from the modification of the gluon condensates simulated by the variation of dilaton field ([Formula: see text]) and a quark mass term in the magnetized medium. The open bottom mesons and upsilon states experience a mass drop in the magnetized medium. The masses of these mesons initially increase with a rise in temperature, and beyond a high value of temperature, their masses are observed to drop. When the temperature is below 90[Formula: see text]MeV, the in-medium masses of the mesons increase with an increase in the magnetic field. However, at high temperatures (T &gt; 90 MeV), the masses are observed to drop with an increase in the magnetic field. These in-medium modifications can have observable effects in asymmetric heavy-ion collisions experiments.

Analyses of pp, Cu-Cu, Au-Au and Pb-Pb Collisions by Tsallis-Pareto Type Function at RHIC and LHC Energies.

The parameters revealing the collective behavior of hadronic matter extracted from the transverse momentum spectra of , , , , p, , , , , or , and or or produced in the most central and most peripheral gold–gold (–), copper–copper (–) and lead–lead (–) collisions at 62.4 GeV, 200 GeV and 2760 GeV, respectively, are reported. In addition to studying the nucleus–nucleus () collisions, we analyzed the particles mentioned above produced in collisions at the same center of mass energies (62.4 GeV, 200 GeV and 2760 GeV) to compare with the most peripheral collisions. We used the Tsallis–Pareto type function to extract the effective temperature from the transverse momentum spectra of the particles. The effective temperature is slightly larger in a central collision than in a peripheral collision and is mass-dependent. The mean transverse momentum and the multiplicity parameter () are extracted and have the same result as the effective temperature. All three extracted parameters in collisions are closer to the peripheral collisions at the same center of mass energy, revealing that the extracted parameters have the same thermodynamic nature. Furthermore, we report that the mean transverse momentum in the – collision is larger than that of the – and – collisions. At the same time, the latter two are nearly equal, which shows their comparatively strong dependence on energy and weak dependence on the size of the system. The multiplicity parameter, in central , depends on the interacting system’s size and is larger for the bigger system.

Impact of Dynamical Tides on the Reconstruction of the Neutron Star Equation of State.

Gravitational waves (GWs) from inspiraling neutron stars afford us a unique opportunity to infer the as-of-yet unknown equation of state of cold hadronic matter at supranuclear densities. During the inspiral, the dominant matter effects arise due to the star's response to their companion's tidal field, leaving a characteristic imprint in the emitted GW signal. This unique signature allows us to constrain the cold neutron star equation of state. At GW frequencies above ≳800 Hz, however, subdominant tidal effects known as dynamical tides become important. In this Letter, we demonstrate that neglecting dynamical tidal effects associated with the fundamental (f) mode leads to large systematic biases in the measured tidal deformability of the stars and hence in the inferred neutron star equation of state. Importantly, we find that f-mode dynamical tides will already be relevant for Advanced LIGO's and Virgo's fifth observing run (∼2025)-neglecting dynamical tides can lead to errors on the neutron radius of O(1 km), with dramatic implications for the measurement of the equation of state. Our results demonstrate that the accurate modeling of subdominant tidal effects beyond the adiabatic limit will be crucial to perform accurate measurements of the neutron star equation of state in upcoming GW observations.

Relativistic mean field model parametrizations in the light of GW170817, GW190814, and PSR J0740+6620

Three parametrizations DOPS1, DOPS2, and DOPS3 (named after the Department of Physics Shimla) of the relativistic mean field model have been proposed with the inclusion of all possible self and mixed interactions between the scalar-isoscalar ($\ensuremath{\sigma}$), vector-isoscalar ($\ensuremath{\omega}$), and vector-isovector ($\ensuremath{\rho}$) mesons up to quartic order. The generated parameter sets are in harmony with the finite and bulk nuclear matter properties. A set of equations of state (EOSs) composed of pure hadronic (nucleonic) matter and nucleonic with quark matter (hybrid EOSs) for superdense hadron-quark matter in $\ensuremath{\beta}$ equilibrium is obtained. The quark matter phase is calculated by using the three-flavor Nambu-Jona-Lasinio (NJL) model. The maximum mass of a nonrotating neutron star with DOPS1 parametrization is found to be around $2.6M\ensuremath{\bigodot}$ for the pure nucleonic matter, which satisfies the recent gravitational wave analysis of GW190814 [Abbott et al., Astrophys. J. Lett. 896, L44 (2020)] with possible maximum mass constraint indicating that the secondary component of GW190814 could be a nonrotating heaviest neutron star composed of pure nucleonic matter. EOSs computed with the DOPS2 and DOPS3 parametrizations satisfy the x-ray observational data [Steiner et al., Astrophys. J. 722, 33 (2010)] and the recent observations of GW170817 maximum mass constraint of a stable nonrotating neutron star in the range $2.01\ifmmode\pm\else\textpm\fi{}0.04--2.16\ifmmode\pm\else\textpm\fi{}0.03M\ensuremath{\bigodot}$ [Rezzolla et al., Astrophys. J. Lett. 852, L25 (2018)] and also in good agreement with constraints on mass and radius measurement for PSR $\mathrm{J}0740+6620$ (NICER) [Riley et al., Astrophys. J. Lett. 918, L27 (2021); Miller et al., Astrophys. J. Lett. 918, L28 (2021)]. The hybrid EOSs obtained with the NJL model also satisfy astrophysical constraints on the maximum mass of a neutron star from PSR J1614-2230 [Demorest et al., Nature (London) 467, 1081 (2010)]. We also present the results for dimensionless tidal deformability, $\mathrm{\ensuremath{\Lambda}}$ which are consistent with the waveform models analysis of GW170817.

Chiral condensates for neutron stars in hadron-quark crossover; from a parity doublet nucleon model to an NJL quark model

In this contribution, we summarize our recent studies on the chiral invariant mass and the chiral condensates in neutron star matter. We construct a unified equations of state assuming the crossover phase transition from hadronic matter described by a parity doublet model to quark matter by an Nambu--Jona-Lasinio type quark model. We first show that the chiral invariant mass is constrained to be $600\,\mbox{MeV}\, \lesssim\, m_0 \,\lesssim \, 900\,\mbox{MeV}$ from recent observations of neutron stars. We then determine the density dependence of the chiral condensate in the crossover description, and show that the chiral condensates are actually smoothly connected from the hadronic matter where the change is driven by the positive chiral scalar charge in a nucleon, to the quark matter where the change is by the modification of the quark Dirac sea, reflecting the hadron-quark crossover.

Probing the high-density nuclear symmetry energy with the Ξ−/Ξ0 ratio in heavy-ion collisions at sNN≈3 GeV

Recent beam energy scan experiments at the BNL Relativistic Heavy Ion Collider by the STAR Collaboration [Phys. Lett. B 827, 137003 (2022) and Phys. Rev. Lett. 128, 202303 (2022)] found that hadronic interactions dominate the collective flow and the proton cumulant ratios are driven by baryon number conservation in a region of high baryon density in $\sqrt{{s}_{NN}}=3$ GeV $\mathrm{Au}+\mathrm{Au}$ reactions, indicating that the dense medium formed in such collisions is likely hadronic matter. Within an updated a relativistic transport model with momentum dependent isoscalar and isovector single-nucleon mean-field potentials corresponding to different symmetry energies at suprasaturation densities, the $n/p, {\ensuremath{\pi}}^{\ensuremath{-}}/{\ensuremath{\pi}}^{+}, {K}_{s}^{0}/{K}^{+}, {\mathrm{\ensuremath{\Sigma}}}^{\ensuremath{-}}/{\mathrm{\ensuremath{\Sigma}}}^{+}$, and ${\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}}/{\mathrm{\ensuremath{\Xi}}}^{0}$ ratios are studied for central $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{{s}_{NN}}=3$ GeV, where the maximum central density reaches about $(3.6--4.0){\ensuremath{\rho}}_{0}$. The doubly strange ${\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}}/{\mathrm{\ensuremath{\Xi}}}^{0}$ ratio is found to have the strongest sensitivity to the variation of high-density nuclear symmetry energy. Thus, the ${\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}}/{\mathrm{\ensuremath{\Xi}}}^{0}$ ratio in relativistic heavy-ion reactions at $\sqrt{{s}_{NN}}\ensuremath{\sim}3$ GeV may help probe sensitively the poorly known symmetry energy of dense neutron-rich matter critically important for understanding various properties of neutron stars.

Study of general relativistic shocks and their propagation in neutron stars

Astrophysical shocks are very common and are interesting as they are responsible for particle acceleration in supernovas, blazers, and neutron stars. In this work, we study general relativistic shocks in which the shock front is at rest. We derive the jump conditions and the Taub adiabat equation for both the space-like and time-like shocks. We solve these equations for a neutron star where the shock wave is followed by a combustion front deconfining hadronic matter to quark matter. We find that the maximum mass of the daughter quark star (generated from the combustion of the parent neutron star) is consistent with the maximum mass limit for the equation of state sequence. The matter velocities under some conditions become super-luminous, which although disputed may indicate a very fast combustion process. Also, the matter velocities imply that for space-like shocks, the combustion process is most probably a deflagration, and for time-like shocks, it is a detonation and can even proceed with velocities that are super-luminous.

Dynamic density correlations in baryon rich fluid using Mori–Zwanzig–Nakajima projection operator method

In this work, we calculate the dynamic density correlations using Mori–Zwanzig–Nakajima projection operator method. With a judicious choice of slow variables we derive the evolution equations for these slow variables starting from generalised Langevin equation. We get the hydrodynamic form of density correlations function which consist of two acoustic peaks: also called Brillouin peaks, and one thermal peak: also called Rayleigh peak. We then estimate the dynamic density correlations near the critical point using critical exponents extracted from the statistical bootstrap model of hadronic matter. We find that the bulk viscosity contributes to the sound attenuation at leading order sim |t|^{-frac{5}{4}} while the thermal conductivity contribute at sub-leading order sim |t|^{-frac{3}{4}}. On the other hand, only the thermal conductivity contributes at leading order sim |t|^{frac{1}{4}} to the thermal diffusivity. We discuss the implications of these results in search for the QCD critical point in the heavy-ion collision experiments.

Diffusion matrix associated with the diffusion processes of multiple conserved charges in a hot and dense hadronic matter

Bulk matter produced in heavy ion collisions has multiple conserved quantum numbers like baryon number, strangeness and electric charge. The diffusion process of these charges can be described by a diffusion matrix describing the interdependence of diffusion of different charges. The diffusion coefficient matrix is estimated here from the Boltzmann kinetic theory for the hadronic phase within relaxation time approximation. In the derivation for the same, we impose the Landau-Lifshitz conditions of fit. This leads to e.g. the diagonal diffusion coefficients to be manifestly positive definite. The explicit calculations are performed within the ambit of hadron resonance gas model with and without excluded volume corrections. It is seen that the off-diagonal components can be significant to affect the charge diffusion in a fluid with multiple conserved charges. The excluded volume correction effects is seen to be not significant in the estimation of the elements of the diffusion matrix.

Open charm mesons and charmonia in magnetized strange hadronic matter * *A.J.C.S acknowledges the support towards this work from the Department of Science and Technology, Government of India, via an INSPIRE fellowship (INSPIRE Code IF170745). AM acknowledges financial support from Department of Science and Technology (DST), Government of India (CRG/2018/002226)

We investigate the in-medium masses of open charm mesons (D( , ), ( , ), ( , )) and charmonium states ( , , , , ) in strongly magnetized isospin asymmetric strange hadronic matter using a chiral effective model. In the presence of a magnetic field, the number and scalar densities of charged baryons have contributions from Landau energy levels. The mass modifications of open charm mesons result from their interactions with nucleons, hyperons, and the scalar fields (the non-strange field σ, strange field ζ, and isovector field δ) in the presence of a magnetic field. The mass modifications of the charmonium states result from the modification of gluon condensates in a medium simulated by the variation in the dilaton field (χ) in the chiral effective model. The effects of finite quark masses are also incorporated in the trace of the energy-momentum tensor in quantum chromodynamics to investigate the mass shifts of charmonium states. The in-medium masses of open charm mesons and charmonia are observed to decrease with an increase in baryon density. The charged , , , and mesons have additional positive mass shifts due to Landau quantization in the presence of a magnetic field. The effects of the strangeness fraction are observed to be more dominant for mesons compared with D mesons. The mass shifts of charmonia are observed to be larger in hyperonic media compared with nuclear media when the effect of the finite quark mass term is neglected. These medium mass modifications can have observable consequences on the production of the open charm mesons and charmonia in high-energy asymmetric heavy-ion collision experiments.

Implications of NICER for Neutron Star Matter: The QHC21 Equation of State

The recent NICER measurement of the radius of the neutron star PSR J0740+6620, and the inferred small variation of radii from 1.4 to 2.1 M ⊙, reveal key features of the equation of state of neutron star matter. The pressure rises rapidly in the regime of baryon density n ∼ 2–4 times nuclear saturation density, n 0—the region where we expect hadronic matter to be undergoing transformation into quark matter—and the pressure in the nuclear regime is greater than predicted by microscopic many-body variational calculations of nuclear matter. To incorporate these insights into the microscopic physics from the nuclear to the quark matter regimes, we construct an equation of state, QHC21, within the framework of quark–hadron crossover. We include nuclear matter results primarily based on the state-of-the-art chiral effective field theory, but also note results of using nuclear matter variational calculations based on empirical nuclear forces. We employ explicit nuclear degrees of freedom only up to n ∼ 1.5 n 0, in order to explore the possibility of further physical degrees of freedom than nucleonic here. The resulting QHC21, which has a peak in sound velocity in ∼2–4 n 0, is stiffer than the earlier QHC19 below 2 n 0, predicting larger radii in substantial agreement with the NICER data.

Multiplicity of the doubly charmed state Tcc+ in heavy-ion collisions

We study the evolution of the doubly charmed state $T_{cc}^+$ in a hot hadron gas produced in the late stage of heavy-ion collisions. We use effective Lagrangians to calculate the thermally averaged cross sections of $T_{cc}^+$ production in reactions such as $ D^{(*)} D^{(*)} \rightarrow T_{cc}^+ \pi, T_{cc}^+ \rho $ and its absorption in the corresponding inverse processes. We then solve the rate equation to follow the time evolution of the $T_{cc}^+$ multiplicity, and determine how it is affected by the considered reactions during the expansion of the hadronic matter. We compare the evolution of the $T_{cc}^+$ abundance treated as a hadronic $S$-wave molecule and as a tetraquark state. Our results show that the tetraquark yield increases by a factor of about 2 at freeze-out, but it is still one order of magnitude smaller than the final yield of molecules formed from hadron coalescence. Also, the results indicate that $N_{T_{cc}}$ is more affected by interactions with hadronic medium than $ N_{X(3872)} $ in similar conditions. We also show that yields depend very weakly on the system size, represented by $\mathcal{N} = \left[ d N_{ch} / d \eta (\eta < 0.5)\right]^{1/3}$.

Production of ψ(4040) , ψ(4160) , and ψ(4415) mesons in hadronic matter

We present the first study of production of $\ensuremath{\psi}(4040)$, $\ensuremath{\psi}(4160)$, and $\ensuremath{\psi}(4415)$ mesons in hadronic matter. Quark interchange between two colliding charmed mesons leads to the production of the three mesons. We calculate unpolarized cross sections for the reactions $D\overline{D}\ensuremath{\rightarrow}\ensuremath{\rho}R$, $D{\overline{D}}^{*}\ensuremath{\rightarrow}\ensuremath{\pi}R$, $D{\overline{D}}^{*}\ensuremath{\rightarrow}\ensuremath{\rho}R$, ${D}^{*}\overline{D}\ensuremath{\rightarrow}\ensuremath{\pi}R$, ${D}^{*}\overline{D}\ensuremath{\rightarrow}\ensuremath{\rho}R$, ${D}^{*}{\overline{D}}^{*}\ensuremath{\rightarrow}\ensuremath{\pi}R$, and ${D}^{*}{\overline{D}}^{*}\ensuremath{\rightarrow}\ensuremath{\rho}R$, where $R$ stands for $\ensuremath{\psi}(4040)$, $\ensuremath{\psi}(4160)$, and $\ensuremath{\psi}(4415)$. In the temperature region covering hadronic matter, the peak cross sections of producing $\ensuremath{\psi}(4040)$ are similar to or larger than the ones of producing $\ensuremath{\psi}(4415)$, and the latter are generally larger than those of producing $\ensuremath{\psi}(4160)$. With the cross sections, we establish new master rate equations for $\ensuremath{\psi}(4040)$, $\ensuremath{\psi}(4160)$, and $\ensuremath{\psi}(4415)$. The equations are solved for central Pb-Pb collisions at $\sqrt{{s}_{NN}}=5.02\text{ }\text{ }\mathrm{TeV}$ at the Large Hadron Collider. Solutions of the equations show that the $\ensuremath{\psi}(4040)$ number density at kinetic freeze-out of hadronic matter is larger than the $\ensuremath{\psi}(4415)$ number density, which is larger than the $\ensuremath{\psi}(4160)$ number density.