Hadronic Phase Research Articles

Thermal Fluctuations of Matter Composition and Quark Nucleation in Compact Stars

At the extreme densities reached in the core of neutron stars, it is possible that deconfined quark matter is produced. The formation of this new phase of strongly interacting matter is likely to occur via a first-order phase transition for the typical temperatures reached in astrophysical processes. The first seeds of quark matter would then form through a process of nucleation within the metastable hadronic phase. Here, we address the role of the thermal fluctuations in the hadronic composition on the nucleation of two-flavor quark matter. At finite temperature, the thermodynamic quantities in a system fluctuate around average values. Nucleation being a local process, it is possible that it occurs in a subsystem whose composition makes the nucleation easier. We will consider the total probability of the nucleation as the product between the probability that a subsystem has a certain hadronic composition different from the average in the bulk, and the nucleation probability in that subsystem. We will show how those fluctuations of the hadronic composition can increase the efficiency of nucleation already for temperatures ∼(0.1−1) keV. However, for temperatures ≲(1−10) MeV, the needed overpressure exceeds the maximum pressure reached in compact stars. Finally, for even larger temperatures the process of nucleation can take place, even taking into account finite-size effects.

Far-from-equilibrium attractors with full relativistic Boltzmann approach in boost-invariant and non-boost-invariant systems

We study the universal behavior associated with a Relativistic Boltzmann Transport (RBT) approach with the full collision integral in 0+1D conformal systems. We show that all momentum moments of the distribution function exhibit universal behavior. Furthermore, the RBT approach allows to calculate the full distribution function, showing that an attractor behavior is present in both the longitudinal and transverse momentum dependence. We compare our results to the far-from-equilibrium attractors determined with other approaches, such as kinetic theory in Relaxation Time Approximation (RTA) and relativistic hydrodynamic theories, both in their viscous (DNMR) an anisotropic (aHydro) formulations, finding a very similar evolution, but an even faster thermalization in RBT for higher order moments. For the first time, we extended this analysis also to study the attractor behavior under a temperature-dependent viscosity η/s(T)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\eta /s(T)$$\\end{document}, accounting also for the rapid increase toward the hadronic phase. We find that a partial breaking of the scaling behavior with respect to τ/τeq\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au /\ au _{eq}$$\\end{document} emerges only at T≈Tc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T \\approx T_c$$\\end{document} generating a transient deviation from attractors; interestingly this in realistic finite systems may occur around the freeze-out dynamics. Finally, we investigate for the first time results beyond the boost-invariant picture, finding that also in such a case the system evolves toward the universal attractor. In particular, we present the forward and pull-back attractors at different space-time rapidities including rapidity regions where initially the distribution function is even vanishing.

Revealing the mystery of the double charm tetraquark in pp collision

A novel approach is proposed to probe the nature of the double charm tetraquark through the prompt production asymmetry between Tc¯c¯-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{\\bar{c}\\bar{c}}^-$$\\end{document} and Tcc+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{cc}^+$$\\end{document} in pp collisions. When comparing two theoretical pictures, i.e. the compact tetraquark and hadronic molecular pictures, we find that the former one exhibits a significantly larger production asymmetry, enabling the unambiguous determination of the tetraquark’s internal structure. Additionally, distinctive differences in the transverse momentum and rapidity distributions of Tc¯c¯-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{\\bar{c}\\bar{c}}^-$$\\end{document} and Tcc+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{cc}^+$$\\end{document} cross sections emerge, particularly at pT≈2GeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p_\ extrm{T}\\approx 2~\ extrm{GeV}$$\\end{document} and y≈±6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$y\\approx \\pm 6$$\\end{document} at a center-of-mass energy of 14TeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$~\ extrm{TeV}$$\\end{document}. The insignificant asymmetry in hadronic molecular picture is because that hadronic molecules are produced in hadronic phase, where the phase space of their constituents needs to be taken into account rigorously. Our work can be extended to the exploration of other double heavy tetraquark candidates, offering a versatile approach to advance our understanding of exotic hadrons.

Scalarized hybrid neutron stars in scalar tensor gravity

Hybrid neutron stars, the compact objects consisting hadronic matter and strange quark matter, can be considered as the probes for the scalar tensor gravity. In this work, we explore the scalarization of hybrid neutron stars in the scalar tensor gravity. For the hadronic phase, we apply a piecewise polytropic equation of state constrained by the observational data of GW170817 and the data of six low-mass X-ray binaries with thermonuclear burst or the symmetry energy of the nuclear interaction. In addition, to describe the strange quark matter inside the hybrid neutron star, different MIT bag models are employed. We study the effects of the value of bag constant, the mass of s quark, the perturbative quantum chromodynamics correction parameter, and the density jump at the surface of quark-hadronic phase transition on the scalarization of hybrid neutron stars. Our results confirm that the scalarization is more sensitive to the value of bag constant, the mass of s quark, and the density jump compared to the perturbative quantum chromodynamics correction parameter.

Hadron-quark phase transition in the neutron star with vector MIT bag model and Korea-IBS-Daegu-SKKU functional

Employing the Korea-IBS-Daegu-SKKU (KIDS) density functional for the hadron phase and the MIT bag model with vector (vBag) model for the quark phase, we obtain hadron-quark phase transition in neutron stars considering Maxwell construction. The structural properties of the resultant hybrid stars are computed for three different values of bag constant (B) in the range B1/4=145−160 MeV). We study the effects of symmetry energy (J) on the hybrid star properties with the different KIDS model and found that J has important influence not only on the transition properties like the transition mass, transition radius and jump in density due to phase transition, but also on the stability of the hybrid stars. The vector repulsion of the quark phase via the parameter GV has profound influence in obtaining reasonable hybrid star configurations, consistent with the recent astrophysical constraints on the structural properties of compact stars. Within the aforesaid range of B, the value of GV is constrained to be 0.3 ≲GV≲ 0.4 in order to obtain reasonable hybrid star configurations.

Use of the Meta-Analysis and Kolmogorov Criteria in the Finding of Singularities of a Nuclear Matter Created in Ultra-Relativistic Nuclear Collisions

Published theoretical data from several models – PHSD/HSD both with and without chiral symmetry restoration (CSR), applied to experimental data on nuclear collisions from BEVALAC/SIS to LHC energies were analyzed using meta-analysis and Kolmogorov criteria. This made it possible to localize possible features of nuclear matter created in central nucleus-nucleus collisions. Ignition of a drop of quark-gluon plasma (QGP) begins already at an energy of about √s<SUB>NN</SUB> = 2 GeV. The assessment showed that this QGP droplet occupies a small fraction, 15% (average radius of about 5.3 fm, if the fireball radius is 10 fm), of the total volume of the fireball created at √s<SUB>NN</SUB> = 2.7 GeV. A drop of exotic matter undergoes a split phase transition – separated boundaries of sharp (1<sup>st</sup> order) crossover and CSR in chiral limit, between QGP and Quarkyonic matter at an energy about √s<SUB>NN</SUB> = 3.5 GeV. The critical endpoint of 2<sup>nd</sup> order probably cannot be reached in nuclear collisions. The triple phase area occupies interval from √s<SUB>NN</SUB> =12 GeV to 15 GeV, the critical endpoint of 1<sup>st</sup> order – at around √s<SUB>NN</SUB> = 20 GeV. The boundary of smooth (2<sup>nd</sup> order) crossover transition with CSR in chiral limit between Quarkyonic matter and QGP was localized between √s<SUB>NN</SUB> = 9.3 GeV and 12 GeV, and between Hadronic and QGP in the interval from √s<SUB>NN</SUB> = 15 GeV to 20 GeV, the boundary of sharp (1<sup>st</sup> order) crossover transition with CSR in chiral limit between Hadronic matter and QGP was localized after √s<SUB>NN</SUB> = 20 GeV. The phase trajectory of the hadronic corona, enveloping the exotic droplet, always remains in the hadronic phase. The possible phase diagram of nuclear matter created in mid-central heavy ion collisions is also presented in the same energy range as for central collisions. Taking into account the quantum nature of the fireball created in nuclear collisions, emphasis is on the existence of events in central nuclear collisions at energy range from √s<SUB>NN</SUB> = 2 GeV to 2.76 TeV, at which no exotic matter is created and nuclear matter in the fireball remains in the hadronic phase throughout its (fireball) evolution.

Spin relaxation rate for baryons in a thermal pion gas

We study the relaxation dynamics of the spin polarization of baryons (nucleon and Λ baryon), in a thermal pion gas as a simple model of the hadronic phase of the QCD plasma produced in relativistic heavy-ion collisions. For this purpose, we formulate the quantum kinetic theory for the spin density matrix of baryons in the leading order of the gradient expansion. Considering the baryon-pion elastic scattering processes as the dominant interaction between baryons and thermal pions, we compute the spin relaxation rate of nucleons and Λ baryons in a pion gas up to temperature 200 MeV. In the case of nucleons, we evaluate the spin relaxation rate in the s-channel resonance approximation, based on the known experimental data on Δ resonances. We also estimate the spin relaxation rate for Λ baryons, based on experimental inputs and theoretical models for the low-energy Λπ scattering, including the chiral perturbation theory. Published by the American Physical Society 2024

Non-extensive effects on the QCD equation of state and fluctuations of conserved charges within Polyakov quark meson model

The influence of non-extensive Tsallis statistics on the hadron phase structure has been investigated using the Polyakov-quark-meson (PQM) model. The analysis examines the non-extensive effects on the temperature dependence of PQM order parameters, thermodynamic quantities related to the quantum chromodynamics (QCD) equation of state, and fluctuations of conserved charges at varying chemical potentials. The results show that non-extensive effects have the most significant deviations near the crossover region. The pseudo-critical temperature T χ (μ B ) is not a universal constant and decreases with increasing non-extensive q parameter. The chiral phase diagram of the PQM model indicates a decrease in the behavior of the (T χ − μ B ) plane with increasing non-extensive q parameter. The PQM model exhibits good qualitative agreement with lattice QCD calculations. Moreover, these findings suggest the existence of a Tsallis limit, which serves as an alternative to the Stefan–Boltzmann limit for the massless ideal gas. The critical endpoint exhibits lower temperature but higher chemical potential with increasing non-extensive q parameter. Overall, this study highlights the importance of non-extensive Tsallis statistics in characterizing the quark-hadron phase structure of the PQM model and contributes to a deeper understanding of non-extensive effects in the quark-hadron phase transition.

Study of Photon Emission at High Temperature of Quark Gluon Interaction

In this paper, the photons emission rate from the interaction of quark with gluon is calculated and studied based on quantum chromodynamics theory. The photonic rate is calculated for u g→d g γ system at bremsstrahlung processes with Bag constant B1/4=0.235GeV and B1/4=0.275GeV, system temperature (325-625) MeV and the value of fugacity of quark λQ=0.9 and gluon λG=0.02 to emit photons with energy 0.5 ≤ Eγ ≤ 5GeV in hadronic phase. The effect of system temperature on the photons emission rate was studied and discussed, it was found that it increases with increases of system temperature and decreases of coupling strength due to the deconfinement phenomena furthermore the photonic yield at B1/4=0.235GeV is less than the photonic yield at B1/4=0.275GeV.

Observation of abnormal suppression of f0(980) production in p–Pb collisions at [formula omitted] = 5.02 TeV

The dependence of f0(980) production on the final-state charged-particle multiplicity in p–Pb collisions at sNN=5.02 TeV is reported. The production of f0(980) is measured with the ALICE detector via the f0(980)→π+π− decay channel in a midrapidity region of −0.5<y<0. Particle yield ratios of f0(980) to π and K⁎(892)0 are found to be decreasing with increasing charged-particle multiplicity. The magnitude of the suppression of the f0(980)/π and f0(980)/K⁎(892)0 yield ratios is found to be dependent on the transverse momentum pT, suggesting different mechanisms responsible for the measured effects. Furthermore, the nuclear modification factor QpPb of f0(980) is measured in various multiplicity ranges. The QpPb shows a strong suppression of the f0(980) production in the pT region up to about 4 GeV/c. The results on the particle yield ratios and QpPb for f0(980) may help to understand the late hadronic phase in p–Pb collisions and the nature of the internal structure of f0(980) particle.

K*(892)± resonance production in Pb-Pb collisions at sNN=5.02 TeV

The production of K*(892)± meson resonance is measured at midrapidity (|y|&lt;0.5) in Pb−Pb collisions at sNN=5.02 TeV using the ALICE detector at the CERN Large Hadron Collider. The resonance is reconstructed via its hadronic decay channel K*(892)±→KS0π±. The transverse momentum distributions are obtained for various centrality intervals in the pT range of 0.4−16 GeV/c. Measurements of integrated yields, mean transverse momenta, and particle yield ratios are reported and found to be consistent with previous ALICE measurements for K*(892)0 within uncertainties. The pT-integrated yield ratio 2K*(892)±/(K++K−) in central Pb−Pb collisions shows a significant suppression at a level of 9.3σ relative to pp collisions. Thermal model calculations result in an overprediction of the particle yield ratio. Although both hadron resonance gas in partial chemical equilibrium (HRG-PCE) and + simulations consider the hadronic phase, only HRG-PCE accurately represents the measurements, whereas + simulations tend to overpredict the particle yield ratio. These observations, along with the kinetic freeze-out temperatures extracted from the yields measured for light-flavored hadrons using the HRG-PCE model, indicate a finite hadronic phase lifetime, which decreases with increasing collision centrality percentile. The pT-differential yield ratios 2K*(892)±/(K++K−) and 2K*(892)±/(π++π−) are presented and compared with measurements in pp collisions at s=5.02 TeV. Both particle ratios are found to be suppressed by up to a factor of five at pT&lt;2.0 GeV/c in central Pb−Pb collisions and are qualitatively consistent with expectations for rescattering effects in the hadronic phase. The nuclear modification factor (RAA) shows a smooth evolution with centrality and is found to be below unity at pT&gt;8 GeV/c, consistent with measurements for other light-flavored hadrons. The smallest values are observed in most central collisions, indicating larger energy loss of partons traversing the dense medium. ©2024 CERN, for the ALICE Collaboration 2024 CERN

Λ(1520) resonance production with respect to transverse spherocity using EPOS3+UrQMD

Resonances are sensitive to the properties of the medium created in heavy ion collision. They also provide insight into the properties of the hadronic phase. Studying the dependence of the yield of resonances on transverse spherocity and multiplicity allows us to understand the resonance production mechanism with event topology and system size, respectively. The results reported pertain to \Lambda(1520)Λ(1520), using predictions from EPOS3+UrQMD event generator.

Non-zero temperature study of spin 1/2 charmed baryons using lattice gauge theory

We study the behaviour of spin 1/2 charmed baryons as the temperature increases. We make use of anisotropic lattice QCD simulations with Nf=2+1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_f = 2 + 1$$\\end{document} dynamical flavours. After determining the positive and negative parity ground state masses at the lowest temperature, we investigate the effect of rising temperature using ratios of thermal lattice correlators with both so-called reconstructed correlators and with simple model correlators. This avoids difficulties associated with non-zero temperature fitting or spectral reconstruction. We find that temperature effects are prominent throughout the hadronic phase for all negative parity channels considered and for some positive parity channels. Subsequently and where possible, we determine the masses of the ground states as a function of temperature. Finally we consider the effect of chiral symmetry restoration and extract an estimate of the pseudocritical temperature from singly charmed baryonic correlators.

Examining the influence of hadronic interactions on the directed flow of identified particles in RHIC Beam Energy Scan energies using UrQMD model

The directed flow of identified particles can serve as a sensitive tool for investigating the interactions during initial and final states in heavy ion collisions. This study examines the rapidity distribution ([Formula: see text]), rapidity-odd directed flow ([Formula: see text]) and its slope ([Formula: see text]) for [Formula: see text], [Formula: see text], p, and [Formula: see text] in Au+Au collisions at different collision centralities and beam energies ([Formula: see text], 11.5, 14.5, 19.6, 27, and 39[Formula: see text]GeV) using the UrQMD model. We investigate the impact of late-stage hadronic interactions on charge-dependent [Formula: see text] and its slope by modifying the duration of the hadronic cascade lifetime ([Formula: see text]). The energy dependence of [Formula: see text] for p ([Formula: see text]) exhibits distinct pattern compared to [Formula: see text] and [Formula: see text]. Notably, we observe a change in the sign reversal position of proton [Formula: see text] at different beam energies with varying [Formula: see text] in central and mid-central collisions. Moreover, the difference in [Formula: see text] between positively and negatively charged hadrons ([Formula: see text]) demonstrates a stark centrality dependence for different particle species. The deuteron displays a significant increase in [Formula: see text] with increasing [Formula: see text] compared to p and n. This investigation underscores the importance of considering the temporal evolution and duration of the hadronic phase when interpreting the sign reversal, charge splitting of [Formula: see text] and light nuclei formation at lower RHIC energies.

Chemical potential (in)dependence of hadron scatterings in the hadronic phase of QCD-like theories and its applications

We formulate a method for calculating the hadron-hadron scattering amplitudes at nonzero chemical potential (μ) in the hadronic phase at zero temperature, where the baryon number symmetry remains to be violated. Although it is widely believed that the physical quantities do not change even if we turn on a small μ at zero temperature, the shape of correlation functions for a single hadron depends on μ. Then, the dispersion relation of the single hadron is modified to E(p, μ) = p2+m2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{{\ extbf{p}}^2+{m}^2} $$\\end{document} – μnO. Here, m and nO denote the hadron mass at μ = 0 and the quantum number, respectively. From this relation, it is possible that the effective mass of the hadron depends on μ. We extend the HAL QCD method at μ = 0 to the case of μ ≠ 0, which allows us to extract the scattering phase shifts via the interaction potential. We have found that the interaction potential can depend on μ only through the effective mass while the scattering phase shifts, obtained by solving the Schrödinger equation with the interaction potential, are independent of μ. We also numerically analyze the S-wave scatterings of two pions with isospin I = 2 and two scalar diquarks within the framework of QC2D at nonzero quark chemical potential. While the lattice is not exactly set to zero temperature, the μ-independence can be observed. Furthermore, we improve the results for the S-wave scatterings of two hadrons obtained above by taking the μ-independence for granted. Thanks to the asymmetric property of the correlation functions for diquarks at μ ≠ 0, we can access a long-τ regime and can reduce the systematic error coming from inelastic contributions.

Toward a universal description of hadronic phase of QCD

Mean-field model quantum field theories of hadrons were traditionally developed to describe cold and dense nuclear matter and are by now very well constrained from the recent neutron star merger observations. We show that when augmented with additional known hadrons and resonances but not included earlier, these mean-field models can be extended beyond its regime of applicability. Calculating some specific ratios of baryon number susceptibilities for finite temperature and moderate values of baryon densities within mean-field approximation, we show that these match consistently with the lattice QCD data available at lower densities, unlike the results obtained from a noninteracting hadron resonance gas model. We also estimate the curvature of the line of constant energy density, fixed at its corresponding value at the chiral crossover transition in QCD, in the temperature-density plane. The number density at low temperatures and high density is found to be about twice the nuclear saturation density. Moreover from this line we can indirectly constrain the critical endpoint of QCD to be beyond μB=596 MeV for temperature ∼125 MeV. Published by the American Physical Society 2024

Probing the interplay of multiplicity and effective energy on strangeness production in pp collisions with ALICE

The strong interaction between quarks and gluons, the elementary constituents of the hadronic matter, is described by quantum chromodynamics (QCD). Under extreme conditions of high temperature and energy density, the QCD predicts a transition from the hadronic phase to a colour deconfined medium called quark-gluon plasma (QGP). The QGP can be investigated in the laboratory through ultrarelativistic heavy-ion collisions, such as the ones between lead (Pb) ions at the Large Hadron Collider (LHC) at CERN. The enhanced production of strange hadrons in heavy-ion collisions with respect to proton-proton (pp) collisions was historically considered one of the signatures of QGP formation. At the LHC, the ALICE Collaboration observed that the ratio of strange to non-strange hadron yields increases with the charged-particle multiplicity at midrapidity, starting from pp collisions and evolving smoothly across larger interaction systems and energies, ultimately reaching Pb-Pb collisions. The origin of this effect in small collision systems remains an open question. This work exploits a novel approach to study strangeness production in pp collisions, introducing, for the first time, the concept of effective energy in hadronic collisions at the LHC.

Proving Rho Meson Is a Dynamical Gauge Boson of Hidden Local Symmetry

The rho meson has long been successfully identified with a dynamical gauge boson of Hidden Local Symmetry (HLS) Hlocal in the non-linear sigma model G/H gauge equivalent to the model having the symmetry Gglobal×Hlocal, with G=[SU(2)L×SU(2)R]≃O(4),H=SU(2)V≃O(3). However, under a hitherto unproven assumption that its kinetic term is dynamically generated, together with an ad hoc choice of the auxiliary field parameter “a=2”, we prove this assumption, thereby solving the long-standing mystery. The rho meson kinetic term is generated simply by the large N limit of the Grassmannian model G/H=O(N)/[O(N−3)×O(3)] gauge equivalent to O(N)global×[O(N−3)×O(3)]local, extrapolated to N=4, O(4)global×O(3)local, with all the phenomenologically successful “a=2 results”, i.e., ρ-universality, KSRF relation, and the Vector Meson Dominance, realized independently of the parameter “a”. This in turn establishes validity of the large N dynamics at the quantitative level directly by the experiments. The relevant cutoff reads Λ≃4πFπ for N=4, which is regarded as a matching scale of the HLS as a “magnetic dual” to QCD. Skyrmion is stabilized by such a dynamically generated rho meson without recourse to the underlying QCD, a further signal of the duality. The unbroken phase with a massless rho meson may be realized as a novel chiral-restored hadronic phase in the hot/dense QCD.

Evolution of midrapidity average transverse momentum of pions, kaons, protons and antiprotons in Au+Au collisions in (snn)1∕2= 7–39-GeV energy range from the beam energy scan program

The [Formula: see text] dependencies of the experimental average transverse momentum, [Formula: see text], of the charged pions, charged kaons, protons and antiprotons produced at midrapidity ([Formula: see text]) in [Formula: see text] collisions from the Beam Energy Scan (BES) program at the RHIC (Relativistic Heavy Ion Collider), measured by STAR Collaboration in the [Formula: see text]–39-GeV energy range, have been described quite well with the power-law model function. We have obtained [Formula: see text] inequality at all BES energies, indicating the clear mass ordering (dependence) of the power parameter [Formula: see text]. On the whole, the exponent parameter [Formula: see text] for the charged kaons as well as (anti)protons decreases noticeably with increasing [Formula: see text] collision energy from [Formula: see text][Formula: see text]GeV to [Formula: see text][Formula: see text]GeV. Drastic change observed in the energy ([Formula: see text]) dependence of the parameter [Formula: see text] for the charged kaons at [Formula: see text][Formula: see text]GeV could possibly indicate a significant change in the mechanism(s) of the charged kaon production in [Formula: see text] collisions at around [Formula: see text][Formula: see text]GeV. Significant change in the [Formula: see text] dependence of the parameter [Formula: see text] for the charged pions observed at around [Formula: see text][Formula: see text]GeV is consistent with a possible change in the mechanism(s) of the particle production in [Formula: see text] collisions at around [Formula: see text][Formula: see text]GeV, reported earlier by STAR Collaboration. Significant gaps between [Formula: see text] (protons) and [Formula: see text] (antiprotons) as well as between ([Formula: see text]) and [Formula: see text] have been seen in the region [Formula: see text]–20[Formula: see text]GeV. These gaps diminish and practically disappear with [Formula: see text] and [Formula: see text] (protons) [Formula: see text] (antiprotons) in the region [Formula: see text][Formula: see text]GeV. Altogether, the findings, regarding collision energy dependencies of the parameter [Formula: see text] for the studied particle species, could indicate the probable phase transition of a nuclear matter to the mixed phase of QGP and hadrons taking place in [Formula: see text] collisions at around [Formula: see text][Formula: see text]GeV. The differences found between parameter [Formula: see text] versus [Formula: see text] dependencies of the particles and antiparticles have been connected with the ratios of antiparticle and particle yields and differences in the mechanisms of production of particles and antiparticles. It is deduced that the exponent parameter [Formula: see text] should be sensitive to the degree of particle (system) thermalization and particle production mechanisms, and its drastic change could be related to the change in the mechanisms of particle production or/and phase transitions in the nuclear/hadronic matter.

Elliptic flow of inclusive charged hadrons in Au+Au collisions at E lab = 35 A GeV using the PHSD model

Elliptic flow (v 2) of inclusive charged hadrons at mid-rapidity (∣η∣ < 1.0) in Au+Au collisions at E lab = 35 A GeV using the parton hadron string dynamics (PHSD) model are presented as a function of centrality, transverse momentum (p T) and pseudo-rapidity (η). The v 2 results are obtained using the η-sub event plane method with respect to the event plane angle (ψ 2) and participant plane angle (). p T-integrated charged hadron v 2 shows a strong centrality dependence in Au+Au collisions at E lab = 35 A GeV. The eccentricity-scaled elliptic flow (v 2/ε 2) also shows centrality dependence. The higher values of v 2/ε 2 in central collisions suggest the development of stronger collectivity. The calculations are compared with the results from Au+Au collisions at published by the STAR experiment at RHIC. We also compare the results of HSD and PHSD modes to investigate the contribution of hadronic and partonic phases of the medium on the calculated v 2. The current results serve as a prediction of the collective behavior of the matter produced in baryon-rich and moderate temperature conditions for the upcoming multi-purpose detector at the nuclotron-based Ion collider facility (NICA) and compressed baryonic matter experiment at the facility for antiproton and ion research. These predictions are also useful for interpreting data measured at relativistic heavy ion collider (RHIC) beam energy scan program.