Search Results (31)

We investigate the spatial z-correlators of meson operators in $N_f=2+1+1+1$ lattice QCD with optimal domain-wall quarks across eight temperatures ranging from 325 to 3250 MeV. The meson operators include a complete set of Dirac bilinears for ten flavor combinations. Our findings reveal a hierarchical restoration of chiral symmetry in QCD with $(u,d,s,c,b)$ quarks, progressing sequentially from $SU{\left(2\right)}_L\times SU{\left(2\right)}_R\times U{\left(1\right)}_A$ to $SU{\left(3\right)}_L\times SU{\left(3\right)}_R\times U{\left(1\right)}_A$, then to $SU{\left(4\right)}_L\times SU{\left(4\right)}_R\times U{\left(1\right)}_A$, and finally to $SU{\left(5\right)}_L\times SU{\left(5\right)}_R\times U{\left(1\right)}_A$ as the temperature increases. Additionally, we explore the emergence of the $SU{\left(2\right)}_{CS}$ chiral-spin symmetry and compare the temperature windows for all flavor combinations. Our results indicate that the temperature windows for the emergent $SU{\left(2\right)}_{CS}$ symmetry are primarily dominated by the $\overline{u}b$ and $\overline{s}b$ sectors. Full article

Using a Dyson–Schwinger approach, we perform an analysis of the non-trivial ground state of thermal $SU\left(N\right)$ Yang–Mills theory in the non-perturbative regime where chiral symmetry is dynamically broken by a mass gap. Basic thermodynamic observables such as energy density and pressure are derived analytically, using Jacobi elliptic functions. The results are compared with the lattice results. Good agreement is found at low temperatures, providing a viable scenario for a gas of massive glue states populating higher levels of the spectrum of the theory. At high temperatures, a scenario without glue states consistent with a massive scalar field is observed, showing an interesting agreement with lattice data. The possibility is discussed that the results derived in this analysis open up a novel pathway beyond lattice to precision studies of phase transitions with false vacuum and cosmological relics that depend on the equations of state in strong coupled gauge theories of the type of Quantum Chromodynamics (QCD). Full article

Quark–Gluon plasma driven by the strong force is subject to the conservativeness of the baryon number, net electric charge, strangeness, etc. However, the fluctuations around their mean values at specific temperatures and chemical potentials can provide viable signals for the production of Quark–Gluon plasma. These fluctuations can be captured theoretically as moments of different orders in the expansion of pressure or the thermodynamic potential of the system under concern. Here, we look for possible explanations in the methodologies used for capturing them by using the framework of the Polyakov–Nambu–Jona-Lasinio (PNJL) model under the 2 + 1 flavor consideration with mean-field approximation. The various quantities thus explored can act to signify meaningfully near the phase transitions. Justifications are also made for some of the quantities capable of serving necessarily under experimental scenarios. Additionally, variations in certain quantities are also made for the different collision energies explored in the high-energy experiments. Rectification of the quantitative accuracy, especially in the low-temperature hadronic sector, is of prime concern, and it is also addressed. It was found that most of the observables stay in close proximity with the existing lattice QCD results at the continuum limit, with some artifacts still remaining, especially in the strange sector, which needs further attention. Full article

QCD with the isospin chemical potential ${\mu }_I$ is a useful laboratory to delineate the microphysics in dense QCD. To study the quark–hadron continuity, we use a quark–meson model that interpolates hadronic and quark matter physics at microscopic level. The equation of state is dominated by mesons at low density but taken over by quarks at high density. We extend our previous studies with two flavors to the three-flavor case to study the impact of the strangeness, which may be brought by kaons $(K_{+},K_0)=(u\overline{s},s\overline{d})$ and the U_A(1) anomaly. In the normal phase, the excitation energies of kaons are reduced by ${\mu }_I$ in the same way as hyperons in nuclear matter at the finite baryon chemical potential. Once pions condense, kaon excitation energies increase as ${\mu }_I$ does. Moreover, strange quarks become more massive through the U_A(1) coupling to the condensed pions. Hence, at zero and low temperature, the strange hadrons and quarks are highly suppressed. The previous findings in two-flavor models, sound speed peak, negative trace anomaly, gaps insensitive to ${\mu }_I$, persist in our three-flavor model and remain consistent with the lattice results to ${\mu }_I\sim$ 1 GeV. We discuss the non-perturbative power corrections and quark saturation effects as important ingredients to understand the crossover equations of state measured on the lattice. Full article

We study in detail the influence of different chemical potentials (baryon, electric charge, strange, and neutrino) on how and how fast a free gas of quarks in the zero-temperature limit reaches the conformal limit. We discuss the influence of non-zero masses, the inclusion of leptons, and different constraints, such as charge neutrality, zero-net strangeness, and fixed lepton fraction. We also investigate for the first time how the symmetry energy of the system under some of these conditions approaches the conformal limit. We find that the inclusion of all quark masses (even the light ones) can produce different results depending on the chemical potential values or constraints assumed. A positive or negative deviation of 10% from the pressure of free massless quarks with the same chemical potential was found to take place as low as ${\mu }_B=77$ to as high as $48,897$ MeV. This illustrates the fact that the “free” or conformal limit is not a unique description. Finally, we briefly discuss what kind of corrections are expected from perturbative QCD as one goes away from the conformal limit. Full article

Inspired by the fact that both the dilaton potential encoding the trace anomalies of QCD and the Polyakov loop potential measuring the deconfinement phase transition can be expressed in the logarithmic forms, as well as the fact that the scale symmetry is expected to be restoring and colors are deconfined in extreme conditions such as high temperatures and/or densities, we conjecture a relation between the dilaton potential and the Polyakov loop potential. Explicitly, we start from the Coleman–Weinberg type potential of a real scalar field—a dilaton or conformal compensator—and make an ansatz of the relation between this scalar field and the Polyakov loop to obtain the Polyakov loop potential, which can be parameterized in Lattice QCD (LQCD) in the pure glue sector. We find that the coefficients of Polyakov potential fitted from Lattice data are automatically satisfied in this ansatz, the locations of deconfinement and scale restoration are locked to each other, and the first-order phase transition can be realized. Extensions to the low-energy effective quark models are also discussed. The conjectured relation may deepen our understanding of the evolution of the universe, the mechanism of electroweak symmetry breaking, the phase diagram of QCD matter, and the properties of neutron stars. Full article

The violation of the $U\left(1\right)$ axial symmetry in QCD is stricter than the chiral $SU\left(2\right)$ breaking simply because of the presence of the quantum axial anomaly. If the QCD gauge coupling is sent to zero (the asymptotic free limit, where the $U\left(1\right)$ axial anomaly does not exist), the strength of the $U\left(1\right)$ axial breaking coincides with that of the chiral $SU\left(2\right)$ breaking, which we, in short, call an axial–chiral coincidence. This coincidence is trivial since QCD then becomes a non-interacting theory. Actually, there exists another limit in the QCD parameter space, where an axial–chiral coincidence occurs even with nonzero QCD gauge coupling, which can be dubbed a nontrivial coincidence: it is the case with the massive light quarks $(m_l\ne 0)$ and the massless strange quark ($m_s=0$) due to the flavor-singlet nature of the topological susceptibility. This coincidence is robust and tied to the anomalous chiral Ward–Takahashi identity, which is operative even at hot QCD. This implies that the chiral $SU\left(2\right)$ symmetry is restored simultaneously with the $U\left(1\right)$ axial symmetry at high temperatures. This simultaneous restoration is independent of $m_l(\ne 0)$ and, hence, is irrespective of the order of the chiral phase transition. In this paper, we discuss how the real-life QCD can be evolved from the nontrivial chiral–axial coincidence limit by working on a Nambu–Jona–Lasinio model with the $U\left(1\right)$ axial anomaly contribution properly incorporated. It is shown that, at high temperatures, the large differences between the restorations of the chiral $SU\left(2\right)$ symmetry and the $U\left(1\right)$ axial symmetry for two light quarks and a sufficiently large current mass for the strange quark are induced by a significant interference of the topological susceptibility. Thus, the deviation from the nontrivial coincidence, which is monitored by the strange quark mass controlling the topological susceptibility, provides a new way of understanding the chiral $SU\left(2\right)$ and $U\left(1\right)$ axial breaking in QCD. Full article

Utilizing the Modified Hagedorn function with embedded flow, we analyze the transverse momenta ($p_T$) and transverse mass ($m_T$) spectra of ${\pi }^{+}$ in Au–Au, Cu–Cu, and d–Au collisions at $\sqrt{s_{NN}}$ = 200 GeV across various centrality bins. Our study reveals the centrality and system size dependence of key freezeout parameters, including kinetic freezeout temperature $\left(T_0\right)$, transverse flow velocity $\left({\beta }_T\right)$, entropy-related parameter $\left(n\right)$, and kinetic freezeout volume (V). Specifically, $T_0$ and n increase from central to peripheral collisions, while ${\beta }_T$ and V show the opposite trend. These parameters also exhibit system size dependence; $T_0$ and ${\beta }_T$ are smaller in larger collision systems, whereas V is larger. Importantly, central collisions correspond to a stiffer Equation of State (EOS), characterized by larger ${\beta }_T$ and smaller $T_0$, while peripheral collisions indicate a softer EOS. These insights are crucial for understanding the properties of Quark–Gluon Plasma (QGP) and offer valuable constraints for Quantum Chromodynamics (QCD) models at high temperatures and densities. Full article

We compute the canonical partition functions and the Lee–Yang zeros in $N_f=2$ lattice QCD at temperature $T=1.20T_c$ lying above the Roberge–Weiss phase transition temperature $T_{RW}$. The phase transition is characterized by the discontinuities in the baryon number density at specific values of imaginary baryon chemical potential. We further develop our method to compute the canonical partition functions using the asymptotic expression for respective integral. Then, we compute the Lee–Yang zeros and study their behavior in the limit of high baryon density. Full article

This review covers several recent developments in the physics of dense QCD with an emphasis on the impact of multiple phase transitions on astrophysical manifestations of compact stars. To motivate the multi-phase modeling of dense QCD and delineate the perspectives, we start with a discussion of the structure of its phase diagram and the arrangement of possible color-superconducting and other phases. It is conjectured that pair-correlated quark matter in $\beta$-equilibrium is within the same universality class as spin-imbalanced cold atoms and the isospin asymmetrical nucleonic matter. This then implies the emergence of phases with broken space symmetries and tri-critical (Lifshitz) points. The beyond-mean-field structure of the quark propagator and its non-trivial implications are discussed in the cases of two- and three-flavor quark matter within the Eliashberg theory, which takes into account the frequency dependence (retardation) of the gap function. We then construct an equation of state (EoS) that extends the two-phase EoS of dense quark matter within the constant speed of sound parameterization by adding a conformal fluid with a speed of sound $c_{\mathrm{conf}.}=1/\sqrt{3}$ at densities $\ge 10n_{\mathrm{sat}}$, where $n_{\mathrm{sat}}$ is the saturation density. With this input, we construct static, spherically symmetrical compact hybrid stars in the mass–radius diagram, recover such features as the twins and triplets, and show that the transition to conformal fluid leads to the spiraling-in of the tracks in this diagram. Stars on the spirals are classically unstable with respect to the radial oscillations but can be stabilized if the conversion timescale between quark and nucleonic phases at their interface is larger than the oscillation period. Finally, we review the impact of a transition from high-temperature gapped to low-temperature gapless two-flavor phase on the thermal evolution of hybrid stars. Full article

In the QCD-like effective model, the Polyakov linear-sigma model, the isospin sigma field (${\overline{\sigma }}_3=f_{K^{\pm }}-f_{K^0}$) and the third generator of the matrix of the explicit symmetry breaking [$h_3=m_{a_0}^2\left(f_{K^{\pm }}-f_{K^0}\right)$] are estimated in terms of the decay constants of the neutral ($f_K^0$) and charged Kaon ($f_{K^{\pm }}$) and the mass of $a_0$ meson. Both quantities ${\overline{\sigma }}_3$ and $h_3$ are then evaluated, at finite baryon (${\mu }_B$), isospin chemical potential (${\mu }_I$), and temperature (T). Thereby, the dependence of the critical temperature on isospin chemical potential could be mapped out in the ($T-{\mu }_I$) phase diagram In the QCD-like effective model, the Polyakov linear-sigma model, the isospin sigma field (${\overline{\sigma }}_3=f_{K^{\pm }}-f_{K^0}$) and the third generator of the matrix of the explicit symmetry breaking [$h_3=m_{a_0}^2\left(f_{K^{\pm }}-f_{K^0}\right)$] are estimated in terms of the decay constants of the neutral ($f_K^0$) and charged Kaon ($f_{K^{\pm }}$) and the mass of $a_0$ meson. Both quantities ${\overline{\sigma }}_3$ and $h_3$ are then evaluated, at finite baryon (${\mu }_B$), isospin chemical potential (${\mu }_I$), and temperature (T). Thereby, the dependence of the critical temperature on isospin chemical potential could be mapped out in the ($T-{\mu }_I$) phase diagram. The in-medium modifications of pseudoscalars ($J^{pc}=0^{-+}$), scalars ($J^{pc}=0^{++}$), vectors ($J^{pc}=1^{--}$), and axial-vectors ($J^{pc}=1^{++}$) meson states are then analyzed in thermal and dense medium. We conclude that the QCD phase diagram ($T-{\mu }_I$) is qualitatively similar to the ($T-{\mu }_B$) phase diagram. We also conclude that both temperature and isospin chemical potential enhance the in-medium modifications of the meson states $a_0$, $\sigma$, ${\eta }^{\prime }$, $\pi$, $f_0$, $\kappa$, $\eta$, K, $\rho$, $\omega$, ${\kappa }^{*}$, $\varphi$, $a_1$, $f_1$, $K^{*}$, and $f_1^{*}$. Regarding their chemical potential, at high temperatures the various meson states likely dissolve into colored partonic phase. In this limit, the meson masses form a universal bundle. Thus, we conclude that the increase in the chemical potential similar to temperature derives the colorless confined meson states into the colored deconfined parton phase. Full article

We explore the chemical potential of a QCD-motivated van der Waals (VDW) phase change model for the six-quark color-singlet, strangeness S = −2 particle known as the hexaquark with quark content (uuddss). The hexaquark may have internal structure, indicated by short range correlations that allow for non-color-singlet diquark and triquark configurations whose interactions will change the magnitude of the chemical potential. In the multicomponent VDW Equation of State (EoS), the quark-quark particle interaction terms are sensitive to the QCD color factor, causing the pairing of these terms to give different interaction strengths for their respective contributions to the chemical potential. This results in a critical temperature near 163 MeV for the color-singlet states and tens of MeV below this for various mixed diquark and triquark states. The VDW chemical potential is also sensitive to the number density, leading to chemical potential isotherms that exhibit spinodal extrema, which also depend upon the internal hexaquark configurations. These extrema determine regions of metastability for the mixed states near the critical point. We use this chemical potential with the chemical potential-modified TOV equations to investigate the properties of hexaquark formation in cold compact stellar cores in beta equilibrium. We find thresholds for hexaquark layers and changes in maximum mass values that are consistent with observations from high mass compact stellar objects such as PSR 09043 + 10 and GW 190814. In general, we find that the VDW-TOV model has an upper stability mass and radius bound for a chemical potential of 1340 MeV with a compactness of C~0.2. Full article

In the QCD, a transition restoring the chiral symmetry occurs at a high temperature and density. Searching for the signals of the QCD phase transition is one of the goals of the current relativistic heavy-ion physics programs. The metastable state is a unique feature of the first-order phase transition. Using the van der Waals equation of state, the role of the metastable state in finite-size effects is analyzed. It is found that the finite-size effects of the first-order phase transition are closely related to the metastable state. Metastability can be observed in the distribution of the order parameters and the probability of its occurrence depends on the system scale. A sizable probability of the metastability requires a small enough system size. The possibility of observing the metastability in the RHIC/BES is discussed. Full article

Energy level interaction and electron concentration are crucial aspects that affect the response performance of quantum cascade detectors (QCDs). In this work, two different-structured array QCDs are prepared, and the detectivity reaches 10⁹ cm·Hz^1/2/W at room temperature. The overlap integral (OI) and oscillator strength (OS) between different energy levels under a series of applied biases are fitted and reveal the influence of energy level interaction on the response performance. The redistribution of electrons in the cascade structure at room temperatures is established. The coupled doped-well structure shows a higher electron concentration at room temperature, which represents a high absorption efficiency in the active region. Even better responsivity and detectivity are exhibited in the coupled doped-well QCD. These results offer a novel strategy to understand the mechanisms that affect response performance and expand the application range of QCDs for long-wave infrared (LWIR) detection. Full article

Nuclear matter, at sufficiently energy density and high temperature, undergoes a transition to a state of strongly interacting QCD matter in which quarks and gluons are not confined known as the Quark–Gluon Plasma (QGP). QGP is usually produced in high-energy collisions of heavy nuclei in the laboratory, where an enhancement of strange hadrons’ production is observed. Many of the effects which are typical of heavy ion phenomenology have been observed in high-multiplicity proton–proton (pp) collisions. The enhancement of strange particles’ production in pp collisions was reported at $\sqrt{s}=7$ TeV and $\sqrt{s}=13$ TeV in 2017 and 2020, respectively, and it was found that the integrated yields of strange particles, relative to pions, increase notably with the charged-particle multiplicity of events. Here, we report the multiplicity dependence of strange particles at $\left|y\right|<0.5$ in pp collisions at $\sqrt{s}$ = 7 TeV, 13 TeV, 20 TeV, and 27 TeV from a Monte Carlo simulation using PYTHIA8, EPOS-LHC, and Herwig7. Full article