Strangeness Chemical Potentials Research Articles

Curvature of the chiral phase transition line from the magnetic equation of state of ( 2+1 )-flavor QCD

We analyze the dependence of the chiral phase transition temperature on baryon number and strangeness chemical potentials by calculating the leading order curvature coefficients in the light and strange quark flavor basis as well as in the conserved charge (B, S) basis. Making use of scaling properties of the magnetic equation of state (MEoS) and including diagonal as well as off-diagonal contributions in the expansion of the energylike scaling variable that enters the parametrization of the MEoS, allows to explore the variation of Tc(μB,μS)=Tc(1−(κ2Bμ^B2+κ2Sμ^S2+2κ11BSμ^Bμ^S)) along different lines in the (μB,μS) plane. On lattices with fixed cutoff in units of temperature, aT=1/8, we find κ2B=0.015(1), κ2S=0.0124(5) and κ11BS=−0.0050(7). We show that the chemical potential dependence along the line of vanishing strangeness chemical potential is about 10% larger than along the strangeness neutral line. The latter differs only by about 3% from the curvature on a line of vanishing strange quark chemical potential, μs=0. We also show that close to the chiral limit the strange quark mass contributes like an energylike variable in scaling relations for pseudocritical temperatures. The chiral phase transition temperature decreases with decreasing strange quark mass, Tc(ms)=Tc(msphy)(1−0.097(2)(ms−msphys)/msphy+O((Δms)2). Published by the American Physical Society 2024

Anomalous strangeness transport

Nondissipative transport of strangeness is studied in a chiral hadronic plasma with three flavors. In the phase in which chiral symmetry is preserved, strangeness transport is found to be driven by both an external magnetic field and fluid vorticity. As for the constitutive relations of the baryon and electromagnetic currents, they exhibit vortical terms proportional to the strangeness chemical potential. In the superfluid phase, transverse nondissipative diffusion of the baryon, electromagnetic, and strangeness charges is found, which survives in the limit of vanishing chiral imbalance and mixes in a fashion similar to standard dissipative diffusion in quark-gluon plasma.

Lattice QCD equation of state at finite chemical potential from an alternative resummation: Strangeness neutrality and beyond

In this contribution we present a resummation of the Quantum Chromodynamics (QCD) equation of state from lattice simulations at imaginary chemical potentials. We generalize the scheme introduced in a previous work [1], to the case of non-zero strangeness chemical potential. We present continuum extrapolated results for thermodynamic observables in the temperature range 130MeV ≤ T ≤ 280 MeV, for chemical potentials up to μB/T = 3:5, along the strangeness neutral line. Furthermore, we relax the constraint of strangeness neutrality, by extrapolating to small values of the strangeness-to-baryon-number ratio R = nS / nB.

Lattice-QCD-based equations of state at finite temperature and density

The equation of state (EoS) of QCD is a crucial input for the modeling of heavy-ion-collision (HIC) and neutron-star-merger systems. Calculations of the fundamental theory of QCD, which could yield the true EoS, are hindered by the infamous Fermi sign problem which only allows direct simulations at zero or imaginary baryonic chemical potential. As a direct consequence, the current coverage of the QCD phase diagram by lattice simulations is limited. In these proceedings, two different equations of state based on first-principle lattice QCD (LQCD) calculations are discussed. The first is solely informed by the fundamental theory by utilizing all available diagonal and non-diagonal susceptibilities up to O(µ 4 B) in order to reconstruct a full EoS at finite baryon number, electric charge and strangeness chemical potentials. For the second, we go beyond information from the lattice in order to explore the conjectured phase structure, not yet determined by LQCD methods, to assist the experimental HIC community in their search for the critical point. We incorporate critical behavior into this EoS by relying on the principle of universality classes, of which QCD belongs to the 3D Ising Model. This allows one to study the effects of a singularity on the thermodynamical quantities that make up the equation of state used for hydrodynamical simulations of HICs. Additionally, we ensure that these EoSs are valid for applications to HICs by enforcing conditions of strangeness neutrality and fixed charge-to-baryonnumber ratio.

Taylor expansions and Padé approximants for cumulants of conserved charge fluctuations at nonvanishing chemical potentials

Using high statistics datasets generated in ($2+1$)-flavor QCD calculations at finite temperature, we present results for low-order cumulants of net-baryon-number fluctuations at nonzero values of the baryon chemical potential. We calculate Taylor expansions for the pressure (zeroth-order cumulant), the net-baryon-number density (first-order cumulant), and the variance of the distribution on net-baryon-number fluctuations (second-order cumulant). We obtain series expansions from an eighth-order expansion of the pressure and compare these to diagonal Pad\'e approximants. This allows us to estimate the range of values for the baryon chemical potential in which these expansions are reliable. We find ${\ensuremath{\mu}}_{B}/T\ensuremath{\le}2.5$, 2.0, and 1.5 for the zeroth-, first-, and second-order cumulants, respectively. We, furthermore, construct estimators for the radius of convergence of the Taylor series of the pressure. In the vicinity of the pseudocritical temperature ${T}_{pc}\ensuremath{\simeq}156.5\text{ }\text{ }\mathrm{MeV}$, we find ${\ensuremath{\mu}}_{B}/T\ensuremath{\gtrsim}2.9$ at vanishing strangeness chemical potential and somewhat larger values for strangeness neutral matter. These estimates are temperature dependent and range from ${\ensuremath{\mu}}_{B}/T\ensuremath{\gtrsim}2.2$ at $T=135\text{ }\text{ }\mathrm{MeV}$ to ${\ensuremath{\mu}}_{B}/T\ensuremath{\gtrsim}3.2$ at $T=165\text{ }\text{ }\mathrm{MeV}$. The estimated radius of convergences is the same for any higher-order cumulant.

Transport properties and equation-of-state of hot and dense QGP matter near the critical endpoint in the phenomenological dynamical quasiparticle model

We extend the effective dynamical quasiparticle model (DQPM)---constructed for the description of nonperturbative QCD phenomena of the strongly interacting quark-gluon plasma (QGP)---to large baryon chemical potentials, ${\ensuremath{\mu}}_{B}$, including a critical endpoint (CEP) and a first-order phase transition. The DQPM description of quarks and gluons is based on partonic propagators with complex self-energies where the real part of the self-energies is related to the quasiparticle mass and the imaginary part to a finite width of their spectral functions (i.e., the imaginary parts of the propagators). In DQPM the determination of complex self-energies for the partonic degrees of freedom at zero and finite ${\ensuremath{\mu}}_{B}$ has been performed by adjusting the entropy density to the lattice QCD data. The temperature-dependent effective coupling (squared) ${g}^{2}(T/{T}_{c})$, as well as the effective masses and widths of the partons are based on this adjustments. The novel extended dynamical quasiparticle model, named ``DQPM-CP,'' makes it possible to describe thermodynamical and transport properties of quarks and gluons in a wide range of temperature, $T$, and baryon chemical potential, ${\ensuremath{\mu}}_{B}$, and reproduces the equation of state of lattice QCD calculations in the crossover region of finite $T,{\ensuremath{\mu}}_{B}$. We apply a scaling ansatz for the strong coupling constant near the CEP, located at $({T}^{\mathrm{CEP}},{\ensuremath{\mu}}_{B}^{\mathrm{CEP}})=(0.100,0.960)\text{ }\text{ }\mathrm{GeV}$. We show the equation of state as well as the speed of sound for $T>{T}_{c}$ and for a wide range of ${\ensuremath{\mu}}_{B}$, which can be of interest for hydrodynamical simulations. Furthermore, we consider two settings for the strange quark chemical potentials, (I) ${\ensuremath{\mu}}_{q}={\ensuremath{\mu}}_{u}={\ensuremath{\mu}}_{s}={\ensuremath{\mu}}_{B}/3$ and (II) ${\ensuremath{\mu}}_{s}=0,{\ensuremath{\mu}}_{u}={\ensuremath{\mu}}_{d}={\ensuremath{\mu}}_{B}/3$. The isentropic trajectories of the quark-gluon plasma matter are compared for these two cases. The phase diagram of DQPM-CP is close to PNJL calculations. The leading order pQCD transport coefficients of both approaches differ. This elucidates that the knowledge of the phase diagram alone is not sufficient to describe the dynamical evolution of strongly interacting matter.

Corrections to the hadron resonance gas from lattice QCD and their effect on fluctuation-ratios at finite density

The hadron resonance gas (HRG) model is often believed to correctly describe the confined phase of QCD. This assumption is the basis of many phenomenological works on QCD thermodynamics and of the analysis of hadron yields in relativistic heavy ion collisions. We use first-principle lattice simulations to calculate corrections to the ideal HRG. Namely, we determine the sub-leading fugacity expansion coefficients of the grand canonical free energy, receiving contributions from processes like kaon-kaon or baryon-baryon scattering. We achieve this goal by performing a two dimensional scan on the imaginary baryon number chemical potential ($\mu_B$) - strangeness chemical potential ($\mu_S$) plane, where the fugacity expansion coefficients become Fourier coefficients. We carry out a continuum limit estimation of these coefficients by performing lattice simulations with temporal extents of $N_\tau=8,10,12$ using the 4stout-improved staggered action. We then use the truncated fugacity expansion to extrapolate ratios of baryon number and strangeness fluctuations and correlations to finite chemical potentials. Evaluating the fugacity expansion along the crossover line, we reproduce the trend seen in the experimental data on net-proton fluctuations by the STAR collaboration.

Mott Dissociation and Kaon to Pion Ratio in the EPNJL Model

The behaviour of pseudoscalar mesons within the SU(3) PNJL-like models is considered for finite T and $${{\mu }_{B}}$$ . We compare the pole approximation (Breit–Wigner) with the Beth–Uhlenbeck approach. We evaluate the $$K{\text{/}}\pi $$ ratios along the phase transition line in the T– $${{\mu }_{B}}$$ plane with constant and $$T{\text{/}}{{\mu }_{B}}$$ -dependent pion and strange quark chemical potentials. Using the model, we can show that the splitting of kaon and anti-kaon masses appears as a result of introduction of density and this explains the difference in the $${{K}^{ + }}{\text{/}}{{\pi }^{ + }}$$ ratio and $${{K}^{ - }}{\text{/}}{{\pi }^{ - }}$$ ratio at low $$\sqrt {{{s}_{{NN}}}} $$ and their tendency to the same value at high $$\sqrt {{{s}_{{NN}}}} $$ . A sharp “horn” effect in the $${{K}^{ + }}{\text{/}}{{\pi }^{ + }}$$ ratio is explained by the enhanced pion production which can be described by occurrence of a nonequilibrium pion chemical potential of the order of the pion mass. We elucidate that the horn effect is not related to the existence of a critical endpoint in the QCD phase diagram.

QCD equation of state at finite densities for nuclear collisions

We construct the QCD equation of state at finite chemical potentials including net baryon, electric charge, and strangeness based on the results of lattice QCD simulations and the hadron resonance gas model. The situation of strangeness neutrality and a fixed charge-to-baryon ratio, which resembles that of heavy nuclei, is considered for the application to relativistic heavy-ion collisions. This increases the values of baryon chemical potential compared to the case of vanishing strangeness and electric charge chemical potentials, modifying the fireball trajectory in the phase diagram. We perform viscous hydrodynamic simulations and demonstrate the importance of multiple chemical potentials for identified particle production in heavy-ion collisions at the RHIC and SPS beam energy scan energies.

Strange hadron production in Au+Au collisions at sNN=7.7 , 11.5, 19.6, 27, and 39 GeV

We present STAR measurements of strange hadron ($\mathrm{K}^{0}_{\mathrm S}$, $\Lambda$, $\overline{\Lambda}$, $\Xi^-$, $\overline{\Xi}^+$, $\Omega^-$, $\overline{\Omega}^+$, and $\phi$) production at mid-rapidity ($|y| < 0.5$) in Au+Au collisions at $\sqrt{s_{_{\mathrm{NN}}}}$ = 7.7 - 39 GeV from the Beam Energy Scan Program at the Relativistic Heavy Ion Collider (RHIC). Transverse momentum spectra, averaged transverse mass, and the overall integrated yields of these strange hadrons are presented versus the centrality and collision energy. Antibaryon-to-baryon ratios ($\overline{\Lambda}$/$\Lambda$, $\overline{\Xi}^+$/$\Xi^-$, $\overline{\Omega}^+$/$\Omega^-$) are presented as well, and used to test a thermal statistical model and to extract the temperature normalized strangeness and baryon chemical potentials at hadronic freeze-out ($\mu_{B}/T_{\rm ch}$ and $\mu_{S}/T_{\rm ch}$) in central collisions. Strange baryon-to-pion ratios are compared to various model predictions in central collisions for all energies. The nuclear modification factors ($R_{\textrm{CP}}$) and antibaryon-to-meson ratios as a function of transverse momentum are presented for all collision energies. The $\mathrm{K}^{0}_{\mathrm S}$ $R_{\textrm{CP}}$ shows no suppression for $p_{\rm T}$ up to 3.5 $\mathrm{GeV} / c$ at energies of 7.7 and 11.5 GeV. The $\overline{\Lambda}$/$\mathrm{K}^{0}_{\mathrm S}$ ratio also shows baryon-to-meson enhancement at intermediate $p_{\rm T}$ ($\approx$2.5 $\mathrm{GeV} / c$) in central collisions at energies above 19.6 GeV. Both observations suggest that there is likely a change of the underlying strange quark dynamics at collision energies below 19.6 GeV.

Pion and kaon condensation at zero temperature in three-flavor \u03c7PT at nonzero isospin and strange chemical potentials at next-to-leading order

We consider three-flavor chiral perturbation theory (χPT) at zero temperature and nonzero isospin (μI) and strange (μS) chemical potentials. The effective potential is calculated to next-to-leading order (NLO) in the π±-condensed phase, the K±-condensed phase, and the {K}^0/{overline{K}}^0 -condensed phase. It is shown that the transitions from the vacuum phase to these phases are second order and take place when, left|{mu}_Iright|={m}_{pi },left|frac{1}{2}{mu}_I+{mu}_Sright|={m}_K , and left|-frac{1}{2}{mu}_I+{mu}_Sright|={m}_K , respectively at tree level and remains unchanged at NLO. The transition between the two condensed phases is first order. The effective potential in the pion-condensed phase is independent of μS and in the kaon-condensed phases, it only depends on the combinations pm frac{1}{2}{mu}_I+{mu}_S and not separately on μI and μS. We calculate the pressure, isospin density and the equation of state in the pion-condensed phase and compare our results with recent (2 + 1)-flavor lattice QCD data. We find that the three-flavor χPT results are in good agreement with lattice QCD for μI< 200 MeV, however for larger values χPT produces values for observables that are consistently above lattice results. For μI> 200 MeV, the two-flavor results are in better agreement with lattice data. Finally, we consider the observables in the limit of very heavy s-quark, where they reduce to their two-flavor counterparts with renormalized couplings. The disagreement between the predictions of two and three flavor χPT can largely be explained by the differences in the experimental values of the low-energy constants.

Shear viscosity in microscopic calculations of A+A collisions at energies available at the Nuclotron-based Ion Collider fAcility (NICA)

Time evolution of shear viscosity $\eta$, entropy density $s$, and their ratio $\eta / s$ in the central area of central gold-gold collisions at NICA energy range is studied within the UrQMD transport model. The extracted values of energy density, net baryon density and net strangeness density are used as input to (i) statistical model of ideal hadron gas to define temperature, baryo-chemical potential and strangeness chemical potential, and to (ii) UrQMD box with periodic boundary conditions to study the relaxation process of highly excited matter. During the relaxation stage, the shear viscosity is determined in the framework of Green-Kubo approach. The procedure is performed for each of 20 time slices, corresponding to conditions in the central area of the fireball at times from 1~fm/$c$ to 20~fm/$c$. For all tested energies the ratio $\eta / s$ reaches minimum, $\left( \eta/s \right)_{min} \approx 0.3$ at $t \approx 5$~fm/$c$. Then it increases up to the late stages of the system evolution. This rise is accompanied by the drop of both, temperature and strangeness chemical potential, and increase of baryo-chemical potential.

Lattice-based equation of state at finite baryon number, electric charge, and strangeness chemical potentials

We construct an equation of state for Quantum Chromodynamics (QCD) at finite temperature and chemical potentials for baryon number $B$, electric charge $Q$ and strangeness $S$. We use the Taylor expansion method, up to the fourth power for the chemical potentials. This requires the knowledge of all diagonal and non-diagonal $BQS$ correlators up to fourth order: these results recently became available from lattice QCD simulations, albeit only at a finite lattice spacing $N_t=12$. We smoothly merge these results to the Hadron Resonance Gas (HRG) model, to be able to reach temperatures as low as 30 MeV; in the high temperature regime, we impose a smooth approach to the Stefan-Boltzmann limit. We provide a parameterization for each one of these $BQS$ correlators as functions of the temperature. We then calculate pressure, energy density, entropy density, baryonic, strangeness, electric charge densities and compare the two cases of strangeness neutrality and $\mu_S=\mu_Q=0$. We also calculate the isentropic trajectories and compare them in the two cases. Our equation of state can be readily used as an input of hydrodynamical simulations of matter created at the Relativistic Heavy Ion Collider (RHIC).

Strangeness neutrality and baryon-strangeness correlations

We derive a simple relation between strangeness neutrality and baryon-strangeness correlations. In heavy-ion collisions, the former is a consequence of quark number conservation of the strong interactions while the latter are sensitive probes of the character of QCD matter. This relation allows us to directly extract baryon-strangeness correlations from the strangeness chemical potential at strangeness neutrality. The explicit calculations are performed within a low energy theory of QCD with 2+1 dynamical quark flavors at finite temperature and density. Non-perturbative quark and hadron fluctuations are taken into account within the functional renormalization group. The results show the pronounced sensitivity of baryon-strangeness correlations on the QCD phase transition and the crucial role that strangeness neutrality plays for this observable.

Effects of a non-zero strangeness-chemical potential in strong interaction models

The effect of a non-zero strangeness chemical potential on the strong interaction phase diagram has been studied within the framework of the SU(3) quark-hadron chiral parity-doublet model. Both, the nuclear liquid-gas and the chiral/deconfinement phase transitions are modified. The first-order line in the chiral phase transition is observed to vanish completely, with the entire phase boundary becoming a crossover. These changes in the nature of the phase transitions are expected to modify various susceptibilities, the effects of which might be detectable in particle-number distributions resulting from moderate-temperature and high-density heavy-ion collision experiments.

Equation of state at finite densities for QCD matter in nuclear collisions

We construct the QCD equation of state at finite chemical potentials including net baryon, electric charge, and strangeness, based on the conserved charge susceptibilities determined from lattice QCD simulations and the equation of state of the hadron resonance gas model. For the application to relativistic heavy ion collisions we consider the situation of strangeness neutrality and matter with a fixed electric charge-to-baryon ratio, resembling that of heavy nuclei. The importance of finite electric charge and strangeness chemical potentials for particle production in heavy ion collisions is demonstrated using hydrodynamic simulations.

Chiral crossover in QCD at zero and non-zero chemical potentials

We present results for pseudo-critical temperatures of QCD chiral crossovers at zero and non-zero values of baryon (B), strangeness (S), electric charge (Q), and isospin (I) chemical potentials μX=B,Q,S,I. The results were obtained using lattice QCD calculations carried out with two degenerate up and down dynamical quarks and a dynamical strange quark, with quark masses corresponding to physical values of pion and kaon masses in the continuum limit. By parameterizing pseudo-critical temperatures as Tc(μX)=Tc(0)[1−κ2X(μX/Tc(0))2−κ4X(μX/Tc(0))4], we determined κ2X and κ4X from Taylor expansions of chiral observables in μX. We obtained a precise result for Tc(0)=(156.5±1.5) MeV. For analogous thermal conditions at the chemical freeze-out of relativistic heavy-ion collisions, i.e., μS(T,μB) and μQ(T,μB) fixed from strangeness-neutrality and isospin-imbalance, we found κ2B=0.012(4) and κ4B=0.000(4). For μB≲300 MeV, the chemical freeze-out takes place in the vicinity of the QCD phase boundary, which coincides with the lines of constant energy density of 0.42(6)GeV/fm3 and constant entropy density of 3.7(5)fm−3.

Towards the equation of state at finite density from the lattice

A new precision lattice simulation set is analyzed for the equation of state to sixth order. We used lattice results at imaginary chemical potentials to calculate the Taylor coefficients, from which the pressure, trace anomaly, energy and entropy density as well as the baryon number can be derived. We discuss an alternative extrapolation strategy and show first results for zero strangeness chemical potential.

Hyperon polarization in heavy-ion collisions and holographic gravitational anomaly

We study the energy dependence of global polarization of $\Lambda$ hyperons in peripheral $Au-Au$ collisions. We combine the calculation of vorticity and strange chemical potential in the framework of kinetic Quark-Gluon String Model with the anomalous mechanism related to axial vortical effect. The earlier found effect of helicity separation implies the quadrupole structure of longitudinal vorticity. We pay special attention to the temperature dependent contribution related to gravitational anomaly and found that the preliminary RHIC data are compatible with its suppression discovered earlier in lattice calculations. The antihyperons polarization is excessing that of hyperons and the difference is more pronounced at smaller energies.

Meson properties in asymmetric matter

In this work we study dynamic and thermodynamic (at T = 0) properties of mesons in asymmetric matter in the framework of Chiral Perturbation Theory. We consider a system at vanishing temperature with nonzero isospin chemical potential and strangeness chemical potential; meson masses and mixing in the normal phase, the pion condensation phase and the kaon condensation phase are described. We find differences with previous works, but the results presented here are supported by both theory group analysis and by direct calculations. Some pion decay channels in the normal and the pion condensation phases are studied, finding a nonmonotonic behavior of the decay width as a function of µI. Furthermore, pressure, density and equation of state of the system at T = 0 are studied, finding remarkable agreement with analogue studies performed by lattice calculations.