Strangeness Neutrality Research Articles

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.

Resummed lattice QCD equation of state at finite baryon density: Strangeness neutrality and beyond

We calculate a resummed equation of state with lattice QCD simulations at imaginary chemical potentials. This work presents a generalization of the scheme introduced in 2102.06660 to the case of non-zero $\mu_S$, focusing on the line of strangeness neutrality. We present results up to $\mu_B/T \leq 3.5$ on the strangeness neutral line $\left\langle S \right\rangle = 0$ in the temperature range $130 \rm{MeV} \leq T \leq 280 \rm{MeV}$. We also extrapolate the finite baryon density equation of state to small non-zero values of the strangeness-to-baryon ratio $R=\left\langle S \right\rangle / \left\langle B \right\rangle$. We perform a continuum extrapolation using lattice simulations of the 4stout-improved staggered action with 8, 10, 12 and 16 timeslices.

Longitudinal dynamics and particle production in relativistic nuclear collisions

This work presents a three-dimensional dynamical initialization model for relativistic heavy-ion collisions, implementing local energy-momentum conservation and baryon charge fluctuations at string junctions. Constraining parameters using experimental data from p+p collisions at various collision energies, the model provides a very good description of the charged hadron and net proton rapidity distributions in Au+Au collisions from 7.7 to 200 GeV and Pb+Pb collisions at 8.77 and 17.3 GeV. We demonstrate the importance of fluctuations of baryon densities to string junctions for describing net-proton distributions at collision energies of 62.4 and 200 GeV. Including this improved baryon stopping description along with the requirement of strangeness neutrality also yields a good description of identified particle yields as functions of the collision energy above 7.7 GeV. We further study asymmetric p+Al and (p, d, $^3$He)+Au collisions at the top RHIC energy and p+Pb, Xe+Xe, and Pb+Pb collisions at LHC energies. We identify the produced particle rapidity distributions in asymmetric collision systems as particularly useful for constraining models of the early-time longitudinal dynamics.

Correlations of conserved charges and QCD phase structure * *Supported by the National Natural Science Foundation of China (11775041)

Correlations of conserved charges, i.e., the baryon number, electric charge, and strangeness, are calculated at finite temperature and chemical potentials up to the fourth order. The calculations are done in a 2+1 flavor low energy effective theory, in which the quantum and thermal fluctuations are encoded through the evolution of flow equations within the functional renormalization group approach. Strangeness neutrality and a fixed ratio of the electric charge to the baryon number density are implemented throughout the computation. We find that higher-order correlations incorporate more sensitive critical dynamics than the quadratic ones. In addition, a non-monotonic dependence of the fourth-order correlations between the baryon number and strangeness, i.e., and , on the collision energy is also observed.

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.

Radius of convergence in lattice QCD at finite μB with rooted staggered fermions

In typical statistical mechanical systems the grand canonical partition function at finite volume is proportional to a polynomial of the fugacity $e^{\mu/T}$. The zero of this Lee-Yang polynomial closest to the origin determines the radius of convergence of the Taylor expansion of the pressure around $\mu=0$. The computationally cheapest formulation of lattice QCD, rooted staggered fermions, with the usual definition of the rooted determinant, does not admit such a Lee-Yang polynomial. We argue that the radius of convergence is then bounded by the spectral gap of the reduced matrix of the unrooted staggered operator. This is a cutoff effect that potentially affects all estimates of the radius of convergence with the standard staggered rooting. We suggest a new definition of the rooted staggered determinant at finite chemical potential that allows for a definition of a Lee-Yang polynomial, and, therefore of the numerical study of Lee-Yang zeros. We also describe an algorithm to determine the Lee-Yang zeros and apply it to configurations generated with the 2-stout improved staggered action at $N_t = 4$. We perform a finite-volume scaling study of the leading Lee-Yang zeros and estimate the radius of convergence of the Taylor expansion extrapolated to an infinite volume. We show that the limiting singularity is not on the real line, thus giving a lower bound on the location of any possible phase transitions at this lattice spacing. In the vicinity of the crossover temperature at zero chemical potential, the radius of convergence turns out to be $\mu_B/T \approx 2$ and roughly temperature independent. Our simulations are performed at strange quark chemical potential $\mu_s=0$, but the method can be straightforwardly extended to strangeness chemical potential $\mu_S=0$ or strangeness neutrality.

Hadron-quark hybrid model reliable for equations of state with μB≤400 MeV

We present a simple version of hadron-quark hybrid (HQH) model in the $\mu_B$--$T$ plain, where $T$ is temperature and $\mu_{B}$ is the baryon-number chemical potential. The model is composed of the independent-quark model for quark-gluon states and an improved version of excluded-volume hadron resonance gas (EV-HRG) model for hadronic states. In the improved version of EV-HRG, the pressure has charge conjugation and is obtained by a simple analytic form. The switching function from hadron states to quark-gluon states in the present model has no chemical potential dependence. The simple HQH model is successful in reproducing LQCD results on the transition region of chiral crossover and the EoS in $\mu_{B} \leq 400$ MeV. We then predict the chiral-crossover region in $400 \leq \mu_{B} \leq 800$ MeV. We also predict a transition line derived from isentropic trajectories in $0 \leq \mu_{B} \leq 800$ MeV and find that the effect of strangeness neutrality is small there.

Strangeness neutrality and QCD thermodynamics

Since the incident nuclei in heavy-ion collisions do not carry strangeness, the global net strangeness of the detected hadrons has to vanish. We investigate the impact of strangeness neutrality on the phase structure and thermodynamics of QCD at finite baryon and strangeness chemical potential. To this end, we study the low-energy sector of QCD within a Polyakov loop enhanced quark-meson effective theory with 2+1 dynamical quark flavors. Non-perturbative quantum, thermal, and density fluctuations are taken into account with the functional renormalization group. We show that the impact of strangeness neutrality on thermodynamic quantities such as the equation of state is sizable.

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.

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.

Higher order fluctuations and correlations of conserved charges from lattice QCD

We calculate several diagonal and non-diagonal fluctuations of conserved charges in a system of 2+1+1 quark flavors with physical masses, on a lattice with size 483 × 12. Higher order fluctuations at μB = 0 are obtained as derivatives of the lower order ones, simulated at imaginary chemical potential. From these correlations and fluctuations we construct ratios of net-baryon number cumulants as functions of temperature and chemical potential, which satisfy the experimental conditions of strangeness neutrality and proton/baryon ratio. Our results qualitatively explain the behavior of the measured cumulant ratios by the STAR collaboration.

The QCD Equation of state and critical end-point estimates at [formula omitted

We present results for the QCD Equation of State at non-zero chemical potentials corresponding to the conserved charges in QCD using Taylor expansion upto sixth order in the baryon number, electric charge and strangeness chemical potentials. The latter two are constrained by the strangeness neutrality and a fixed electric charge to baryon number ratio. In our calculations, we use the Highly Improved Staggered Quarks (HISQ) discretization scheme at physical quark masses and at different values of the lattice spacings to control lattice cut-off effects. Furthermore we calculate the pressure along lines of constant energy density, which serve as proxies for the freeze-out conditions and discuss their dependence on μB, which is necessary for hydrodynamic modelling near freezeout. We also provide an estimate of the radius of convergence of the Taylor series from the 6th order coefficients which provides a new constraint on the location of the critical end-point in the T-μB plane of the QCD phase diagram.

The QCD equation of state at finite density from analytical continuation

We want to study thermodynamical observables at finite density. Since direct lattice simulations at finite μB are hindered by the sign problem an efficient way to study the QCD phase diagram at small finite density is to extrapolate observables from imaginary chemical potential. In this talk we present results on several observables for the equation of state. The observables are calculated along the isentropic trajectories in the (T, μB) plane corresponding to the RHIC Beam Energy Scan collision energies. The simulations are performed at the physical mass for the light and strange quarks. μS was tuned in a way to enforce strangeness neutrality to match the experimental conditions; the results are continuum extrapolated and systematic effects are taken into account for the error estimate.

The QCD equation of state at finite density from analytical continuation

An effcient way to study the QCD phase diagram at small finite density is to extrapolate thermodynamical observables from imaginary chemical potential. In this talk we present results on several observables for the equation of state to order (μB /T )6 . The observables are calculated along the isentropic trajectories in the (T , μB ) plane corresponding to the RHIC Beam Energy Scan collision energies. The simulations are performed at the physical mass for the light and strange quarks. μs was tuned in a way to enforce strangeness neutrality to match the experimental conditions; the results are continuum extrapolated using lattices of up to Nt = 16 temporal resolution.

Towards the QCD phase diagram from analytical continuation

We calculate the QCD cross-over temperature, the equation of state and fluctuations of conserved charges at finite density by analytical continuation from imaginary to real chemical potentials. Our calculations are based on new continuum extrapolated lattice simulations using the 4stout staggered actions with a lattice resolution up to Nt=16. The simulation parameters are tuned such that the strangeness neutrality is maintained, as it is in heavy ion collisions.

The QCD phase diagram from analytic continuation

We present the crossover line between the quark gluon plasma and the hadron gas phases for small real chemical potentials. First we determine the effect of imaginary values of the chemical potential on the transition temperature using lattice QCD simulations. Then we use various formulas to perform an analytic continuation to real values of the baryo-chemical potential. Our data set maintains strangeness neutrality to match the conditions of heavy ion physics. The systematic errors are under control up to μB≈300 MeV. For the curvature of the transition line we find that there is an approximate agreement between values from three different observables: the chiral susceptibility, chiral condensate and strange quark susceptibility. The continuum extrapolation is based on Nt=10, 12 and 16 lattices. By combining the analysis for these three observables we find, for the curvature, the value κ=0.0149±0.0021.

QCD bulk thermodynamics and conserved charge fluctuations with HISQ fermions

After briefly reviewing recent progress by the HotQCD collaboration in studying the 2+1 flavor QCD equation of state, we will focus on results on fluctuations of conserved charges by the BNL-Bielefeld and HotQCD collaborations. Higher order cumulants of the net-charge distributions are increasingly dominated by a universal scaling behavior, which arises due to a critical point of QCD in the chiral limit. Considering cumulants up to the 6th order, we observe that they generically behave as expected from universal scaling laws, which is quite different from cumulants calculated within the hadron resonance gas model. Taking ratios of these cumulants, we obtain volume independent results that can be compared to the experimental measurements. We will argue that the freeze-out chemical potentials and the freeze-out temperature, usually obtained by a HRG model fit to the measured hadronic yields, can also be obtained in a model independent way from ab-initio lattice QCD calculations by utilizing observables related to conserved charge fluctuations. Further, we will show that the freeze-out strangeness and electric charge chemical potentials can be fixed by imposing strangeness neutrality and isospin asymmetry constraints in the lattice QCD calculations, in order to accommodate conditions met in heavy ion collisions. All results have been obtained with the highly improved staggered quark action (HISQ) and almost physical quark masses on lattices with temporal extent of Nτ = 6, 8, 10, 12.

Equation of state of hadron resonance gas and the phase diagram of strongly interacting matter

The equation of state of hadron resonance gas at finite temperature and baryon density is calculated taking into account finite-size effects within the excluded volume model. Contributions of known hadrons with masses up to 2 GeV are included in the zero-width approximation. Special attention is paid to the role of strange hadrons in the system with zero total strangeness. A density- dependent mean field is added to guarantee that the nuclear matter has a saturation point and a liquid-gas phase transition. The deconfined phase is described by the bag model with lowest order perturbative corrections. The phase transition boundary is found by using the Gibbs conditions with the strangeness neutrality constraint. The sensitivity of the phase diagram to the hadronic excluded volume and to the parametrization of the mean-field is investigated. The possibility of strangeness-antistrangeness separation in the mixed phase is analyzed. It is demonstrated that the peaks in the kaon to pion and lambda to pion multiplicity ratios can be explained by a nonmonotonous behavior of the strangeness fugacity along the chemical freeze-out line.