Strange Quark Chemical Potential 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

Strangeness chemical potential from the baryons relative to the kaons particle ratios

From a systematic analysis of the energy-dependence of four antibaryon-to-baryon ratios relative to the antikaon-to-kaon ratio, we propose an alternative approach determining the strange-quark chemical potential ([Formula: see text]). It is found that [Formula: see text] generically genuinely equals one-fifth the baryon chemical potential ([Formula: see text]). An additional quantity depending on [Formula: see text] and the freezeout temperature ([Formula: see text]) should be added in order to assure averaged strangeness conversation. This quantity gives a genuine estimation for the possible strangeness enhancement with the increase in the collision energy. At the chemical freezeout conditioned to constant entropy density normalized to temperature cubed, various particle ratios calculated at [Formula: see text] and [Formula: see text] and the resultant [Formula: see text] excellently agree with the statistical-thermal calculations.

Equation of state of imbalanced cold matter from chiral perturbation theory

We study the thermodynamic properties of matter at vanishing temperature for non-extreme values of the isospin chemical potential and of the strange quark chemical potential. From the leading order pressure obtained by maximizing the static chiral Lagrangian density we derive a simple expression for the equation of state in the pion condensed phase and in the kaon condensed phase. We find an analytical expression for the maximum of the ratio between the energy density and the Stefan-Boltzmann energy density as well as for the isospin chemical potential at the peak both in good agreement with lattice simulations of quantum chromodynamics. We speculate on the location of the crossover from the Bose-Einstein condensate state to the Bardeen-Cooper-Schrieffer state by a simple analysis of the thermodynamic properties of the system. For $\mu_I \gtrsim 2 m_\pi$ the leading order chiral perturbation theory breaks down; as an example it underestimates the energy density of the system and leads to a wrong asymptotic behavior.

Intriguing aspects of meson condensation

We analyze various aspects of pion and kaon condensation in the framework of chiral perturbation theory. Considering a system at vanishing temperature and varying the isospin chemical potential and the strange quark chemical potential we reproduce known results about the phase transition to the pion condensation phase and to the kaon condensation phase. However, we obtain mesonic mixings and masses in the condensed phases that are in disagreement with the results reported in previous works. Our findings are obtained both by a theory group analysis and by direct calculation by means of the same low-energy effective Lagrangian used in previous works. We also study the leptonic decay channels in the normal phase and in the pion condensed phase, finding that some of these channels have a peculiar nonmonotonic behavior as a function of the isospin chemical potential. Regarding the semileptonic decays, we find that that they should be efficient feeding processes for the stable charged pion state.

Curvature of the chiral pseudocritical line in QCD

We determine the curvature of the pseudo-critical line of strong interactions by means of numerical simulations at imaginary chemical potentials. We consider $N_f=2+1$ stout improved staggered fermions with physical quark masses and the tree level Symanzik gauge action, and explore two different sets of lattice spacings, corresponding to temporal extensions $N_t = 6$ and $N_t = 8$. Both the renormalized chiral condensate and the renormalized chiral susceptibility are used to locate the transition. The determinations obtained from the two quantities are in good agreement, a preliminary continuum extrapolation yields $\kappa = 0.013(2)(1)$. We also investigate the impact of a non-zero strange quark chemical potential and compare our results to previous determinations in the literature, discussing the possible sources of systematic errors affecting the various procedures.

Strangeness in the PNJL model

We discuss the isentropic trajectories on the QCD phase diagram in the temperature and the quark chemical potential plane using the Nambu–Jona–Lasinio model with the Polyakov loop coupling (PNJL model). We impose a constraint on the strange quark chemical potential so that the strange quark density is kept to zero to mimic a situation in the ultra relativistic heavy-ion collisions. We then find an interesting relation between the induced strange quark chemical potential and the ratio of the Polyakov loop and the anti-Polyakov loop.

Isentropic thermodynamics in the Polyakov–Nambu–Jona-Lasinio model

We discuss the isentropic trajectories on the QCD phase diagram in the temperature and the quark chemical potential plane using the Nambu--Jona-Lasinio model with the Polyakov loop coupling (PNJL model). We impose a constraint on the strange quark chemical potential so that the strange quark density is zero, which is the case in the ultra relativistic heavy-ion collisions. We compare our numerical results with the truncated estimates by the Taylor expansion in terms of the chemical potential to quantify the reliability of the expansion used in the lattice QCD simulation. We finally discuss the strange quark chemical potential induced by the strangeness neutrality condition and relate it to the ratio of the Polyakov loop and the anti-Polyakov loop.

The strange-quark chemical potential as an experimentally accessible ‘order parameter’ of the deconfinement phase transition for finite baryon density

We consider the change of the strange-quark chemical potential in the phase diagram of nuclear matter, employing the Wilson loop and scalar quark condensate order parameters, mass-scaled partition functions and enforcing flavour conservation. Assuming the region beyond the hadronic phase to be described by massive, correlated and interacting quarks, in the spirit of lattice and effective QCD calculations, we find the strange-quark chemical potential to change sign: from positive in the hadronic phase, to zero upon deconfinement, to negative in the partonic domain. We propose this change in the sign of the strange-quark chemical potential to be an experimentally accessible order parameter and a unique, concise and well-defined indication of the quark-deconfinement phase transition in nuclear matter.

Variation of the strange-quark chemical potential in the phase diagram of nuclear matter**Work supported in part by the Research Secretariat of the University of Athens.

On the basis of lattice calculations, we require the existence of a deconfined quark matter region (0 < as < 1) beyond the hadron gas phase, which goes asymptotically into the ideal quark–gluon plasma domain, in the phase diagram of nuclear matter. We consider empirically the dynamics of this region in terms of the order parameters and mass-scaled partition functions and derive an EoS. Then, the strange-quark chemical potential is expressed in a functional form of the temperature and light-quark chemical potential and its variation throughout the 3-region phase diagram is studied. We propose the change of the sign of the strange-quark chemical potential, from positive in the hadronic region to negative beyond, to be a unique, concise and well-defined indication of the quark-deconfinement phase transition in nuclear matter. Analysis of the nucleus–nucleus collision data from AGS and SPS is presented giving strong support to our proposal.

Systematics of thermodynamic quantities in a 3-region phase diagramme from strange particle ratios

Using the strange-hadron mass spectrum, theμ q/T andμ s/T values obtained from strange particle ratios, we estimate the temperature of the equilibrated primordial state for several nuclear interactions at AGS and SPS. Fitting the systematics forT,μ q and transverse flow velocity we predict their values at RHIC. On the basis of lattice calculations and experimental evidence, we propose the existence of an intermediate phase: the Deconfined Quark Matter (DQM) phase with massive and correlated quarks. We define theμ s = 0 curve as the boundary between the HG and DQM phases for the strange-hadron sector and write an empirical EoS for the latter region. Its distinct characteristic is the negative strange-quark chemical potential. Experimental suggestion forμ s < 0 may have been seen in S+A interactions at 200A GeV.

Chemical freeze-out conditions in central S-S collisions at 200A GeV

We determine the chemical freeze-out parameters of hadronic matter formed in central S-S collisions at 200 A GeV, analyzing data from the NA35 collaboration at CERN. In particular we study the quark (baryon number) and strange quark fugacities, as well as the strange quark phase-space occupancy and the freeze-out temperature. The strange quark chemical potential is found to be consistent with zero, and the strange quark abundance is found to be saturated as would be expected for the deconfined phase. We study the stability of our results against variations in the analysis procedure and with respect to a restriction of the data to the central rapidity region. The same analysis applied to nucleonnucleon data yields significantly different freeze-out parameters, in particular regarding the degree of strangeness saturation.