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Register a new userConserved charge fluctuations at vanishing and non-vanishing chemical potential
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Frithjof Karsch
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Up to 6th order cumulants of fluctuations of net baryon-number, net electric charge and net strangeness as well as correlations among these conserved charge fluctuations are now being calculated in lattice QCD. These cumulants provide a wealth of information on the properties of strong-interaction matter in the transition region from the low temperature hadronic phase to the quark-gluon plasma phase. They can be used to quantify deviations from hadron resonance gas (HRG) model calculations which frequently are used to determine thermal conditions realized in heavy ion collision experiments. Already some second order cumulants like the correlations between net baryon-number and net strangeness or net electric charge differ significantly at temperatures above 155 MeV in QCD and HRG model calculations. We show that these differences increase at non-zero baryon chemical potential constraining the applicability range of HRG model calculations to even smaller values of the temperature.
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We update lattice QCD results for second order cumulants of conserved charge fluctuations and correlations at non-zero temperature and vanishing values of the conserved charge chemical potentials. We compare these results to hadron resonance gas calculations with and without excluded volume terms as well as S-matrix results in the hadronic phase of QCD, and comment on their current limitations. We, furthermore, use these results to characterize thermal conditions in the vicinity of the pseudo-critical line of the chiral transition in QCD. We argue that the ratio of strange to baryon chemical potentials is a robust observable that, on the one hand, deviates only little from hadron resonance gas results, but, on the other hand, is very sensitive to the spectrum of strange baryon resonances.
We discuss the next-to-leading order Taylor expansion of ratios of cumulants of net-baryon number fluctuations. We focus on the relation between the skewness ratio, $S_Bsigma_B = chi_3^B/chi_1^B$, and the kurtosis ratio, $kappa_Bsigma_B^2 =chi_4^B/chi_2^B$. We show that differences in these two cumulant ratios are small for small values of the baryon chemical potential. The next-to-leading order correction to $kappa_Bsigma_B^2$ however is approximately three times larger than that for $S_Bsigma_B$. The former thus drops much more rapidly with increasing beam energy, $sqrt{s_{NN}}$. We argue that these generic patterns are consistent with current data on cumulants of net-proton number fluctuations measured by the STAR Collaboration at $sqrt{s_{NN}}ge 19.6$~GeV.
Lattice QCD at finite chemical potential is difficult due to the sign problem. We use stochastic quantization and complex Langevin dynamics to study this issue. First results for QCD in the hopping expansion are encouraging. U(1) and SU(3) one link models are used to gain further insight into why the method appears to be successful.
We investigate the properties of QCD at finite isospin chemical potential at zero and non-zero temperatures. This theory is not affected by the sign problem and can be simulated using Monte-Carlo techniques. With increasing isospin chemical potential and temperatures below the deconfinement transition the system changes into a phase where charged pions condense, accompanied by an accumulation of low modes of the Dirac operator. The simulations are enabled by the introduction of a pionic source into the action, acting as an infrared regulator for the theory, and physical results are obtained by removing the regulator via an extrapolation. We present an update of our study concerning the associated phase diagram using 2+1 flavours of staggered fermions with physical quark masses and the comparison to Taylor expansion. We also present first results for our determination of the equation of state at finite isospin chemical potential and give an example for a cosmological application. The results can also be used to gain information about QCD at small baryon chemical potentials using reweighting with respect to the pionic source parameter and the chemical potential and we present first steps in this direction.
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 $mu_{X=B,Q,S,I}$. 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 $ T_c(mu_X) = T_c(0) left[ 1 -kappa_2^{X}(mu_{X}/T_c(0))^2 -kappa_4^{X}(mu_{X}/T_c(0))^4 right] $, we determined $kappa_2^X$ and $kappa_4^X$ from Taylor expansions of chiral observables in $mu_X$. We obtained a precise result for $T_c(0)=(156.5pm1.5);mathrm{MeV}$. For analogous thermal conditions at the chemical freeze-out of relativistic heavy-ion collisions, i.e., $mu_{S}(T,mu_{B})$ and $mu_{Q}(T,mu_{B})$ fixed from strangeness-neutrality and isospin-imbalance, we found $kappa_2^B=0.012(4)$ and $kappa_4^B=0.000(4)$. For $mu_{B}lesssim300;mathrm{MeV}$, the chemical freeze-out takes place in the vicinity of the QCD phase boundary, which coincides with the lines of constant energy density of $0.42(6);mathrm{GeV/fm}^3$ and constant entropy density of $3.7(5);mathrm{fm}^{-3}$.
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