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Register a new userSecond order cumulants of conserved charge fluctuations revisited I. Vanishing chemical potentials
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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.
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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.
We present lattice QCD calculations of higher order cumulants of electric charge distributions for small baryon chemical potentials $mu_B$ by using up to NNNLO Taylor expansions. Ratios of these cumulants are evaluated on the pseudo-critical line, $T_{pc}(mu_B)$, of the chiral transition and compared to corresponding measurements in heavy ion collision experiments by the STAR and PHENIX Collaborations. We demonstrate that these comparisons give strong constraints on freeze-out parameters. Furthermore, we use strangeness fluctuation observables to compute the ratio $mu_S/mu_B$ on the crossover line and compare it to $mu_S/mu_B$ at freeze-out stemming from fits to strange baryon yields measured by the STAR Collaboration.
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.
Using combined strong coupling and hopping parameter expansions, we derive an effective three-dimensional theory from thermal lattice QCD with heavy Wilson quarks. The theory depends on traced Polyakov loops only and correctly reflects the centre symmetry of the pure gauge sector as well as its breaking by finite mass quarks. It is valid up to certain orders in the lattice gauge coupling and hopping parameter, which can be systematically improved. To its current order it is controlled for lattices up to N_tausim 6 at finite temperature. For nonzero quark chemical potentials, the effective theory has a fermionic sign problem which is mild enough to carry out simulations up to large chemical potentials. Moreover, by going to a flux representation of the partition function, the sign problem can be solved. As an application, we determine the deconfinement transition and its critical end point as a function of quark mass and all chemical potentials.
Recently, a framework has been developed to study form factors of two-hadron states probed by an external current. The method is based on relating finite-volume matrix elements, computed using numerical lattice QCD, to the corresponding infinite-volume observables. As the formalism is complicated, it is important to provide non-trivial checks on the final results and also to explore limiting cases in which more straightforward predications may be extracted. In this work we provide examples on both fronts. First, we show that, in the case of a conserved vector current, the formalism ensures that the finite-volume matrix element of the conserved charge is volume-independent and equal to the total charge of the two-particle state. Second, we study the implications for a two-particle bound state. We demonstrate that the infinite-volume limit reproduces the expected matrix element and derive the leading finite-volume corrections to this result for a scalar current. Finally, we provide numerical estimates for the expected size of volume effects in future lattice QCD calculations of the deuterons scalar charge. We find that these effects completely dominate the infinite-volume result for realistic lattice volumes and that applying the present formalism, to analytically remove an infinite-series of leading volume corrections, is crucial to reliably extract the infinite-volume charge of the state.
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