Fluctuations and Correlations of net baryon number, electric charge, and strangeness: A comparison of lattice QCD results with the hadron resonance gas model (1203.0784v2)

Abstract: We calculate the quadratic fluctuations of net baryon number, electric charge and strangeness as well as correlations among these conserved charges in (2+1)-flavor lattice QCD at zero chemical potential. Results are obtained using calculations with tree level improved gauge and the highly improved staggered quark (HISQ) actions with almost physical light and strange quark masses at three different values of the lattice cut-off. Our choice of parameters corresponds to a value of 160 MeV for the lightest pseudo scalar Goldstone mass and a physical value of the kaon mass. The three diagonal charge susceptibilities and the correlations among conserved charges have been extrapolated to the continuum limit in the temperature interval 150 MeV <T < 250 MeV. We compare our results with the hadron resonance gas (HRG) model calculations and find agreement with HRG model results only for temperatures T<= 150 MeV. We observe significant deviations in the temperature range 160 MeV < T < 170 MeV and qualitative differences in the behavior of the three conserved charge sectors. At T < 160 MeV quadratic net baryon number fluctuations in QCD agree with HRG model calculations while, the net electric charge fluctuations in QCD are about 10% smaller and net strangeness fluctuations are about 20% larger. These findings are relevant to the discussion of freeze-out conditions in relativistic heavy ion collisions.

• The paper rigorously examines fluctuations and correlations of net baryon, electric charge, and strangeness using a (2+1)-flavor lattice QCD framework with improved actions.
• It finds that baryon fluctuations match HRG predictions below 160 MeV, while significant deviations indicate the onset of QGP effects at higher temperatures.
• The results provide a lattice-calculated baseline essential for interpreting freeze-out conditions in heavy-ion collisions and guiding further high-precision studies.

Analysis of Fluctuations and Correlations of Conserved Charges in Lattice QCD and Comparison to HRG Model

The investigation into the quantitative behavior of thermodynamic fluctuations in QCD has garnered significant academic interest, particularly in the context of heavy ion collisions. The paper by the HotQCD Collaboration rigorously examines the quadratic fluctuations and correlations of conserved charges—specifically net baryon number, electric charge, and strangeness—in a (2+1)-flavor lattice QCD framework, subsequently contrasting these findings with predictions made by the Hadron Resonance Gas (HRG) model. These fluctuations and correlations provide pivotal insights into the characteristics of the QCD phase transition and freeze-out conditions pertinent to relativistic heavy-ion collisions.

Numerical Results and Methodology

In their computational paper, the authors employ improved lattice actions, namely the tree-level improved gauge and highly improved staggered quark (HISQ) actions, to mitigate lattice artifacts and compute thermodynamic quantities across three distinct lattice cut-offs. The continuum limit extrapolation of various susceptibilities is performed over a temperature interval of 150 MeV to 250 MeV, emphasizing the juxtaposition with HRG model predictions.

The paper systematically detects that:

1. Baryon Number Fluctuations: These are largely consistent with HRG predictions up to about 160 MeV. Beyond this temperature, notable discrepancies emerge, suggesting deviations from HRG behavior.
2. Electric Charge and Strangeness Fluctuations: At approximately 160 MeV, electric charge fluctuations are observed to be about 10% below HRG expectations, whereas strangeness fluctuations exceed HRG predictions by around 20%.

These observations remain consistent with theoretical expectations for a crossover transition to the QGP phase, with the data indicating a breakdown of the HRG model's validity in capturing higher temperature features.

Implications and Further Investigation

The disparities noted between HRG model expectations and lattice results are critical for interpreting freeze-out conditions in high-energy nuclear collisions, where observing differences in net-proton and other conserved charge fluctuations provides empirical probes of the QCD phase transition. The findings underscore the preliminary deviations seen at $T \sim 160$ MeV, delineating a regime where HRG model simplifications, such as free resonance gas approximations, begin to fail. More concretely, these results facilitate a nuanced interpretation of measurements from experiments such as those conducted at the RHIC and LHC, offering a lattice-calculated baseline against which experimental data can be contrasted.

Future Directions

The paper highlights several future avenues and unresolved questions:

• Enhanced precision in lattice computations may be required to fine-tune the continuum extrapolation and definitively resolve discrepancies between the lattice data and HRG model beyond the crossover region.
• Exploration into higher-order cumulants and multi-charge correlations could provide further depth in understanding the critical fluctuations near the QCD critical point, potentially unveiling subtle signatures of critical behavior.
• Improvements in lattice algorithms to effectively reduce taste violations while accessing finer lattice spacings will be imperative for sharpening theoretical predictions and comparisons with experimentally accessible quantities.

These research trajectories are instrumental for expanding our understanding of the QGP and its transition dynamics, continuing to bridge theory with the experimental quests of unveiling the QCD phase diagram in nonzero temperature and baryon density regimes.