Non-Gaussian fluctuations near the QCD critical point

We study the effect of the QCD critical point on non-Gaussian moments (cumulants) of fluctuations of experimental observables in heavy-ion collisions. We find that these moments are very sensitive to the proximity of the critical point, as measured by the magnitude of the correlation length xi. For example, the cubic central moment of multiplicity ~ xi^4.5 and the quartic cumulant ~ xi^7. We estimate the magnitude of critical point contributions to non-Gaussian fluctuations of pion and proton multiplicities.Comment: 4 pages, 3 figure

Acceptance dependence of fluctuation measures near the QCD critical point

We argue that a crucial determinant of the acceptance dependence of fluctuation measures in heavy-ion collisions is the range of correlations in the momentum space, e.g., in rapidity, $\Delta y_{\rm corr}$. The value of $\Delta y_{\rm corr}\sim1$ for critical thermal fluctuations is determined by the thermal rapidity spread of the particles at freezeout, and has little to do with position space correlations, even near the critical point where the spatial correlation length $\xi$ becomes as large as $2-3$ fm (this is in contrast to the magnitudes of the cumulants, which are sensitive to $\xi$). When the acceptance window is large, $\Delta y\gg\Delta y_{\rm corr}$, the cumulants of a given particle multiplicity, $\kappa_k$, scale linearly with $\Delta y$, or mean multiplicity in acceptance, $\langle N\rangle$, and cumulant ratios are acceptance independent. While in the opposite regime, $\Delta y\ll\Delta y_{\rm corr}$, the factorial cumulants, $\hat\kappa_k$, scale as $(\Delta y)^k$, or $\langle N\rangle^k$. We demonstrate this general behavior quantitatively in a model for critical point fluctuations, which also shows that the dependence on transverse momentum acceptance is very significant. We conclude that extension of rapidity coverage proposed by STAR should significantly increase the magnitude of the critical point fluctuation signatures.Comment: 9 pages, 4 figures, references adde

Proton number fluctuation as a signal of the QCD critical end-point

We argue that the event-by-event fluctuation of the proton number is a meaningful and promising observable for the purpose of detecting the QCD critical end-point in heavy-ion collision experiments. The long range fluctuation of the order parameter induces a characteristic correlation between protons which can be measured. The proton fluctuation also manifests itself as anomalous enhancement of charge fluctuations near the end-point, which might be already seen in existing data.Comment: 4 pages, version accepted in PR

Dynamic universality class of the QCD critical point

We show that the dynamic universality class of the QCD critical point is that of model H and discuss the dynamic critical exponents. We show that the baryon diffusion rate vanishes at the critical point. The dynamic critical index $z$ is close to 3.Comment: 12 pages. To be published in PRD. Appendix about isospin density added, introduction expande