Baryon number fluctuations in chiral effective models and their phenomenological implications

Abstract

We study the critical properties of net-baryon-number fluctuations at the chiral restoration transition in a medium at finite temperature and net baryon density. The chiral dynamics of quantum chromodynamics (QCD) is modeled by the Polykov-loop extended Quark-Meson Lagrangian, that includes the coupling of quarks to vector meson and temporal gauge fields. The Functional Renormalization Group is employed to properly account for the $O(4)$ criticality at the phase boundary. We focus on the properties and systematics of ratios of the net-baryon-number cumulants ${\chi }_B^n$, for $1\le n\le 6$, near the phase boundary. The results are presented in the context of the recent experimental data of the STAR Collaboration on fluctuations of the net proton number in heavy ion collisions at RHIC. We show that the model results for the energy dependence of the cumulant ratios are in good overall agreement with the data, with one exception. At center-of-mass energies below $19.6\mathrm{GeV}$, we find that the measured fourth-order cumulant deviates considerably from the model results, which incorporate the expected $O(4)$ and $Z(2)$ criticality. We assess the influence of model assumptions and in particular of repulsive vector-interactions, which are used to modify the location of the critical endpoint in the model, on the cumulants ratios. Finally, we discuss a possibility to test to what extent the fluctuations are affected by nonequilibrium dynamics by comparing certain ratios of cumulants.

15 pages, 13 figures

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• Fluctuations near the liquid-gas and chiral phase transitions in hadronic matter
• Fourier coefficients of the net-baryon number density and chiral criticality
• Baryon number probability distribution at finite temperature
• Axial anomaly and hadronic properties in a nuclear medium
• Continuum extrapolated high order baryon fluctuations
• The presence of a critical end point in the QCD phase diagram from the net-baryon number fluctuations
• A model-free procedure to correct for volume fluctuations in E-by-E analyses of particle multiplicities
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• Enhanced pion-to-proton ratio at the onset of the QCD phase transition
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• Cumulants of the chiral order parameter at lower RHIC energies
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• Modeling chiral criticality