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Register a new userNet-baryon number variance and kurtosis within nonequilibrium chiral fluid dynamics
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We study the variance and kurtosis of the net-baryon number in a fluid dynamical model for heavy-ion collisions. It is based on an effective chiral model with dilatons for the strong coupling regime of QCD. Taking into account spinodal instabilities, we demonstrate that this model exhibits a diverging quark number susceptibility and kurtosis all along the spinodal lines of the first-order phase transition, with a change of universality class at the critical end point. During the (3+1) dimensional expansion of a hot and dense fireball, instabilities are created by fluctuations in the explicitly propagated chiral and dilaton field. We find a clear enhancement of event-by-event fluctuations of the baryon number at the critical point and first-order phase transition in comparison with an evolution through the crossover region.
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We explore the potential of net-baryon, net-proton and net-charge kurtosis measurements to investigate the properties of hot and dense matter created in relativistic heavy-ion collisions. Contrary to calculations in a grand canonical ensemble we explicitly take into account exact electric and baryon charge conservation on an event-by-event basis. This drastically limits the width of baryon fluctuations. A simple model to account for this is to assume a grand-canonical distribution with a sharp cut-off at the tails. We present baseline predictions of the energy dependence of the net-baryon, net-proton and net-charge kurtosis for central ($bleq 2.75$ fm) Pb+Pb/Au+Au collisions from $E_{lab}=2A$ GeV to $sqrt{s_{NN}}=200$ GeV from the UrQMD model. While the net-charge kurtosis is compatible with values around zero, the net-baryon number decreases to large negative values with decreasing beam energy. The net-proton kurtosis becomes only slightly negative for low $sqrt{s_{NN}}$.
We present results for the ratios of mean ($M_B$), variance ($sigma_B^2$), skewness ($S_B)$ and kurtosis ($kappa_B$) of net baryon-number fluctuations obtained in lattice QCD calculations with a physical light to strange quark mass ratio. Using next-to-leading order Taylor expansions in baryon chemical potential we find that qualitative features of these ratios closely resemble the corresponding experimentally measured cumulants ratios of net proton-number fluctuations for beam energies down to $sqrt{s_{_{NN}}} ge 19.6$ GeV. We show that the difference in cumulant ratios for the mean net baryon-number, $M_B/sigma_B^2=chi_1^B(T,mu_B)/chi_2^B(T,mu_B)$ and the normalized skewness, $S_Bsigma_B=chi_3^B(T,mu_B)/chi_2^B(T,mu_B)$, naturally arises in QCD thermodynamics. Moreover, we establish a close relation between skewness and kurtosis ratios, $S_Bsigma_B^3/M_B=chi_3^B(T,mu_B)/chi_1^B(T,mu_B)$ and $kappa_Bsigma_B^2=chi_4^B(T,mu_B)/chi_2^B(T,mu_B)$, valid at small values of the baryon chemical potential.
The appearance of large, none-Gaussian cumulants of the baryon number distribution is commonly discussed as a signal for the QCD critical point. We review the status of the Taylor expansion of cumulant ratios of baryon number fluctuations along the freeze-out line and also compare QCD results with the corresponding proton number fluctuations as measured by the STAR Collaboration at RHIC. To further constrain the location of a possible QCD critical point we discuss poles of the baryon number fluctuations in the complex plane. Here we use not only the Taylor coefficients obtained at zero chemical potential but perform also calculations of Taylor expansion coefficients of the pressure at purely imaginary chemical potentials.
The kurtosis and skewness of net baryon-number fluctuations are studied for the magnetized phase diagram of three-flavor quark matter within the Polyakov extended Nambu$-$Jona-Lasinio model. Two models with magnetic catalysis and inverse magnetic catalysis are considered. Special attention is given to their behavior in the neighborhood of the light and strange critical end points (CEPs). Several isentropic trajectories that come close the CEPs are studied in order to analyze possible signatures of a CEP in the presence of external magnetic fields. The effect of the magnetic field on the velocity of sound, $v_s^2$, when both the light and strange CEPs are approached from the crossover region is also investigated by calculating their temperature and baryon chemical potential dependencies at fixed distances from these CEPs. Regions with large fluctuations but no CEP in nonmagnetized matter develop a CEP under the action of a strong magnetic field. Besides, the Landau quantization of the quark trajectories may result in the appearance of extra CEPs, in particular, in the strange sector for strong magnetic fields, identifiable by the net baryon-number fluctuations. Stiffer (smoother) fluctuations in the region of the CEP are characteristic of models that do not predict (do predict) the inverse magnetic catalysis at zero chemical potential. Particularly interesting is the ratio $chi^4_B/chi^2_B$ that has a more pronounced peak structure, indicating that it is eventually a more convenient probe for the search of a CEP. The speed of sound shows a much richer structure in magnetized quark matter and allows one to identify both chiral and deconfinement transitions.
Based on the observation that the skyrmion in Skyrme theory can be viewed as a dressed monopole, we show that the skyrmions have two independent topology, the baryon topology $pi_3(S^3)$ and the monopole topology $pi_2(S^2)$. With this we propose to classify the skyrmions by two topological numbers $(m,n)$, the monopole number $m$ and the shell (radial) number $n$. In this scheme the popular (non spherically symmetric) skyrmions are classified as the $(m,1)$ skyrmions but the spherically symmetric skyrmions are classified as the $(1,n)$ skyrmions, and the baryon number $B$ is given by $B=mn$. Moreover, we show that the vacuum of the Skyrme theory has the structure of the vacuum of the Sine-Gordon theory and QCD combined together, which can also be classified by two topological numbers $(p,q)$. This puts the Skyrme theory in a totally new perspective.
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