Baryon Fluctuations Research Articles

Continuum-extrapolated high-order baryon fluctuations

Fluctuations play a key role in the study of QCD phases. Lattice QCD is a valuable tool to calculate them, but going to high orders is challenging. Up to the fourth order, continuum results have been available since 2015. We present the first continuum results for sixth-order baryon fluctuations for temperatures between T=130 and 200 MeV and eighth order at T=145 MeV in a fixed volume. Comparison with earlier studies with imaginary chemical potential suggests that the volume effect is under control for T<145 MeV. Our results are in sharp contrast with well-known results in the literature obtained at finite lattice spacing. Published by the American Physical Society 2024

Impact of hadronic interactions and conservation laws on cumulants of conserved charges in a dynamical model

Understanding the phase diagram of QCD by measuring fluctuations of conserved charges in heavy-ion collision is one of the main goals of the beam energy scan program at the BNL Relativistic Heavy Ion Collider (RHIC). Within this work, we calculate the role of hadronic interactions and momentum cuts on cumulants of conserved charges up to fourth order in a system in equilibrium within a hadronic transport approach (smash). In our model the net baryon, net charge, and net strangeness are perfectly conserved on an event-by-event basis and the cumulants are calculated as a function of subvolume sizes and compared to analytic expectations. We find a modification of the kurtosis due to charge annihilation processes in systems with simplified degrees of freedom. Furthermore the result of the full smash hadron gas for the net baryon and net proton number fluctuations is presented for systems with zero and finite values of baryon chemical potential. Additionally we find that due to dynamical correlations the cumulants of the net baryon number cannot easily be recovered from the net protons. Finally the influence of deuteron cluster formation on the net proton and net baryon fluctuations in a simplified system is shown. This analysis is important to better understand the relation between measurements of fluctuations in heavy-ion collisions and theoretical calculations which are often performed in a grand canonical ensemble.

Coupled baryon, electric charge and strangeness fluctuations in heavy-ion collisions

We present for the first time quantitative results for the coupled dynamics of second order fluctuations in the three conserved charges of QCD based on stochastic diffusion equations for a Bjorken-type expanding hadronic medium. We show that the fluctuations deviate from local equilibrium expectations which can result in important phenomenological consequences for the interpretation of experimental data.

Isospin Effect on Baryon and Charge Fluctuations from the pNJL Model

We have studied the possible isospin corrections on the skewness and kurtosis of net-baryon and net-charge fluctuations in the isospin asymmetric matter formed in relativistic heavy-ion collisions at RHIC-BES energies, based on a 3-flavor Polyakov-looped Nambu–Jona–Lasinio model. With typical scalar–isovector and vector–isovector couplings leading to the splitting of u and d quark chiral phase transition boundaries and critical points, we have observed considerable isospin effects on the susceptibilities, especially those of net-charge fluctuations. Reliable experimental measurements at even lower collision energies are encouraged to confirm the observed isospin effects.

Baryon Fluctuations in Extended Linear Sigma Model

The existence and the location of the critical end point (CEP) between the crossover and the first order part of the chiral phase transition in the phase diagram of the strongly interacting matter is a heavily studied area of recent particle physics. The baryon number fluctuations and related quantities such as kurtosis and other susceptibility ratios, that are assumed to be good signatures of CEP, are calculated in an (axial)vector meson extended $(2 + 1)$ flavor Polyakov linear sigma model (EL$\sigma$M) at zero and finite $\mu_B$ . It is compared with the results of lattice as well as other effective model calculations. Divergence of the kurtosis is found at the critical end point.

Quark-diquark string tension, excited baryonic resonances and thermal fluctuations

We study the baryonic fluctuations from second to eighth order involving electric charge, baryon number and strangeness below the quark-gluon plasma crossover and numerically known from lattice QCD calculations. By considering a particular realization of the Hadron Resonance Gas model, we provide evidence on the dominant role of quark-diquark degrees of freedom to describe excited baryonic resonances. After proving by means of suitable Polyakov loop correlators that the quark-diquark and the quark-antiquark forces coincide, , we find that the corresponding susceptibilities can be saturated with excited baryonic states in a quark-diquark model picture.

Equation of state for hot QCD and compact stars from a mean-field approach

The thermodynamic properties of high temperature and high density QCD-matter are explored within the Chiral SU(3)-flavor parity-doublet Polyakov-loop quark-hadron mean-field model, CMF. The quark sector of the CMF model is tuned to describe the $\mu_B=0$ thermodynamics data of lattice QCD. The resulting lines of constant physical variables as well as the baryon number susceptibilities are studied in some detail in the temperature/chemical potential plane. The CMF model predicts three consecutive transitions, the nuclear first-order liquid-vapor phase transition, chiral symmetry restoration, and the cross-over transition to a quark-dominated phase. All three phenomena are cross-over, for most of the $T-\mu_B$-plane. The deviations from the free ideal hadron gas baseline at $\mu_B=0$ and $T\approx 100-200$ MeV can be attributed to remnants of the liquid-vapor first order phase transition in nuclear matter. The chiral crossing transition determines the baryon fluctuations at much higher $\mu_B\approx1.5$ GeV, and at even higher baryon densities $\mu_B\approx2.4$ GeV, the behavior of fluctuations is controlled by the deconfinement cross-over. The CMF model also describe well the static properties of high $\mu_B$ neutron stars as well as the new neutron star merger observations. The effective EoS presented here describes simultaneously lattice QCD results at $\mu_B=0$, as well as observed physical phenomena (nuclear matter and neutron star matter) at $T\cong0$ and high densities, $\mu_B>1$ GeV.

Quark-diquark models and baryonic fluctuations in QCD

We study the baryonic fluctuations of electric charge, baryon number and strangeness, by considering a realization of the Hadron Resonance Gas model in the light flavor sector of QCD. We elaborate on the idea that the susceptibilities can be saturated with excited baryonic states with a quark-diquark structure with a linearly confining interaction identical up to a constant to the quark-antiquark potential, VqD′(r)=Vqq‾′(r). We obtain an overall good agreement with the spectrum obtained with other quark models and with lattice data for the fluctuations.

Searching the QCD critical endpoint with lattice simulations

We discuss the usefulness of various lattice observables especially fluctuations to locate the QCD critical endpoint. We apply different models to interpret our results for the baryon fluctuations up to µ8 from simulations at imaginary chemical potentials.

Baryonic susceptibilities, quark-diquark models, and quark-hadron duality at finite temperature

Fluctuations of conserved charges such as baryon number, electric charge and strangeness may provide a test for completeness of states in lattice QCD for three light flavors. We elaborate on the idea that the corresponding susceptibilities can be saturated with excited baryonic states with an underlying quark-diquark structure with a linearly confining interaction. Using Polyakov-loop correlators we show that in the static limit, the quark-diquark potential coincides with the quark-antiquark potential in marked agreement with recent lattice studies. We thus study in a quark-diquark model the baryonic fluctuations of electric charge, baryon number and strangeness: $\chi_{BQ}$, $\chi_{BB}$ and $\chi_{BS}$; by considering a realization of the hadron resonance gas model in the light flavor sector of QCD. These results have been obtained by using the baryon spectrum computed within a relativistic quark-diquark model, leading to an overall good agreement with the spectrum obtained with other quark models and with lattice data for the fluctuations.

Effect of inverse magnetic catalysis on conserved-charge fluctuations in a hadron resonance gas model

The effect of inverse magnetic catalysis (IMC) has been observed on the conserved charge fluctuations and the correlations along the chemical freeze-out curve in a hadron resonance gas model. The fluctuations and the correlations have been compared with and without charge conservations. The charge conservation plays an important role in the calculation of the fluctuations at nonzero magnetic field and for the fluctuations in the strange charge at zero magnetic field. The charge conservation diminishes the correlations $\chi_{BS}$ and $\chi_{QB}$, but enhances the correlation $\chi_{QS}$. The baryonic fluctuations (2nd order) at $B = 0.25$ ${GeV}^2$ increases more than two times compared to $B = 0$ at higher $\mu_{B}$. The fluctuations have been compared at nonzero magnetic field along the freeze-out curve i.e along fitted parameters of the chemical freeze-out temperature and chemical potentials, with the fluctuations at nonzero magnetic field along the freeze-out curve with the IMC effect, and the results are very different with the IMC effect. This is clearly seen in the products of different moments ${{\sigma}^2}/{M}$ and $S\sigma$ of net-kaon distribution.

Trying to constrain the location of the QCD critical endpoint with lattice simulations

We discuss the reliability of available methods to constrain the location of the QCD critical endpoint with lattice simulations. In particular we calculate the baryon fluctuations up to χ8B using simulations at imaginary chemical potentials. We argue that they contain no hint of criticality.

Critical point of nuclear matter and beam-energy dependence of net-proton number fluctuations

The beam energy dependence of net baryon number susceptibilities is studied in the framework of the hadron resonance gas model with the attractive and repulsive van der Waals interactions between baryons. The collision energy dependences for the skewness $S\sigma$ and kurtosis $\kappa\sigma^2$ deviate significantly from the Poisson baseline and demonstrate the existence of rich structures at moderate collision energies. This behavior may result from the critical end point of the nuclear liquid-gas first order phase transition. In particular, $\kappa\sigma^2$ shows a non-monotonic energy dependence, and, in contrast to the standard scenario for the QCD critical point, it does not decrease at low collision energies. It is also found that the measurable net proton fluctuations differ significantly from the net baryon fluctuations when interactions between baryons cannot be neglected. The results are compared with the experimental net proton number fluctuations measured by the STAR collaboration.

Lensing bias to CMB polarization measurements of compensated isocurvature perturbations

Compensated isocurvature perturbations are opposite spatial fluctuations in the baryon and dark matter (DM) densities. They arise in the curvaton model and some models of baryogenesis. While the gravitational effects of baryon fluctuations are compensated by those of DM, leaving no observable impacts on the cosmic microwave background (CMB) at first order, they modulate the sound horizon at recombination, thereby correlating CMB anisotropies at different multipoles. As a result, CIPs can be reconstructed using quadratic estimators similarly to CMB detection of gravitational lensing. Because of these similarities, however, the CIP estimators are biased with lensing contributions that must be subtracted. These lensing contributions for CMB polarization measurement of CIPs are found to roughly triple the noise power of the total CIP estimator on large scales. In addition, the cross power with temperature and $E$-mode polarization are contaminated by lensing-ISW (integrated Sachs-Wolfe) correlations and reionization-lensing correlations respectively. For a cosmic-variance-limited (CVL) temperature and polarization experiment measuring out to multipoles $l_{\max} = 2500$, the lensing noise raises the detection threshold by a factor of 1.5, leaving a $2.7\sigma$ detection possible for the maximal CIP signal in the curvaton model.

Critical point in the phase diagram of primordial quark-gluon matter from black hole physics

Strongly interacting matter undergoes a crossover phase transition at high temperatures $T\sim 10^{12}$ K and zero net-baryon density. A fundamental question in the theory of strong interactions, Quantum Chromodynamics (QCD), is whether a hot and dense system of quarks and gluons displays critical phenomena when doped with more quarks than antiquarks, where net-baryon number fluctuations diverge. Recent lattice QCD work indicates that such a critical point can only occur in the baryon dense regime of the theory, which defies a description from first principles calculations. Here we use the holographic gauge/gravity correspondence to map the fluctuations of baryon charge in the dense quark-gluon liquid onto a numerically tractable gravitational problem involving the charge fluctuations of holographic black holes. This approach quantitatively reproduces ab initio results for the lowest order moments of the baryon fluctuations and makes predictions for the higher order baryon susceptibilities and also for the location of the critical point, which is found to be within the reach of heavy ion collision experiments.

Nonperturbative Strange Sea in Proton Using Wave Functions Inspired by Light Front Holography

We use different light-front wave functions (two inspired by the AdS/QCD formalism), together with a model of the nucleon in terms of meson–baryon fluctuations to calculate the nonperturbative (intrinsic) contribution to the \(s(x) - \bar{s}(x)\) asymmetry of the proton sea. The holographic wave functions for an arbitrary number of constituents, recently derived by us, give results quite close to known parametrizations that appear in the literature.

Universal relations between non-Gaussian fluctuations in heavy-ion collisions

We show that universality near a critical end point implies a characteristic relation between third- and fourth-order baryon susceptibilities $\chi_3$ and $\chi_4$, resulting in a banana-shaped loop when $\chi_4$ is plotted as a function of $\chi_3$ along a freeze-out line. Including the individual enhancements of $\chi_3$ and $\chi_4$ near a critical point, these features may be a consistent set of observations supporting the interpretation of baryon fluctuations data as arising from criticality.

Net baryon fluctuations from a crossover equation of state

We have constructed an equation of state which smoothly interpolates between an excluded volume hadron resonance gas at low energy density to a plasma of quarks and gluons at high energy density. This crossover equation of state agrees very well with lattice calculations at both zero and nonzero baryon chemical potential. We use it to compute the variance, skewness, and kurtosis of fluctuations of baryon number, and compare to measurements of proton number fluctuations in central Au-Au collisions as measured by the STAR collaboration in a beam energy scan at the Relativistic Heavy Ion Collider. The crossover equation of state can reproduce the data if the fluctuations are frozen out at temperatures well below than the average chemical freeze-out.

SpontaneousCPviolating quark scattering from asymmetricZ(3)interfaces in the quark-gluon plasma

In this paper, we extend our earlier study of spontaneous CP violating scattering of quarks and anti-quarks from QCD $Z\left(3\right)$ domain walls for the situation when these walls have asymmetric profiles of the Polyakov loop order parameter $l(x)$. Dynamical quarks lead to explicit breaking of $Z(3)$ symmetry, which lifts the degeneracy of the $Z(3)$ vacua arising from spontaneous breaking of the $Z(3)$ symmetry in the quark-gluon plasma (QGP) phase. Resulting domain walls have asymmetric profile of $l(x)$ (under reflection $x \rightarrow -x$ for a domain wall centered at the origin). We calculate the background gauge field profile $A_0$ associated with this domain wall profile. Interestingly, even with the asymmetric $l(x)$ profile, quark-antiquark scattering from the corresponding gauge field configuration does not reflect this asymmetry. We show that the expected asymmetry in scattering arises when we include the effect of asymmetric profile of $l(x)$ on the effective mass of quarks and antiquarks and calculate resultant scattering. We discuss the effects of such asymmetric Z(3) walls in generating quark and antiquark density fluctuations in cosmology, and in relativistic heavy-ion collisions e.g. event-by-event baryon fluctuations.

Fluctuations in the quark-meson model for QCD with isospin chemical potential

We study the two-flavor quark-meson (QM) model with the functional renormalization group (FRG) to describe the effects of collective mesonic fluctuations on the phase diagram of QCD at finite baryon and isospin chemical potentials, μB and μI. With only isospin chemical potential there is a precise equivalence between the competing dynamics of chiral versus pion condensation and that of collective mesonic and baryonic fluctuations in the quark-meson-diquark model for two-color QCD at finite baryon chemical potential. Here, finite μB=3μ introduces an additional dimension to the phase diagram as compared to two-color QCD, however. At zero temperature, the (μI,μ) plane of this phase diagram is strongly constrained by the “Silver Blaze problem.” In particular, the onset of pion condensation must occur at μI=mπ/2, independent of μ as long as μ+μI stays below the constituent quark mass of the QM model or the liquid-gas transition line of nuclear matter in QCD. In order to maintain this relation beyond mean field it is crucial to compute the pion mass from its timelike correlator with the FRG in a consistent way.