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The $\phi$ meson and $\Omega$ baryon provide unique probes of the properties of the quark-gluon plasma (QGP) at hadronization in relativistic heavy-ion collisions. Using the quark recombination model with the quark phase-space information parameterized in a viscous blastwave, we perform Bayesian inference of the shear and bulk viscosities of the QGP at hadronization with a temperature of $T\sim 160$ MeV by analyzing the $\phi$ and $\Omega$ data in Au+Au collisions at $\sqrt{s_{\rm NN}}=$ 19.6-200 GeV and Pb+Pb collisions at $\sqrt{s_{\rm NN}}=$ 2.76 TeV, corresponding to a baryon chemical potential variation from $\mu_B\approx 0$ (at $\sqrt{s_{\rm NN}}= 2.76$ TeV) to $200$ MeV (at $\sqrt{s_{\rm NN}}= 19.6$ GeV). We find that the shear viscosity to enthalpy ratio $\eta T/(\epsilon +P)$ of the QGP at hadronization decreases as $\mu_B$ increases, with $\eta T/(\epsilon +P)\approx 0.18$ at $\mu_B=0$ and $\eta T/(\epsilon +P)\approx 0.08$ at $\mu_B=200$ MeV, while the corresponding specific bulk viscosity is essentially constant with $\zeta T/(\epsilon + P)=0.02\sim 0.04$ for $\mu_B<200$ MeV. Our results suggest that the QGP at hadronization ($T\sim 160$ MeV) with finite baryon density is more close to perfect fluid than that with zero baryon density., Comment: 9 pages, 3 figures, 2 tables. Some details and discussions added. Accepted version to appear in PRC

We study the production of charmed and multi-charmed hadrons in ultra-relativistic Heavy Ion Collisions coupling the transport approach for charm dynamics in the medium to an hybrid hadronization model of coalescence plus fragmentation. In this paper, we mainly discuss the particle yields for single charmed and multi-charmed baryons focusing mainly on the production of $\Xi_{cc}$ and $\Omega_{ccc}$. We provide first predictions for PbPb collision in 0-10% centrality class and then we explore the system size dependence through KrKr, to ArAr and OO collisions, planned within the ALICE3 experiment. In these cases, a monotonic behavior for the yields emerges which can be tested in future experimental data. We found about three order of magnitude increase in the production of $\Omega_{ccc}$ in PbPb collisions compared with the yield in small collision systems like OO collisions. Furthermore, we investigate the effects on the $\Omega_{ccc}$ particle production and spectra coming from the modification of the charm quark distribution due to the different size of the collision systems comparing also to the case of thermalized charm distributions. These results suggest that observation on the $\Omega_{ccc}$ spectra and their evolution across system size can give information about the partial thermalization of the charm quark distribution as well as to its wave function width., Comment: 12 pages, 8 figures; minor changes and adding of a figure

We studied the directed flow of heavy quarks in small systems produced in p-Pb collisions due to both the impact of initial vorticity and electromagnetic fields. We employed a relativistic transport code to model the bulk evolution of the small systems and studied the heavy quark momentum evolution using Langevin dynamics. For the heavy quarks interaction with the bulk, we employed a quasiparticle model (QPM). We observed a large directed flow splitting ($\Delta v_1$) of charm quarks due to electromagnetic fields, which is comparable to the directed flow splitting of charm quarks in nucleus-nucleus collisions. However, the magnitude of the directed flow due to the initial tilted matter distribution in p-nucleus collisions is not substantial. The observed directed flow is not rapidity odd due to the asymmetry in the colliding system. The results presented in this manuscript provide an independent way to quantify the initial electromagnetic field produced and the matter distributed in small systems., Comment: 6 pages, 4 figures, Accepted for publication in Physics Letter B

We describe the propagation of charm quarks in the quark-gluon plasma (QGP) by means of an event-by-event transport approach. In our calculations the non-perturbative interaction between heavy quarks and light quarks has been taken into account through a quasi-particle approach with thermal light quark masses tuned to reproduce lQCD thermodynamics. We found that the flow observables $v_2$ and $v_3$ of D mesons are comparable with the experimental measurements for Pb+Pb collisions at 5.02 ATeV in different ranges of centrality selections. The results are analyzed with Event-Shape Engineering technique. The comparison of the anisotropic flow coefficients $v_n$ with experimental data show a quite well agreement with experimental data for different flow vector $q_2$ selections, which confirms the strong coupling between charm quarks and light quarks in the QCD matter. Furthermore, we present here a novel study of the event-by-event correlations between flow harmonics of $D$ mesons and soft hadrons at LHC energy with the Event-Shape Engineering technique that can put further constraints on heavy quark transport coefficients toward a solid comparison between the phenomenological determination and the lattice QCD calculations., Comment: 8 pages, 8 figures

Using the AMPT + MUSIC+UrQMD hybrid model, we study the global and local spin polarizations of $\Lambda$ hyperons as functions of the freeze-out temperature of the spin degree of freedom in the hadronic phase of Au+Au collisions at $\sqrt{s_{NN}}=19.6$ GeV. Including contributions from both the thermal vorticity and thermal shear of the hadronic matter, we find that, with the spin freeze-out temperature dropping from the hadronization temperature of 160 MeV to 110 MeV at the kinetic freeze-out, both the global and local spin polarizations of $\Lambda$ hyperons due to the thermal vorticity decrease by a factor of two, while those due to the thermal shear decrease quickly and become negligibly small at 140 MeV. Our results suggest the importance of understanding the dynamical evolution of the spin degree of freedom in the hadronic stage in relativistic heavy-ion collisions., Comment: 5 pages, 3 figures, references updated

An extraordinary strong magnetic field, $eB_0 \approx 10^{18}$ Gauss, is expected to be generated in non-central ultrarelativistic heavy ion collisions and it is envisaged to induce several effects on hot QCD matter including the possibility of local parity and local parity and charge conjugation symmetry violations. A direct signature of such e.m. fields and a first quantitative measurement of its strength and lifetime are still missing. We point out that both the mean value of leptonic invariant mass of $Z^0$ boson, reconstructed by its decaying lepton pairs, and the relative width are modified in relativistic heavy ion collisions due to the presence of strong initial e.m. fields. We propose a measurement of the leptonic invariant mass of $Z^0$ as a novel probe of the strength of the $B_y$. Both shifts could be up to about few hundred MeV and are found to depend on the integral of $B_y$ over the time duration quadratically (approximate). Hence it provides a novel and clear probe of electromagnetic fields, which can be tested experimentally., Comment: 6 pages, 6 figures

We discuss the generation of the directed flow $v_1(p_T,y_z)$ induced by the electromagnetic field as a function of $p_T$ and $y_z$. Despite the complex dynamics of charged particles due to strong interactions generating several anisotropies in the azimuthal angle, it is possible at $p_T > m$ to directly correlate the splitting in $v_1$ of heavy quarks with different charges to some main features of the magnetic field, and in particular its values at formation and freeze-out time. We further found that the slope of the splitting $d\Delta v_1/dy_z|_{y_z=0}$ of positively and negatively charged particles at high $p_T$ can be formulated as $d\Delta v_1/dy_z|_{y_z=0}=-\alpha \frac{\partial \ln f}{\partial p_T}+\frac{2\alpha-\beta}{p_T}$, where the constants $\alpha$ and $\beta$ are constrained by the $y$ component of magnetic fields and the sign of $\alpha$ is simply determined by the difference $\Delta[tB_y(t)]$ in the center of colliding systems at the formation time of particles and at the time when particles leave the effective range of electromagnetic fields or freeze out. The formula is derived from general considerations and is confirmed by several related numerical simulations; it supplies a useful guide to quantify the effect of different magnetic field configurations and provides an evidence of why the measurement of $\Delta v_1$ of charm, bottom and leptons from $Z^0$ decay and their correlations are a powerful probe of the initial e.m. fields in ultra-relativistic collisions., Comment: 12 pages, 12 figures

Strong electromagnetic fields are expected to be generated in off-central relativistic heavy ion collisions, which can induce a splitting of the directed flow of charged particles and anti-particles ($\Delta v_1$). Such a splitting manifests even for neutral charmed mesons pairs ($D^0,\bar{D}^0$), hence being a direct probe of the formation of deconfined phase with charm quarks as degree of freedom. In the limit of large $p_T$ and weak interaction with the QGP, a formula of $\Delta v_1(p_T,y_z)$ of charged particles and anti-particles as a function of $p_T$ and rapidity $y_z$ can be obtained, which is found to be related to the spectra of charged particles and the integrated effect of the Lorentz force. This formula is expected to be valid to heavy quarks and leptons at high $p_T$, where the modification to their equations of motion due to the interaction with both QGP and electromagnetic fields is small, and should have a general application. We also proposed a measurement of $\Delta v_1(p_T,y_z)$ of leptons from $Z^0$ decay and its correlation to that of $D$ mesons, which would be a strong probe determining whether the large splitting measured in experiments has the electromagnetic origin., Comment: 5 pages, 1 figure, Proceedings to Hard Probes 2020

Ultrarelativistic heavy ion collisions are expected to generate a huge electromagnetic field, $eB \approx 10^{18}\, Gauss$, that induces a splitting of the directed flow, $v_1=\left\langle p_x/p_T \right\rangle $, of charged particles and anti-particles. Such a splitting for charmed meson manifests even for neutral particle/anti-particles pairs ($D^0, \overline{D}^0$), hence being also a unique probe of the formation of the quark-gluon plasma phase. For the first time here we show that electromagnetic field may generate a $v_1(D^0) - v_1( \overline{D}^0)$ as huge as the one recently observed at LHC against early expectations. Within this new research topic we point out a novel measurement: $v_1$ of leptons from $Z^0$ decay and its correlation to that of $D$ and $B$ mesons. The correlation for $\Delta v_1$ of $l^{+} - l^{-}$, $D^0-\overline{D}^0$ and $B^0-\overline{B}^0$ would provide a strong probe of the electromagnetic origin of the splitting and hence of the formation of a quark-gluon plasma phase with heavy quarks as degrees of freedom. The case of the $v_1({l^{\pm}})$ presents features due to the peculiar form of the $p_T$ spectrum never appreciated before in the study of heavy ion collisions. We specifically predict a sudden change of the $\Delta v_1(p_T)$ of leptons at $p_T=45$ GeV$/c$, that can be traced back to a universal relation of $\Delta v_1$ with the slope of the $p_T$ particle distribution and the integrated effect of the Lorentz force., Comment: 6 pages, 4 figures

Based on a generalized side-jump formalism for massless chiral fermions, which naturally takes into account the spin-orbit coupling in the scattering of two chiral fermions and the chiral vortical effect in a rotating chiral fermion matter, we have developed a covariant and total angular momentum conserved chiral transport model to study both the global and local polarizations of this matter. For a system of massless quarks of random spin orientations and finite vorticity in a box, we have demonstrated that the model can exactly conserve the total angular momentum of the system and dynamically generate the quark spin polarization expected from a thermally equilibrated quark matter. Using this model to study the spin polarization in relativistic heavy-ion collision, we have found that the local quark spin polarizations depend strongly on the reference frame where they are evaluated as a result of the nontrivial axial charge distribution caused by the chiral vortical effect. We have further shown that because of the anomalous orbital or side-jump contribution to the quark spin polarization, the local quark polarizations calculated in the medium rest frame are qualitatively consistent with the local polarizations of Lambda hyperons measured in experiments., Comment: 4 pages, 2 figures, Proceedings for Quark Matter 2019

The heavy quarks (HQs) are unique probe of the hot QCD matter properties and their dynamics is coupled to the locally thermalized expanding quark gluon plasma. We present here a novel study of the event by event correlations between light and heavy flavour flow harmonics at LHC energy within a transport approach. Interaction between heavy quarks and light quarks have been taken into account exploring the impact of different temperature dependence of the transport coefficients $D_s$ and $\Gamma$. Our study indicates that $v^{heavy}_n-v^{light}_n$ correlation and the relative fluctuations of anisotropic flows, $\sigma_{v_{n}}/\langle v_n \rangle$, are novel observables to understand the heavy quark-bulk interaction and are sensitive to the temperature dependence even to moderate differences of $D_s(T)$, or $\Gamma(T)$. Hence a comparison of such new observables for HQ to upcoming experimental data at both RHIC and LHC can put further constraints on heavy quark transport coefficients and in particular on its temperature dependence toward a solid comparison between the phenomenological determination and the lattice QCD calculations., Comment: 7 pages, 6 figures

Using a covariant and angular-momentum-conserved chiral transport model, which takes into account the spin-orbit interactions of chiral fermions in their scatterings via the side jumps, we study the quark spin polarization in quark matter. For a system of rotating and unpolarized massless quarks in an expanding box, we find that side jumps can dynamically polarize the quark spin and result in a final quark spin polarization consistent with that of thermally equilibrated massless quarks in a self-consistent vorticity field. For the quark matter produced in noncentral relativistic heavy ion collisions, we find that in the medium rest frame both the quark local spin polarizations in the direction perpendicular to the reaction plane and along the longitudinal beam direction show an azimuthal angle dependence in the transverse plane similar to those observed in experiments for the Lambda hyperon., Comment: 6 pages, 3 figures

We have developed a relativistic transport approach at fixed $\eta/s(T)$ that incorporates initial space fluctuations generated by wounded quark model to study the hadron observables in 5.02 TeV p+Pb collisions. We find that our approach is able to correctly predict quite well several existing experimental measurements assuming a matter with $\eta/s=1/4\pi$, a result similar to previous studies within a viscous hydrodynamics approach. Besides, we further discuss the sensitivity of the results on both $\eta/s(T)$ and the smearing width. Our transport approach has the possibility to include in initial conditions the power law tail associated to minijet, and this improvement extends the agreement with the experimental data to higher $p_T$ ranges. We also perform a comparison to Pb+Pb collisions pointing out that even if the collective flows have a similar magnitude the features of the matter created are different. By studying the correlation between collective flows and initial geometry, we find that the correlation decreases faster in small systems with the increase of $n$ and centrality. In particular we show that the variance of $\sigma_{v_n}/\langle v_n\rangle$ has a quite different evolution with centrality for p+Pb, so their measurement could provide some further hint about the correctness of current modelling., Comment: 10 pages, 15 figures

In the pre-thermal equilibrium stage of relativistic heavy-ion collisions, a strong quasi-classical transverse gluon field emerges at about $\tau_0 \simeq 0.1 \, \rm fm/c$ and evolves together with their longitudinal counterparts according to the classical Yang-Mills (CYM) equations. Recently it has been shown that these fields induce a diffusion of charm quarks in momentum space resulting in a tilt of their spectrum without a significant drag. We find that in nucleus-nucleus collisions at LHC such a novel dynamics of charm quarks leads to an initial enhancement of the nuclear modification factor ($R_{AA}$) at $p_T$ larger than 2 GeV$/c$ contrary to the standard lore. Moreover, the same dynamics leads to a larger final elliptic flow ($v_2$) inducing a relation between $R_{AA}$ and $v_2$ that is quite close to the experimental measurements. Our study also shows that such an initial pre-thermal stage is unlikely to be described in terms of a standard drag and diffusion dynamics, because even if one tune such coefficients to reproduce the same $R_{AA}(p_T)$ this would imply a significantly smaller $v_2$., Comment: 7 pages, 4 figures