Search

We present preliminary results about photons production in relativistic heavy ion collisions. The main novelty of our study is the calculation of the contribution of the pre-equilibrium stage to the photon spectrum. The initial stage is modeled by an ensemble of classical gluon fields which decay to a quark-gluon plasma via the Schwinger mechanism, and the evolution of the system is studied by coupling classical field equations to relativistic kinetic theory; photons production is then computed by adding collision processes into the collision integral. We find that the contribution of early stage photons to the direct photon spectrum is substantial in the transverse momentum region p T ≳ 1.5 GeV .

Ultra-relativistic Heavy-Ion Collision (HIC) generates very strong initial magnetic field ($\vec B$) inducing a vorticity in the reaction plane. The high $\vec{B}$ influences the evolution dynamics that is opposed by the large Faraday current due to electric field generated by the time varying $\vec{B}$. We show that the resultant effects entail a significantly large directed flow ($v_1$) of charm quarks (CQs) compared to light quarks due to a combination of several favorable conditions for CQs, mainly: (i) unlike light quarks formation time scale of CQs, $\tau_f \simeq \, 0.1 \rm fm/c$ is comparable to the time scale when $\vec B$ attains its maximum value and (ii) the kinetic relaxation time of CQs is similar to the QGP lifetime, this helps the CQ to retain the initial kick picked up from the electromagnetic field in the transverse direction. The effect is also odd under charge exchange allowing to distinguish it from the vorticity of the bulk matter due to the initial angular momentum conservation; conjointly thanks to its mass, $M_c >>\Lambda_{QCD}$, there should be no mixing with the chiral magnetic dynamics. Hence CQs provide very crucial and independent information on the strength of the magnetic field produced in HIC., Comment: 7 pages, 5 figures, Accepted for publication in Physics Letters B

Several transport models have been employed in recent years to analyze heavy-flavor meson spectra in high-energy heavy-ion collisions. Heavy-quark transport coefficients extracted from these models with their default parameters vary, however, by up to a factor of 5 at high momenta. To investigate the origin of this large theoretical uncertainty, a systematic comparison of heavy-quark transport coefficients is carried out between various transport models. Within a common scheme devised for the nuclear modification factor of charm quarks in a brick medium of a quark-gluon plasma, the systematic uncertainty of the extracted drag coefficient among these models is shown to be reduced to a factor of 2, which can be viewed as the smallest intrinsic systematical error band achievable at present time. This indicates the importance of a realistic hydrodynamic evolution constrained by bulk hadron spectra and of heavy-quark hadronization for understanding the final heavy-flavor hadron spectra and extracting heavy-quark drag coefficient. The transverse transport coefficient is less constrained due to the influence of the underlying mechanism for heavy-quark medium interaction. Additional constraints on transport models such as energy loss fluctuation and transverse-momentum broadening can further reduce theoretical uncertainties in the extracted transport coefficients., Comment: 20 pages in ReVTex with 11 figures, final version to appear in PRC

We study the effect of a temperature dependent shear viscosity to entropy density ratio η / s ( T ) on the build-up of the anisotropic flows v n ( p T ) within a relativistic kinetic transport approach that incorporates initial state fluctuations. We find that only in ultra-central collisions (0 – 0.2%) the v n ( p T ) have a stronger sensitivity to the T dependence of η / s in the QGP phase and this sensitivity increases with the order of the harmonic n. We study the linear correlation coefficient C ( ϵ n , v n ) for different impact parameters and for two different beam energies: Au+Au at s = 200 GeV at RHIC and Pb + Pb at s = 2.76 TeV at LHC. The study of the correlations shows that at LHC energies there is more correlation than at RHIC energies. At LHC energies and for ultra-central collisions the linear correlation coefficient C ( ϵ n , v n ) ≈ 1 for n = 2, 3, 4 and 5.

We study the propagation of charm quarks in the quark-gluon plasma (QGP) by means of a relativistic Boltzmann transport (RBT) approach. We have take into account for non-perturbative interaction between heavy quarks and light quarks by mean a quasi-particle approach. Such a model is able to catch the main features of non-perturbative interaction as the increasing of the interaction in the region of low temperature near $T_C$. The hadronization of charm quarks in $D$ mesons is described by mean of an hybrid model of fragmentation plus coalescence. We show that the resulting charm in-medium evolution is able to correctly predict simultaneously the experimental data for the nuclear suppression factor $R_{AA}$ and the elliptic flow $v_2(p_T)$at both RHIC and LHC energies at different centralities.

We have studied by means of kinetic theory based on a relativistic Boltzmann-like transport simulation the impact of the out-of-equilibrium initial distribution proper of a Color Glass Condensate into the build-up the elliptic flow. Our main result is that the available data on v 2 are in agreement with a η / s ≈ 1 / 4 π also for Color Glass Condensate initial conditions. We have found that the impact of the nonequilibrium implied by the saturation scale can modify the estimate of the viscosity respect to the assumption of full thermalization in p T -space. In particular we have observed that the estimate of η / s is modified from η / s ≈ 2 / 4 π to η / s ≈ 1 / 4 π at RHIC and from η / s ≈ 3 / 4 π to η / s ≈ 2 / 4 π at LHC

We present results about photons production in relativistic heavy ion collisions. The main novelty of our study is the calculation of the contribution of the early stage photons to the photon spectrum. The initial stage is modeled by an ensemble of classical gluon fields which decay to a quark-gluon plasma via the Schwinger mechanism, and the evolution of the system is studied by coupling classical field equations to relativistic kinetic theory; photons production is then computed by including the pertinent collision processes into the collision integral. We find that the contribution of the early stage photons to the direct photon spectrum is substantial for $p_T \approx 2$ GeV and higher, the exact value depending on the collision energy; therefore we identify this part of the photon spectrum as the sign of the early stage. Moreover, the amount of photons produced during the early stage is not negligible with respect to those produced by a thermalized quark-gluon plasma: we support the idea that there is no dark age in relativistic heavy ion collisions., 11 pages, 9 figures. Matches published version

Simultaneous description of heavy quark nuclear modification factor RAA and the elliptic flow v2 is a top challenge for all the existing models. We highlight how the temperature dependence of the energy loss/transport coefficients is responsible for addressing a large part of such a puzzle along with the full solution of the Boltzmann collision integral for the momentum evolution of heavy quarks in the medium. At the same time Ultra-relativistic Heavy-Ion Collision (HIC) also generates very strong initial magnetic field ( B → ). The high B → influences the evolution dynamics that is opposed by the large Faraday current due to electric field generated by the time varying B → . Since the heavy quark are produced at the early stage of HICs, we argue that their dynamics will be affected by such a strong magnetic field and we demonstrate that the directed flow, v1, of heavy quarks is a superior probe to estimate the magnetic field generated in non-central HICs

We discuss the propagation of heavy quarks (charm and bottom) through the QGP by means of a relativistic Boltzmann transport approach including both collisional and radiative energy loss mechanisms. In particular we investigate the impact of induced gluon radiation by dynamical QCD medium implementing in our transport model a formula for the emitted gluon spectrum calculated in a higher-twist scheme. We notice that in the region of high transverse momentum ($p_T > 10$ GeV) radiative processes play an essential role giving a dominant contribution to the generation of $R_{AA}$ and $v_2$ at momentum values for which the energy loss by collisions is in the perturbative regime., 4 pages, 4 figures, proceeding of Hot Quarks 2016: Workshop for Young Scientists on the Physics of Ultrarelativistic Nucleus-Nucleus Collisions. (HQ2016) 12-17 Sep 2016. South Padre Island, Texas

We investigated isotropization and thermalization of the quark-gluon plasma produced by de-caying color-electric flux tubes created at the very early stages of ultra-relativistic heavy ion collisions. The dynamical evolution of the initial classical field, which decays to a plasma by the Schwinger mechanism, is coupled to the dynamics of the many particles system produced. The evolution of such a system is described by relativistic transport theory at fixed values of the viscosity over entropy density ratio. With a single self-consistent computation we obtained quantities which serve as indicators of the equilibration of the plasma for a 1+1 dimensional expanding geometry and for the more realistic 3+1 dimensional case. We find that the initial color-electric field decays within 1 fm/c and particles production occurs in less than 1 fm/c; however, in the case of large viscosity oscillations of the field appear along the whole time evolution of the system, affecting also the behaviour of the ratio between longitudinal and transverse pressure. In case of small viscosity we find that the isotropization time is about 0.8 fm/c and the thermalization time is about 1 fm/c, in agreement with the common lore of hydrodynamics.

One of the primary aims of the ongoing nuclear collisions at Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC) energies is to create a Quark Gluon Plasma (QGP). The Heavy Quarks (HQ) constitutes a unique probe of the QGP properties. Both at RHIC and LHC energies a puzzling relation between the nuclear modification factor RAA(pT) and the elliptic flow v2(pT) related to heavy quark has been observed which challenged all the existing models. We discuss how the temperature dependence of the heavy quark drag coefficient can address for a large part of such a puzzle. We have considered four different models to evaluate the temperature dependence of drag and diffusion coefficients propagating through a quark gluon plasma (QGP). All the four different models are set to reproduce the same RAA(pT) experimentally observed at RHIC energy. We have found that for the same RAA(pT) one can generate 2–3 times more v2 depending on the temperature dependence of the heavy quark drag coefficient.

The drag and diffusion coefficients of heavy baryons ($\Lambda_c$ and $\Lambda_b$) in the hadronic phase created in the latter stage of the heavy-ion collisions at RHIC and LHC energies have been evaluated recently. In this work we compute some experimental observables, such as the nuclear suppression factor $R_{AA}$ and the elliptic flow $v_2$ of heavy baryons at RHIC and LHC energies, highlighting the role of the hadronic phase contribution to these observables, which are going to be measured at Run 3 of LHC. For the time evolution of the heavy quarks in the QGP and heavy baryons in the hadronic phase we use the Langevin dynamics. For the hadronization of the heavy quarks to heavy baryons we employ Peterson fragmentation functions. We observe a strong suppression of both the $\Lambda_c$ and $\Lambda_b$. We find that the hadronic medium has a sizable impact on the heavy-baryon elliptic flow whereas the impact of hadronic medium rescattering is almost unnoticeable on the nuclear suppression factor. We evaluate the $\Lambda_c/D$ ratio at RHIC and LHC. We find that $\Lambda_c/D$ ratio remain unaffected due to the hadronic phase rescattering which enable it as a nobel probe of QGP phase dynamics along with its hadronization., Comment: 22 pages, 15 figures

Simultaneous description of heavy quark nuclear suppression factor $R_{AA}$ and the elliptic flow $v_2$ is a top challenge for all the existing models. We highlight how the temperature dependence of the energy loss/transport coefficients is responsible to address a large part of such a puzzle along with the the full solution of the Boltzmann collision integral for the momentum evolution of heavy quark. We consider four different models to evaluate the temperature dependence of drag coefficients of the heavy quark in the QGP. We have also highlighted the heavy quark dynamics in the presence of an external electromagnetic field which develops a sizable heavy quark directed flow, $v_1(y)$, can be measurable at LHC., Comment: 4 pages, To appear in the proceedings of SQM-2016

The two key observables related to heavy quarks that have been measured in RHIC and LHC energies are the nuclear suppression factor $R_{AA}$ and the elliptic flow $v_2$. Simultaneous description of these two observables is a top challenge for all the existing models. We have highlighted how a consistent combination of four ingredients i.e the temperature dependence of the energy loss, full solution of the Boltzmann collision integral for the momentum evolution of heavy quark, hadronization by coalescence, then the hadronic rescattering, responsible to address a large part of such a puzzle. We have considered four different models to evaluate the temperature dependence of drag coefficients of the heavy quark in QGP. All these four different models are set to reproduce the same $R_{AA}$ as of the experiments. We have shown that for the same $R_{AA}$, the $v_2$ could be quite different depending on the interaction dynamics as well as other ingredients., Comment: 4 pages, To appear in the proceedings of SQM-2015

In this study we model early time dynamics of relativistic heavy ion collisions by an initial color-electric field which then decays to a plasma by the Schwinger mechanism. The dynamics of the many particles system produced by the decay is described by relativistic kinetic theory, taking into account the backreaction on the color field by solving self-consistently the kinetic and the field equations. Our main results concern isotropization and thermalization for a 1+1D expanding geometry. In case of small η / s ( η / s ≲ 0.3) we find τ isotropization ≈ 0.8 fm/c and τ thermalization ≈ 1 fm/c in agreement with the common lore of hydrodynamics.

We have employed a relativistic kinetic transport approach that incorporates initial state fluctuations to study the effect of a temperature dependent shear viscosity to entropy density ratio η / s ( T ) on the build-up of the anisotropic flows υ n ( p T ). We find that at LHC energies and for ultra-central collisions (0 – 0.2%) the υ n ( p T ) have a stronger sensitivity to the T dependence of η / s in the QGP phase and this sensitivity increases with the order of the harmonic n. Moreover we have studied the correlation between the initial spatial anisotropies ϵ n and the final flow coefficients 〈 υ n 〉 for different centralities and for the two beam energies. The study shows that at LHC energies there is more correlation than at RHIC energies. In particular at LHC energies and for ultra-central collisions the linear correlation coefficient C ( ϵ n , υ n ) ≈ 1 for n = 2, 3, 4 and 5 suggesting that the 〈 υ n 〉 are strongly related to the initial value of ϵ n .

An hadronization model that includes coalescence and fragmentation is used in this work to obtain predictions at both RHIC and LHC energy for light and strange hadrons transverse momentum spectra (π , p , k , Λ) and baryon to meson ratios (p /π , Λ/k ) in a wide range of pT . This is accomplished without changing coalescence parameters. The ratios p /π and Λ/K shows the right behaviour except for some lack of baryon yield in a limited pT range around 6 GeV. This would indicate that the AKK fragmentation functions is too flat at pT < 8 GeV.

In a coalescence plus fragmentation approach we study the pT spectra of charmed hadrons D0, Ds up to about 10 GeV and the Λ+c /D0 ratio from RHIC to LHC energies. In this study we have included the contribution from decays of heavy hadron resonances and also that due to fragmentation of heavy quarks that are left in the system after coalescence. The pT dependence of the heavy baryon/meson ratios is found to be sensitive to the heavy quark mass. In particular we found that the Λc/D0 is much flatter than the one for light baryon/meson ratio like p/π and Λ/K.

We describe the propagation of Heavy quarks (HQs) in the quark-gluon plasma (QGP) within a relativistic Boltzmann transport (RBT) approach. The interaction between heavy quarks and light quarks is described within quasi-particle approach which is able to catch the main features of non-perturbative interaction as the increasing of the interaction in the region of low temperature near TC. In our calculations the hadronization of charm quarks in D mesons is described by mean of an hybrid model of coalescence plus fragmentation. We show that the coalescence play a key role to get a good description of the experimental data for the nuclear suppression factor RAA and the elliptic flow υ2(pT) at both RHIC and LHC energies. Moreover, we show some recent results on the direct flow υ1 and triangular flow υ3 of D meson.

In a coalescence plus independent fragmentation approach we calculate the ${p}_{T}$ spectra of the main hadrons: $\ensuremath{\pi},K,p,\overline{p},\mathrm{\ensuremath{\Lambda}},\ensuremath{\phi}$ in a wide range of transverse momentum from low ${p}_{T}$ up to about 10 GeV. The approach in its main features was developed several years ago at Relativistic Heavy Ion Collider (RHIC) energy. Augmenting the model with the inclusion of some more main resonance decays, we show that the approach correctly predicts the evolution of the ${p}_{T}$ spectra from RHIC to LHC (Large Hadron Collider) energy and in particular the baryon-to-meson ratios $p/\ensuremath{\pi},\overline{p}/\ensuremath{\pi},\mathrm{\ensuremath{\Lambda}}/K$ that reach a value of the order of unit at ${p}_{T}\ensuremath{\sim}3\phantom{\rule{0.16em}{0ex}}\mathrm{GeV}$. This is achieved without any change of the coalescence parameters. The more recent availability of experimental data up to ${p}_{T}\ensuremath{\sim}10\phantom{\rule{0.16em}{0ex}}\mathrm{GeV}$ for $\mathrm{\ensuremath{\Lambda}}$ spectrum as well as for $p/\ensuremath{\pi}$ and $\mathrm{\ensuremath{\Lambda}}/K$ shows some lack of yield in a limited ${p}_{T}$ range around 6 GeV. This indicates that the baryons ${p}_{T}$ spectra from Albino-Kniehl-Kramer fragmentation functions are too flat at ${p}_{T}\ensuremath{\lesssim}8\phantom{\rule{0.16em}{0ex}}\mathrm{GeV}$. We also show that in a coalescence plus fragmentation approach one predicts a nearly ${p}_{T}$ independent $p/\ensuremath{\phi}$ ratio up to ${p}_{T}\ensuremath{\sim}4\phantom{\rule{0.16em}{0ex}}\mathrm{GeV}$ followed by a significant decrease at higher ${p}_{T}$. Such a behavior is driven by a similar radial flow effect at ${p}_{T}l2\phantom{\rule{0.16em}{0ex}}\mathrm{GeV}$ and the dominance of fragmentation for $\ensuremath{\phi}$ at larger ${p}_{T}$.

We have developed a relativistic kinetic transport approach that incorporates initial state fluctuations allowing to study the build up of elliptic flow $v_2$ and high order harmonics $v_3$, $v_4$ and $v_5$ for a fluid at fixed $\eta/s(T)$. We study the effect of the $\eta/s$ ratio and its T dependence on the build up of the $v_n(p_T)$ for two different beam energies: RHIC for Au+Au at $\sqrt{s}=200 \,GeV$ and LHC for $Pb+Pb$ at $\sqrt{s}=2.76 \,TeV$. We find that for the two different beam energies considered the suppression of the $v_n(p_T)$ due to the viscosity of the medium have different contributions coming from the cross over or QGP phase. Our study reveals that only in ultra-central collisions ($0 - 0.2 \%$) the $v_n(p_T)$ have a stronger sensitivity to the T dependence of $\eta/s$ in the QGP phase and this sensitivity increases with the order of the harmonic n. Moreover, the study of the correlations between the initial spatial anisotropies $\epsilon_n$ and the final flow coefficients $v_n$ shows that at LHC energies there is more correlation than at RHIC energies. The degree of correlation increases from peripheral to central collisions, but only in ultra-central collisions at LHC, we find that the linear correlation coefficient $C(n,n) \approx 1$ for $n=2,3,4$ and $5$. This suggests that the final correlations in the ($v_n$,$v_m$) space reflect the initial correlations in the ($\epsilon_n$,$\epsilon_m$) space., Comment: Minor changes. Published on Phys. Rev. C

In this study we model early times dynamics of the system produced in relativistic heavy ion collisions by an initial color electric field which then decays to a plasma by the Schwinger mechanism, coupling the dynamical evolution of the initial color field to the dynamics of the many particles system produced by the decay. The latter is described by relativistic kinetic theory in which we fix the ratio $\eta/s$ rather than insisting on specific microscopic processes. We study isotropization and thermalization of the system produced by the field decay for a static box and for a $1+1$D expanding geometry. We find that regardless of the viscosity of the produced plasma, the initial color electric field decays within $1$ fm/c; however in the case $\eta/s$ is large, oscillations of the field are effective along all the entire time evolution of the system, which affect the late times evolution of the ratio between longitudinal and transverse pressure. In case of small $\eta/s$ ($\eta/s\lesssim0.3$) we find $\tau_{isotropization}\approx 0.8$ fm/c and $\tau_{thermalization}\approx 1$ fm/c in agreement with the common lore of hydrodynamics. Moreover we have investigated the effect of turning from the relaxation time approximation to the Chapman-Enskog one: we find that this improvement affects mainly the early times evolution of the physical quantities, the effect being milder in the late times evolution., Comment: 12 pages, 9 figures

In this article we report on our results about quark production and chemical equilibration of quark-gluon plasma. Our initial condition corresponds to a classic Yang-Mills spectrum, in which only gluon degrees of freedom are considered; the initial condition is then evolved to a quark-gluon plasma by means of relativistic transport theory with inelastic processes which permit the conversion of gluons to $q\bar{q}$ pairs. We then compare our results to the ones obtained with a standard Glauber model initialization. We find that regardless of the initial condition the final stage of the system contains an abundant percentage of $q\bar{q}$ pairs; moreover spanning the possible coupling from weak to strong we find that unless the coupling is unrealistically small, both production rate and final percentage of fermions is quite large., Comment: Minor changes. Published on Nuclear Physics A

We discuss the application of a phase-space coalescence plus fragmentation model for the hadronization of the quark-gluon plasma (QGP) created in ultra-relativistic heavy-ion collisions. Recombination of minijet partons with the partons from the QGP is also included and plays a role at pT ~ 2 – 4 GeV where the baryon to meson anomaly is observed experimentally. We show our prediction for light and strange hadrons transverse momentum spectra (π, p, k, Λ) and baryon to meson ratios (p/π, Λ/k) in a wide range of pT, both for RHIC and LHC energies. The baryon to meson ratio at LHC presents similar features of that at RHIC, but with a shift in the peak of about 0.5 GeV, and this is well predicted by our model.

The two key observables related to heavy quarks that have been measured in experiments are the nuclear suppression factor RAA and the elliptic flow v2. Reproducing these two observables simultaneously is a puzzle which have challenged all the existing models. We have studied two ingredients responsible to address a large part of such a puzzle: the temperature dependence of the energy loss and the full solution of the Boltzmann collision integral for the scattering between the heavy quarks and the particle of the bulk. We have considered four different models to evaluate the temperature dependence of drag and diffusion coefficients of the heavy quark. All these four different models are set to reproduce the same RAA(pT) measured in experiments at RHIC and LHC energy. We have found that for the same RAA(pT) one can generate 2-3 times more v2 depending on the temperature dependence of the heavy quarks drag coefficient. Moreover comparing the Fokker-Planck and the Boltzmann approach we have found that the latter seems more efficient into reproducing the elliptic flow for the same RAA. Even a larger difference between the two approaches emerges from the comparison of a more differential observable, the angular correlation.

The heavy quarks constitutes a unique probe of the quark-gluon plasma properties. Both at RHIC and LHC energies a puzzling relation between the nuclear modification factor $R_{AA}(p_T)$ and the elliptic flow $v_2(p_T)$ has been observed which challenged all the existing models, especially for D mesons. We discuss how the temperature dependence of the heavy quark drag coefficient is responsible for a large part of such a puzzle. In particular, we have considered four different models to evaluate the temperature dependence of drag and diffusion coefficients propagating through a quark gluon plasma (QGP). All the four different models are set to reproduce the same $R_{AA}(p_T)$ observed in experiments at RHIC and LHC energy. We point out that for the same $R_{AA}(p_T)$ one can generate 2-3 times more $v_2$ depending on the temperature dependence of the heavy quark drag coefficient. A non-decreasing drag coefficient as $ T \rightarrow\ T_c \,$ is a major ingredient for a simultaneous description of $R_{AA}(p_T)$ and $v_2(p_T)$., 7 pages, 6 figures, Accepted for publication in Physics Letters B

Heavy quark $R_{AA}$ and $v_2$ have been calculated at RHIC energy considering initial conditions with and without pre-equilibrium phase to highlight the effect of the latter on heavy quark observables. The momentum evolution of the heavy quark has been studied by means of the Boltzmann transport equation. To model the pre-equilibrium phase we have used the KLN initial condition. We have found that the pre-equilibrium phase impacts the $R_{AA}$ of about 20-25 $\%$ whereas the impact on $v_2$ is very negligible. We have also calculated heavy quark $R_{AA}$ and $v_2$ in the case of initializations with early thermalized quark-gluon plasma. We have checked that the particular form of the initial spectrum is not very important for $R_{AA}$, the larger energy density being more important. In fact, comparing the results obtained within the two initializations we have found that one can mimic the impact of the pre-equilibrium phase using a early thermalized QGP medium., Comment: 10 pages, 2 figures, Accepted for publication in Journal of Physics G

The propagation of heavy quarks in the quark-gluon plasma was often treated within the framework of the Langevin equation (LV), i.e., assuming the momentum transfer is small or the scatterings are sufficiently forward peaked, small screening mass ${m}_{D}$. We address a direct comparison between the Langevin dynamics and the Boltzmann collisional integral (BM) when a bulk medium is in equilibrium at fixed temperature. We show that unless the cross section is quite forward peaked $({m}_{D}\ensuremath{\cong}T)$ or the mass to temperature ratio is quite large $({M}_{\mathrm{HQ}}/T\ensuremath{\gtrsim} 8--10)$ there are significant differences in the evolution of the $p$ spectra and consequently on the nuclear modification factor ${R}_{AA}({p}_{T})$. However, for charm quark we find that very similar ${R}_{AA}({p}_{T})$ between the LV and BM can be obtained, but with a modified diffusion coefficient of about $\ensuremath{\sim}15%--50%$ depending on the angular dependence of the cross section which regulates the momentum transfer. Studying also the momentum spread suffered by the single heavy quarks we see that at temperatures $T\ensuremath{\gtrsim}\phantom{\rule{0.16em}{0ex}}250\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}$ the dynamics of the scatterings is far from being of Brownian type for charm quarks. In the case of bottom quarks we essentially find no differences in the time evolution of the momentum spectra between the LV and the BM dynamics independently of the angular dependence of the cross section, at least in the range of temperature relevant for ultrarelativistic heavy-ion collisions (HICs). Finally, we have shown the possible impact of this study on ${R}_{AA}({p}_{T})$ and ${v}_{2}({p}_{T})$ for a realistic simulation of relativistic HICs. For larger ${m}_{D}$ the elliptic flow can be about $50%$ larger for the Boltzmann dynamics with respect to the Langevin. This is helpful for a simultaneous reproduction of ${R}_{AA}({p}_{T})$ and ${v}_{2}({p}_{T})$.

A current goal of relativistic heavy ion collisions experiments is to understand the impact of initial non-equilibrium on final observables. A Color Glass Condensate (CGC) as the limiting state of QCD matter at very high density implies initial non-thermal distribution at least for momenta below the saturation scale. In viscous hydrodynamics simulations, a standard Glauber initial condition leads to estimate 4πη/s ~ 1, while employing the Kharzeev-Levin-Nardi (KLN) modeling of the CGC leads to at least a factor of 2 larger η/s. Within a kinetic theory approach based on a relativistic Boltzmann-like transport simulation, our main result is that the out-of-equilibrium initial distribution in p-space reduces the effciency in building-up the elliptic flow. At RHIC energy we find the available data on υ2 are in agreement with a 4πη/s ~ 1 also for KLN initial conditions.

The propagation of heavy flavor through the quark gluon plasma has been treated commonly within the framework of Langevin dynamics, i.e. assuming the heavy flavor momentum transfer is much smaller than the light one. On the other hand a similar suppression factor RAA has been observed experimentally for light and heavy flavors. We present a thorough comparison in terms of nuclear suppression, RAA, elliptic flow, v2, and c back to back correlation between the Langevin equation and the full collisional Boltzmann collision integral within the framework of Boltzmann transport equation. We have shown that the Langevin dynamics overestimates the interaction and even for a fixed RAA the full two-body collision integral shows that the elliptic flow is larger with respect to that predicted by a Langevin dynamics. Furthermore we have found that Boltzmann approach gives rise to a larger spreading of c correlation in comparison with the Langevin approach.

We study the build up of elliptic flow v2 and high order harmonics vn within a transport approach at fixed shear viscosity to entropy density ratio η/s and with initial state fluctuations. In particular we study the effect of a temperature dependent η/s for two different beam energies: RHIC for Au+Au at = 200 GeV and LHC for Pb + Pb at = 2.76 TeV. We find that for the two different beam energies considered the suppression of the elliptic flow and of higher harmonics v3(pT) and v4(pT) due to the viscosity of the medium have different contributions coming from the cross over or QGP phase. Moreover, we discuss the correlation between the initial spatial anisotropies n and flow coefficients vn. We observe that the elliptic flow v2 is strongly correlated with initial eccentricity 2. While higher harmonics v3 and v4 are weakly correlated to their asymmetry measure in coordinate space 3 and 4.

One of the main results of heavy ions collision at relativistic energy experiments is the very small shear viscosity to entropy density ratio of the Quark-Gluon Plasma, close to the conjectured lower bound η/s = 1/4π for systems in the infinite coupling limit. Transport coefficients like shear viscosity are responsible of non-equilibrium properties of a system: Green- Kubo relations give us an exact expression to compute these coefficients. We computed shear viscosity numerically using Green-Kubo relation in the framework of Kinetic Theory solving the relativistic transport Boltzmann equation in a finite box with periodic boundary conditions. We investigated different cases of particles, for one component system (gluon matter), interacting via isotropic or anisotropic cross-section in the range of temperature of interest for HIC. Green-Kubo results are in agreement with Chapman-Enskog approximation while Relaxation Time approximation can underestimates the viscosity of a factor 2. Another transport coefficient of interest is the electric conductivity σel which determines the response of QGP to the electromagnetic fields present in the early stage of the collision. We study the σel dependence on microscopic details of interaction and we find also in this case that Relaxation Time Approximation is a good approximation only for isotropic cross-section.

A current goal of ultra-relativistic heavy ion collisions experiments is to verify a picture in which the two colliding nuclei can be described as two tiny disks of a Color Glass Condensate (CGC) that is the limiting state of QCD matter at very high density and energy. The searching of CGC in uRHIC experiments is strongly related to the evaluation of the η/s. In fact in viscous hydrodynamics simulations a standard Glauber initial condition leads to estimate η/s ~ 1/4π, while the fKLN initialization, which model the melting of Color Glass Condensate, leads to at least a factor of 2 larger η/s. We have found in the framework of kinetic theory that the out-of-equilibrium initial distribution described by the fKLN reduces the efficiency in building-up the elliptic flow. In particular from our work emerges that the available data on v2 are in agreement with a η/s ~ 1/4π also for fKLN initial conditions.

In this talk, we report on our results about the computation of the elliptic flow of the quark-gluon-plasma produced in relativistic heavy ion collisions, simulating the expansion of the fireball by solving the relativistic Boltzmann equation for the parton distribution function tuned at a fixed shear viscosity to entropy density ratio $\eta/s$. We emphasize the role of saturation in the initial gluon spectrum modelling the shattering of the color glass condensate, causing the initial distribution to be out of equilibrium. We find that the saturation reduces the efficiency in building-up the elliptic flow, even if the thermalization process is quite fast $\tau_{therm} \approx 0.8 \,\rm fm/c$. and the pressure isotropization even faster $\tau_{isotr} \approx 0.3 \,\rm fm/c$. The impact of the initial non-equilibrium manifests for non-central collisions and can modify the estimate of the viscosity respect to the assumption of full thermalization in $p_T$-space., Comment: 8 pages, 3 figures. Talk given at XIV Convegno su Problemi di Fisica Nucleare Teorica, 29-31 October 2013, Cortona, Italy

We study the evolution of a gluon system under conditions of density and temperature similar to those explored in the early stage of ultra-relativistic heavy-ion collisions. We first describe the implementation of Relativistic Boltzmann-Nordheim (RBN) transport approach that includes in the collision integral the quantum effects of Bose-Einstein Statistics. Then, we describe the evolution of a spatially uniform gluon system in a box under elastic collisions solving the RBN for various initial conditions. We discuss the critical phase-space density that leads to the onset of a Bose-Einstein condensate (BEC) and the time scale for this process to occur. In particular, thanks to the fact that RBN allows to relax the small angle approximation, we study the effect at both small and large screening mass $ m_{D} $. For small $ m_{D}\ll T $ we see that our solution of RBN is in agreement with the recent extensive studies within a Fokker-Planck scheme in small angle approximation. For the same total cross section but with large $ m_{D}\simeq 2\, T $ (large angle scatterings), we see a significant time speed-up of the onset of BEC respect to small $m_{D}\ll T$. This further strengthen the possibility that at least a transient BEC is formed in the early stage of ultra-relativistic heavy-ion collisions., Comment: 12 pages, 15 figures

In this article we report on our results about the computation of the elliptic flow of the quark-gluon-plasma produced in relativistic heavy ion collisions, simulating the expansion of the fireball by solving the relativistic Boltzmann equation for the parton distribution function tuned at a fixed shear viscosity to entropy density ratio $\eta/s$. Our main goal is to put emphasis on the role of a saturation scale in the initial gluon spectrum, which makes the initial distribution far from a thermalized one. We find that the presence of the saturation scale reduces the efficiency in building-up the elliptic flow, even if the thermalization process is quite fast $\tau_{therm} \approx 0.8 \,\rm fm/c$ and the pressure isotropization even faster $\tau_{isotr} \approx 0.3 \,\rm fm/c$. The impact of the non-equilibrium implied by the saturation scale manifests for non-central collisions and can modify the estimate of the viscosity respect to the assumption of full thermalization in $p_T$-space. We find that the estimate of $\eta/s$ is modified from $\eta/s \approx 2/4\pi$ to $\eta/s \approx 1/4\pi$ at RHIC and from $\eta/s \approx 3/4\pi$ to $\eta/s \approx 2/4\pi$ at LHC. We complete our investigation by a study of the thermalization and isotropization times of the fireball for different initial conditions and values of $\eta/s$ showing how the latter affects both isotropization and thermalization. Lastly, we have seen that the range of values explored by the phase-space distribution function $f$ is such that at $p_T, Comment: Published version

A current goal of relativistic heavy ion collisions experiments is the search for a Color Glass Condensate as the limiting state of QCD matter at very high density. In viscous hydrodynamics simulations, a standard Glauber initial condition leads to estimate $4\pi \eta/s \sim 1$, while a Color Glass Condensate modeling leads to at least a factor of 2 larger $\eta/s$. Within a kinetic theory approach based on a relativistic Boltzmann-like transport simulation, we point out that the out-of-equilibrium initial distribution proper of a Color Glass Condensate reduces the efficiency in building-up the elliptic flow. Our main result at RHIC energy is that the available data on $v_2$ are in agreement with a $4\pi \eta/s \sim 1$ also for Color Glass Condensate initial conditions, opening the possibility to describe self-consistently also higher order flow, otherwise significantly underestimated, and to pursue further the search for signatures of the Color Glass Condensate., Comment: 6 pages, 4 figures. // Title changed, some discussion added, main conclusions unchanged. Version accepted for publication on Phys. Lett. B

The shear viscosity has been calculated by using the Green-Kubo relation in the framework of a partonic transport approach solved at cascade level. We compare the numerical results for obtained from the Green-Kubo correlator with the analytical formulas in both the Relaxation Time Approximation (RTA) and the Chapman-Enskog approximation (CE). We investigate and emphasize the dierences between the isotropic and anisotropic cross sections and between the massless and massive particles. We show that in the range of temperature explored in a Heavy Ion collision and for pQCD-like cross section the RTA signicantly underestimates the viscosity by about a factor of 2-3, while a good agreement is found between the CE approximation and GreeKubo relation already at rst order of approximation. The agreement with the CE approximation supplies an analytical formula that allows to develop kinetic transport theory at xed shear viscosity to entropy density ratio, =s . This open the possibility to explore dissipative non-equilibrium evolution of the distribution functions vs T-dependent =s and particle momenta in the dynamics of the Quark-Gluon Plasma created in ultra-relativistic heavy-ion collisions.

The propagation of heavy flavor through the quark gluon plasma has been treated commonly within the framework of Langevin dynamics, i.e. assuming the heavy flavor momentum transfer is much smaller than the light one. On the other hand a similar suppression factor $R_{AA}$ has been observed experimentally for light and heavy flavors. We present a thorough study of the approximations involved by Langevin equation by mean of a direct comparison with the full collisional integral within the framework of Boltzmann transport equation. We have compared the results obtained in both approaches which can differ substantially for charm quark leading to quite different values extracted for the heavy quark diffusion coefficient. In the case of bottom quark the approximation appears to be quite reasonable., 4 pages, 3 figures, Talk given at SQM-2013 (Birmingham, UK)

We studied isotropization and thermalization of the quark-gluon plasma produced by decaying color-electric flux tubes created at the very early stages of relativistic heavy ion collisions. We coupled the dynamical evolution of the initial field, which decays to a plasma by the Schwinger mechanism, to the dynamics of the many particles system produced by the decay. The evolution of such a system is described by relativistic transport theory at fixed values of the viscosity over entropy density ratio. Within a single self-consistent calculation scheme we computed quantities which serve as indicators of the equilibration of the plasma for a 1+1 dimensional expanding geometry. We find that the initial color-electric field decays within 1 fm/c and particles production occurs in less than 1 fm/c; however, in the case of large viscosity oscillations of the field appear along the entire time evolution of the system, affecting also the behaviour of the ratio between longitudinal and transverse pressure. In case of small viscosity we find that the isotropization time is about 0.8 fm/c and the thermalization time is about 1 fm/c, in agreement with the common lore of hydrodynamic approaches.

We have investigated, in the frame work of the transport approach, different aspects of the QGP created in Heavy Ion Collisions at RHIC and LHC energies. The shear viscosity $\eta$ has been calculated by using the Green-Kubo relation at the cascade level. We have compared the numerical results for $\eta$ obtained from the Green-Kubo correlator with the analytical formula in both the Relaxation Time Approximation (RTA) and the Chapman-Enskog approximation (CE). From this comparison we show that in the range of temperature explored in a Heavy Ion collision the RTA underestimates the viscosity by about a factor of 2, while a good agreement is found between the CE approximation and Gree-Kubo relation already at first order of approximation. The agreement with the CE approximation supplies an analytical formula that allows to develop kinetic transport theory at fixed shear viscosity to entropy density ratio, $\eta/s$. We show some results for the build up of anisotropic flows $v_{2}$ in a transport approach at fixed shear viscosity to entropy density ratio, $\eta/s$. We study the impact of a T-dependent $\eta/s(T)$ on the generation of the elliptic flows at both RHIC and LHC. We show that the transport approach provides, in a unified way, a tool able to naturally describe the $v_{2}(p_{T})$ in a wide range of $p_{T}$, including also the description of the rise and fall and saturation of the $v_{2}(p_{T})$ observed at LHC. Finally, we have studied the evolution of the quark-gluon composition employing a Boltzmann-Vlasov transport approach that include: the mean fields dynamics, associated to the quasi-particle model, and the elastic and inelastic collisions for massive quarks and gluons. Following the chemical evolution from an initial gluon dominated plasma we predict a quark dominance close to $T_{C}$ paving the way to an hadronization via quark coalescence., Comment: 15 pages, 10 figures, Invited Talk given by S. Plumari at the 11th International Conference on Nucleus-Nucleus Collisions (NN2012), San Antonio, Texas, USA, May 27-June 1, 2012. To appear in the NN2012 Proceedings in Journal of Physics: Conference Series (JPCS)

We use a relativistic transport approach to study the role of a temperature dependent shear viscosity to entropy density ratio, η/s(T), on the build-up of the elliptic flow, v2. The recent results from = 62.4GeV at RHIC up to 2.76 TeV at LHC have shown an intriguing property of the v2(pT), which appears to be nearly invariant with energy. We show that in our transport approach this surprising behavior can be described by a particular temperature dependence of η/s(T), typical of matter that undergoes a phase transition or a cross-over, with a rise and fall and the minimum close to critical temperature Tc.

In this talk, we report on our results about the computation of isotropization and thermalization times of the quark-gluon plasma produced in relativistic heavy ion collisions, as well as of the elliptic flow. Simulation of the evolving fireball is achieved by solving the relativistic Boltzmann equation for the parton distribution function tuned at a fixed shear viscosity to entropy density ratio η /s . Our results show that the saturation in the initial spectrum reduces the efficiency in building-up the elliptic flow. Moreover both thermalization and isotropization times are quite small, approximately of 1 fm/c, if the system is in a strong coupling regime.

In this article we discuss the issue of the quark to gluon ratio in the Quark Gluon Plasma (QGP). Our model to describe the QGP evolution is based on transport theory including the mean field dynamics described by a quasi-particle model.The last is able to take into account for the lattice QCD thermodynamics and implies a "chemical" equilibrium ratio between quarks and gluons strongly increasing as T approaches to the temperature of the phase transition Tc. We present first the tests performed in a fixed box to check that our code is able to reproduce the equilibrium ratio and then the results obtained for the simulations of ultra-Relativistic Heavy Ion Collisions (uRHIC's) at RHIC and LHC energies. We observe a rapid evolution from a gluon dominated initial state to a quark dominated plasma and we see that near Tc almost 80% of the particles composing the plasma are quarks. This has potentially a strong impact on several quantitative aspects of QGP probes and furnishes a justification to the coalescence hadronization model.