Hadrons from Coalescence plus Fragmentation in AA collisions from RHIC to LHC energy

In a coalescence plus independent fragmentation approach we calculate the $p_T$ spectra of the main hadrons: $\pi, K, p, \bar p, \Lambda, \phi$ 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 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 energy and in particular the baryon-to-meson ratios $p/\pi,\bar p/\pi,\Lambda/K$ that reach a value of the order of unit at $p_T \sim 3\, \rm GeV$. This is achieved without any change of the coalescence parameters. The more recent availability of experimental data up to $p_T \sim 10\rm\, GeV$ for $\Lambda$ spectrum as well as for $p/\pi$ and $\Lambda/K$ shows some lack of yield in a limited $p_T$ range around 6 GeV. This indicates that the baryons $p_T$ spectra from AKK fragmentation functions are too flat at $p_T\lesssim 8 \,\rm GeV$. We also show that in a coalescence plus fragmentation approach one predicts a nearly $p_T$ independent $p/\phi$ ratio up to $p_T \sim 4 \rm\, GeV$ followed by a significant decrease at higher $p_T$. Such a behavior is driven by a similar radial flow effect at $p_T< 2 \,\rm GeV$ and the dominance of fragmentation for $\phi$ at larger $p_T$.Comment: 11 pages, 12 figures Added the figure and discussion about the proton/phi ratio, as in the accepted version for pubblicatio

Sensitivity of the Jet Quenching Observables to the Temperature Dependence of the Energy Loss

The quenching of minijet (particles with $p_T>> T, \Lambda_{QCD}$) in ultra-relativistic heavy-ion collisions has been one of the main prediction and discovery at RHIC. We analyze the correlation between different observables like the nuclear modification factor \Rapt, the elliptic flow and the ratio of quark to gluon suppressions. We show that the temperature (or entropy density) dependence of the in-medium energy loss strongly affects the relation among these observables. In particular the large elliptic flow and the nearly equal \Rapt of quarks and gluons can be accounted for only if the energy loss occurs mainly around $T_c$ and the $q\leftrightarrow g$ conversion is significant. The use of an equation of state fitted to lattice QCD calculations, slowing down the cooling as $T \to T_c$, seems to contribute to both the enhancement of $v_2$ and the efficiency of the conversion mechanism.Comment: 12 pages, 10 figure

Thermalization, Isotropization and Elliptic Flow from Nonequilibrium Initial Conditions with a Saturation Scale

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 $p_T<0.5\, \rm GeV$ the inner part of the fireball stays with occupation number significantly larger than unity despite the fast longitudinal expansion, which might suggest the possibility of the formation of a transient Bose-Einstein Condensate.Comment: Published versio

Elliptic Flow and Shear Viscosity of the Shattered Color Glass Condensate

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, Ital

Heavy Flavor in Medium Momentum Evolution: Langevin vs Boltzmann

The propagation of heavy quarks in the quark-gluon plasma (QGP) has been 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 ($m_D\cong T$) or the mass to temperature ratio is quite large ($M_{HQ}/T \gtrsim 8-10$) there are significant differences in the evolution of the $p-$spectra and consequently on 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 by about $\sim 15-50\%$ depending on the angular dependence of the cross section which regulates the momentum transfer. Studying also the momentum spread suffered by a single heavy quarks we see that at temperatures $T\gtrsim \, 250\,\rm MeV$ 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 ultra-relativistic heavy-ion collisions. 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 HIC. 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 $v_2(p_T)$.Comment: Accepted for publication in Phys. Rev. C . New figs have been included to describe the experimental result

Toward a simultaneous description of RAAR_{AA} and v2v_2 for heavy quarks

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-201

Heavy Flavor Suppression: Boltzmann vs Langevin

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.Comment: 4 pages, 3 figures, Talk given at SQM-2013 (Birmingham, UK

Initial state fluctuations from mid-peripheral to ultra-central collisions in a event-by-event transport approach

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.

Estimating the Charm Quark Diffusion Coefficient and thermalization time from D meson spectra at RHIC and LHC

We describe the propagation of charm quarks in the quark-gluon plasma (QGP) by means of a Boltzmann transport approach. Non-perturbative interaction between heavy quarks and light quarks have been taken into account through a quasi-particle approach in which light partons are dressed with thermal masses tuned to lQCD thermodynamics. Such a model is able to describe the main feature of the non-perturbative dynamics: the enhancement of the interaction strength near $T_c$. We show that the resulting charm in-medium evolution is able to correctly predict simultaneously the nuclear suppression factor, $R_{AA}$, and the elliptic flow, $v_2$, at both RHIC and LHC energies and at different centralities. The hadronization of charm quarks is described by mean of an hybrid model of fragmentation plus coalescence and plays a key role toward the agreeement with experimental data. We also performed calculations within the Langevin approach which can lead to very similar $R_{AA}(p_T)$ as Boltzmann, but the charm drag coefficient as to be reduced by about a $30\%$ and also generates an elliptic flow $v_2(p_T)$ is about a $15\%$ smaller. We finally compare the space diffusion coefficient $2\pi TD_s$ extracted by our phenomenological approach to lattice QCD results, finding a satisfying agreement within the present systematic uncertainties. Our analysis implies a charm thermalization time, in the $p\rightarrow 0$ limit, of about $4-6 \, fm/c$ which is smaller than the QGP lifetime at LHC energy.Comment: 13 pages, 12 figure

Toward an understanding of the RAAR_{AA} and v2v_2 puzzle for heavy quarks

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 constitutes a unique probe of the QGP properties. Both at RHIC and LHC energies a puzzling relation between the nuclear modification factor $R_{AA}(p_T)$ and the elliptic flow $v_2(p_T)$ 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 $R_{AA}(p_T)$ experimentally observed at RHIC energy. We have found 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.Comment: proceedings of the 2015 Hard Probes conferenc