4 pages, 2 figures, 10 subfigures, 1 table, contributed to the proceedings of the XLVII International Winter Meeting on Nuclear Physics, Bormio (Italy), Jan. 26-30, 2009
We fit the lattice QCD data of Kaczmarek et al for the free energy F1 and internal energy U1 with a class of Coulomb, constant and linear potentials, both pure and screened, matching the large distance to the short distance parts of the lattice QCD finite temperature energies. We also include the hyperfine potential in F1 and U1. We detail the bottomonium (and charmonium) binding and the melting temperatures, both for the groundstate and for the excited states, relevant for Hard Probes in Heavy Ion Collisions at LHC, where temperatures well above Tc will be reached, much higher than the temperatures reached in previous Heavy Ion Collisions.
We study the fate of P wave bottomonium states in the quark-gluon plasma, using a spectral function analysis of euclidean lattice correlators. The correlators are obtained from lattice QCD simulations with two light quark flavours on highly anisotropic lattices, treating the bottom quark nonrelativistically. We find clear indications of melting immediately after the deconfinement transition.
We study the bottomonium screening masses in a 2+1 flavor QCD medium on the lattice using the Highly Improved Staggered Quark(HISQ) discretization for the quarks. We focus on a wide temperature range in the region $350~{\rm MeV}\le T < 1000 ~{\rm MeV}$, and perform our calculations on three different lattice spacings to control the lattice cut-off effects, corresponding to temporal lattice extent of $N_τ=8,10,12$. From a detailed study of the temperature dependence of screening masses we conclude that while the $η_b(1S)$ and $Υ(1S)$ states melt at $T>500$ MeV, the scalar and axial-vector state…
We investigate the phenomenon of Bottomonium melting in a thermal quark-gluon plasma using three-dimensional stochastic simulations based on the concept of open-quantum systems. In this non-relativistic framework, introduced in [Phys.Rev. D85 (2012) 105011], which makes close contact to the potentials derived in effective field theory, the $b\bar{b}$ system evolves unitarily under the incessant kicks by the constituents of the surrounding heat bath. In particular thermal fluctuations and the presence of a complex potential in the EFT are naturally related. An intricate interplay between state …
Bottomonium production in heavy ion collisions is modified compared with any simple extrapolation from elementary collisions. This modification is most likely caused by the presence of a deconfined system of quarks and gluons for times of several fm/c. In such a medium, bottomonium can be destroyed, but the constituent bottom quarks will likely stay spatially correlated due to small mean free paths in this system. With these facts in mind, we describe bottomonium formation with a coupled set of equations. A rate equation describes the destruction of $Υ(1S)$ particles, while a Langevin equation…
The Belle-II experiment is expected to collect large data samples at the $Υ(4S)$ and $Υ(5S)$ resonances to study primarily $B$ and $B_s$ mesons. We discuss what other data above the $B\bar{B}$ threshold are of interest. We propose to perform a high-statistics energy scan from the $B\bar{B}$ threshold up to the highest possible energy, and to collect data at the $Υ(6S)$ and at higher mass states if they are found in the scan. We emphasize the interest in increasing the maximal energy from 11.24\,GeV to 11.5 - 12\,GeV in the future. These data are needed for investigation of bottomonium and bott…
The fraction of heavy vector mesons produced in a heavy ion collision, as compared to a proton proton collision, serves as an important indication of the formation of a thermal medium, the quark gluon plasma. This sort of analysis strongly depends on understanding the thermal effects of a medium like the plasma on the states of heavy mesons. In particular, it is crucial to know the temperature ranges where they undergo a thermal dissociation, or melting. AdS/QCD models are know to provide an important tool for the calculation of hadronic masses, but in general are not consistent with the obser…
We study the temperature dependence of bottomonium for temperatures in the range $0.4 T_c < T < 2.1 T_c$, using nonrelativistic dynamics for the bottom quark and full relativistic lattice QCD simulations for $N_f=2$ light flavors on a highly anisotropic lattice. We find that the $Υ$ is insensitive to the temperature in this range, while the $χ_b$ propagators show a crossover from the exponential decay characterizing the hadronic phase to a power-law behaviour consistent with nearly-free dynamics at $T \simeq 2 T_c$.
We study quarkonium spectral functions at high temperatures using potential model with complex potential. The real part of the potential is constrained by the lattice QCD data on static quark anti-quark correlation functions, while the imaginary part of the potential is taken from perturbative calculations. We find that the imaginary part of the potential has significant effect on quarkonium spectral functions, in particular, it leas to the dissolution of the 1S charmonium and excited bottomonium states at temperatures about 250 MeV and melting of the ground state bottomonium at temperatures s…
The Schroedinger equation for the charmonium and bottomonium states at finite temperature is solved by employing an effective temperature dependent potential given by a linear combination of the color singlet free and internal energies obtained on the lattice from the Polyakov loop correlation functions. The melting temperatures and other properties of the quarkonium states are evaluated. The consistency of the potential model approach with the available lattice data on the quarkonium temporal correlators and spectral functions is explored.
We present results on the bottomonium spectrum at temperatures above and below the deconfinement crossover temperature, $T_c$, from dynamical lattice QCD simulations. The heavy quark is treated with a non-relativistic effective field theory on the lattice and serves as a probe of the hot medium. Ensembles with a finer spatial lattice spacing and a greater range of temperatures below $T_c$ than those previously employed by this collaboration are used. In addition, there are $N_f=2+1$ flavours of Wilson clover quark in the sea with $M_π\approx400$ MeV and we perform a more careful tuning of the …
We investigate the modification of S and P wave states in the bottomonium spectrum above and below the deconfinement crossover temperature through their spectral functions obtained from the maximum entropy method. Anisotropic ensembles with $N_f=2+1$ Wilson clover fermions with tadpole-improvement are used while the bottom quark is treated with an improved non-relativistic action. We observe significant modifications of the P wave $χ_{b1}$ ground state directly above the crossover temperature, $T_c$, while the S wave $Υ$ ground state remains relatively unchanged up to temperatures of almost $2…
A comprehensive parameterization of the colour singlet heavy quark free energy above $T_c$ is given, using the lattice data in quenched ($N_f=0$) and unquenched ($N_f=2$ and $N_f=3$) QCD. The corresponding (temperature dependent) potentials thus obtained are then inserted into the Schrödinger equation for the charmonium and the bottomonium in the deconfined phase of QCD. The solution of the equation provides an estimate of the melting temperature and of the radii for the different $c\bar{c}$ and $b\bar{b}$ bound states.
Recently it has been shown that the gross structure of the bottomonium spectrum is reproduced reasonably well within the non-relativistic boundstate theory based on perturbative QCD. In that calculation, however, the fine splittings and the S-P level splittings are predicted to be considerably narrower than the corresponding experimental values. We investigate the bottomonium spectrum within a specific framework based on perturbative QCD, which incorporates all the corrections up to O(alpha_S^5 m_b) and O(alpha_S^4 m_b), respectively, in the computations of the fine splittings and the S-P spli…
We present an overview of bottomonium spectral functions in the quark-gluon plasma, obtained by the FASTSUM collaboration, using lattice QCD simulations with two light quark flavours on anisotropic lattices. The bottom quark is treated nonrelativistically. While we find that the S wave ground states survive up to the highest temperature we consider, we have strong indications that P wave states melt immediately above Tc.
We use the non-perturbative Q\bar Q potential at finite temperatures derived in the Field Correlator Method to obtain binding energies for the lowest eigenstates in the Q\bar Q and QQQ systems (Q=c,b). The three--quark problem is solved by the hyperspherical method. The solution provides an estimate of the melting temperature and the radii for the different diquark and triquark bound states. In particular we find that J/ψand $ccc$ ground states survive up to T \sim 1.3 T_c, where T_c is the critical temperature, while the corresponding bottomonium states survive even up to higher temperature, …
The temperature dependence of bottomonium states at temperatures above and below $T_c$ is presented, using non-relativistic dynamics for the bottom quark and full relativistic lattice QCD simulations for two light flavors on a highly anisotropic lattice. We find that the S-waves ($Υ$ and $η_b$) show little temperature dependence in this range while the P wave propagators show a crossover from the exponential decay characterizing the hadronic phase to a power-law behavior consistent with nearly-free dynamics at approximately twice the critical temperature.
We explore the spectrum of excited and exotic bottomonia using lattice QCD. Highly excited states are identified with masses up to 11,000 MeV, many of which can be grouped into supermultiplets matching those of the quark model while exotic spin--parity--charge-conjugation quantum numbers $J^{PC}=0^{+-},\,1^{-+},\,2^{+-}$ that cannot be formed from $\bar{q}q$ alone are also identified. Single-meson operator constructions are used that have good $J^{PC}$ in the continuum, these are found to overlap well onto heavy quark states with $J\le4$. A continuum $J^{PC}$ is assigned to each level, based o…
The bottomonium spectrum is the perfect testing ground for the confining potential and unitarisation effects. The bottom quark is about three times heavier than the charm quark, so that $b\bar{b}$ systems probe primarily the short-range part of that potential. Also, the much smaller colour-hyperfine interaction in the $B$ mesons make the $B\bar{B}$ threshold lie significantly higher than the $D\bar{D}$ threshold in charmonium, on a relative scale of course. A further complicating circumstance is that none of the experimentally observed vector $b\bar{b}$ mesons has been positively identified as…
We present the quarkonia correlators for charmonium and bottomonium systems in the pseudoscalar, vector and scalar channels. For the description of quark-antiquark interaction we adopt the temperature dependant colour screening potential of the power law form. The spectroscopic parameters defined from the model are employed in the spectral functions to compute the quarkonia correlators. We find considerable medium modifications to the effective masses of the quarkonia as well as in the behaviour of the respective radial wave functions. These modifications are then reflected in the computed cor…
S-wave states of charmonium and bottomonium are described using bottom-up AdS/QCD. We propose a holographic model that unifies the description of masses and decay constants, leading to a precise match with experimental data on heavy quarkonia. Finite temperature effects are considered by calculating the current-current spectral functions of heavy vector mesons. The identification of quasi-particle states as Breit-Wigner resonances in the holographic spectral function was made. We develop a prescription to subtract background contributions from the spectral function to isolate the Breit-Wigner …
Based on the non-relativistic QCD factorization scheme, we study the hadroproduction of the bottomonium states $Υ(5S)$ and $Υ(6S)$. We argue to search for them in the final states $Υ(1S,2S,3S)π^+π^-$, which are found to have anomalously large production rates at $Υ(5S)$. The enhanced rates for the dipionic transitions in the $Υ(5S)$-energy region could, besides $Υ(5S)$, be ascribed to $Y_b(10890)$, a state reported by the Belle collaboration, which may be interpreted as a tetraquark. The LHC/Tevatron measurements are capable of making a case in favor of or against the existence of $Y_b(10890)$…
A comprehensive study of the color singlet heavy quark states above T_c is given, using the Field Correlator Method (FCM) for nonperturbative Q{\bar Q} potentials and the screened Coulomb potential with the T-dependent Debye radius. Using these potentials we calculate binding energies and melting temperatures of heavy mesons and baryons in the deconfined phase of quark-gluon plasma and the J/ψand Upsilon disintegration cross sections via the gluon absorption.
The sequential melting of the bottomonium states is one of the important signals for the existence of a quark gluon plasma. The study of bottomonia spectral functions on the lattice is a difficult task for many reasons. Calculations based on NRQCD, that are commonly used for such purpose, are not applicable at high temperatures. In this work we propose a new method to study this problem by calculating the spatial screening masses of bottomonium states. We calculate the spatial meson correlators and extract the screening masses for mesons in different quantum channels using highly improved stag…
We derive a static potential for a heavy quark-antiquark pair propagating in Minkowski time at finite temperature, by defining a suitable gauge-invariant Green's function and computing it to first non-trivial order in Hard Thermal Loop resummed perturbation theory. The resulting Debye-screened potential could be used in models that attempt to describe the ``melting'' of heavy quarkonium at high temperatures. We show, in particular, that the potential develops an imaginary part, implying that thermal effects generate a finite width for the quarkonium peak in the dilepton production rate. For qu…
We present the finite temperature spectra of both bottomonium and charmonium, obtained from a consistent lattice QCD based potential picture. Starting point is the complex in-medium potential extracted on full QCD lattices with dynamical u,d and s quarks, generated by the HotQCD collaboration. Using the generalized Gauss law approach, vetted in a previous study on quenched QCD, we fit ${\rm Re}[V]$ with a single temperature dependent parameter $m_D$, the Debye screening mass, and confirm the up to now tentative values of ${\rm Im}[V]$. The obtained analytic expression for the complex potential…
We present continuum extrapolated results of charmonium and bottomonium correlators in the vector channel at several temperatures below and above $T_c$. The continuum extrapolation jointly performed with the interpolations to have physical values of $J/ψ$ and $Υ$ masses in the confined phase is based on calculations on several large quenched isotropic lattices using clover-improved Wilson valence fermions carrying different quark masses. The extrapolated lattice correlators are confronted with perturbation theory results incorporating resummed thermal effects around the threshold from pNRQCD a…
We report on a study of heavy hybrid states using the NRQCD approach on coarse and asymmetric lattices, where we discard vacuum polarisation effects and neglect all spin-correction terms. We find a clear hybrid signal on all our lattices ($a_s= 0.15 ... 0.47$ fm). We have studied in detail the lattice spacing artefacts, finite volume effects and mass dependence. Within the above approximations we predict the hybrid excitation in Charmonium to be 1.323(13) GeV above its ground state. The bottomonium hybrid was found to be 1.542(8) GeV above its ground state.
We extend our lattice QCD potential based study arXiv:1509.07366 (JHEP 1512 (2015) 101) of the in-medium properties of heavy quark bound states to P-wave bottomonium and charmonium. Similar to the behavior found in the S-wave channel their spectra show a characteristic broadening, as well as mass shifts to lower energy with increasing temperature. In contrast to the S-wave states, finite angular momentum leads to the survival of spectral peaks even at temperatures, where the continuum threshold reaches below the bound state remnant mass. We elaborate on the ensuing challenges in defining quark…
We compute masses of bottomonium and charmonium bound states using a Schrödinger equation with a heavy quark-antiquark potential including $1/m$ and $1/m^2$ corrections previously derived in potential Non-Relativistic QCD and computed with lattice QCD. This is a preparatory step for a future project, where we plan to take into account similar corrections to study quarkonium resonances and tetraquarks above the lowest meson-meson thresholds.
We analyse mesons at finite temperature in a chiral, confining string dual. The temperature dependence of low-spin as well as high-spin meson masses is shown to exhibit a pattern familiar from the lattice. Furthermore, we find the dissociation temperature of mesons as a function of their spin, showing that at a fixed quark mass, mesons with larger spins dissociate at lower temperatures. The Goldstone bosons associated with chiral symmetry breaking are shown to disappear above the chiral symmetry restoration temperature. Finally, we show that holographic consideration imply that large-spin meso…
We discuss the behavior of charmonia and bottomonia correlators and spectral functions above the deconfinement temperature and determine melting temperatures for different mesonic states.
In this work, we investigate the melting of charmonium states within a holographic QCD model in the context of Einstein-Maxwell-Dilaton (EMD) theory. In the dual field theory, the model describes the heavy mesons inside a finite temperature and density medium. First, we calculate the spectrum at zero temperature. Then, at finite temperature, we obtain the spectral functions, where the heavy vector meson are represented by peaks. We show that the charmonium melts down at temperatures above the confinement/deconfinement temperature of the quark-gluon plasma. We also observe that the chemical pot…
We extend our analysis of holographic meson dissociation in the presence of an intense magnetic field. In addition to the previously known critical temperature above which the mesons melt, we found that for certain magnetic field intensities there exists a second lower critical temperature, below which stable mesons cease to exist. While we showed before that there is a range of high temperatures for which mesons can be melted by changing the magnetic field intensity, here we show that, as a consequence of the second critical point, there is also a range of low temperatures for which this phen…
In the context of the Hagedorn temperature half-centenary I describe our understanding of the hot phases of hadronic matter both below and above the Hagedorn temperature. The first part of the review addresses many frequently posed questions about properties of hadronic matter in different phases, phase transition and the exploration of quark-gluon plasma (QGP). The historical context of the discovery of QGP is shown and the role of strangeness and strange antibaryon signature of QGP illustrated. In the second part I discuss the corresponding theoretical ideas and show how experimental results…
Ratios of cumulants of conserved net charge fluctuations are sensitive to the degrees of freedom that are carriers of the corresponding quantum numbers in different phases of strong interaction matter. Using lattice QCD with 2+1 dynamical flavors and quenched charm quarks we calculate second and fourth order cumulants of net charm fluctuations and their correlations with other conserved charges such as net baryon number, electric charge and strangeness. Analyzing appropriate ratios of these cumulants we probe the nature of charmed degrees of freedom in the vicinity of the QCD chiral crossover …
