We investigate the nonequilibrium evolution of the quark-meson model using two-particle irreducible effective action techniques. Our numerical simulations, which include the full dynamics of the order parameter of chiral symmetry, show how the model thermalizes into different regions of its phase diagram. In particular, by studying quark and meson spectral functions, we shed light on the real-time dynamics approaching the crossover transition, revealing e.g. the emergence of light effective fermionic degrees of freedom in the infrared. At late times in the evolution, the fluctuation-dissipation relation emerges naturally among both meson and quark degrees of freedom, confirming that the simulation successfully reaches thermal equilibrium.
In this talk, I review the important role played by plasma instabilities in the thermalization of quark-gluon plasmas at very high energy. [Conference talk presented at Strong and Electroweak Mattter 2004, Helsinki, Finland, June 16--19.]
The early thermalization is crucial to the quark-gluon plasma as a perfect liquid and results from many-body scattering. We calculate squared amplitudes for elastic parton-parton-parton scattering in perturbative QCD. Transport equations with the squared amplitudes are established and solved to obtain the thermalization time of initially produced quark-gluon matter and the initial temperature of quark-gluon plasma. We find that the thermalization times of quark matter and gluon matter are different.
Triple-quark elastic scattering amplitudes from perturbative QCD are first calculated and then used in a transport equation to study the thermalization of quark matter. By examining momentum isotropy to which the transport equation leads, we can determine thermalization time and offer an initial thermal quark distribution function. With an anisotropic initial quark distribution, which is relevant to quark matter initially created in a central Au-Au collision at \sqrt {s_{NN}}=200 GeV, the transport equation gives a time of the order of 1.8 fm/c for quark matter itself to thermalize by the trip…
The thermalization time for a Quark-Gluon-Plasma is estimated from a quantum transport model beyond the quasi-particle approach (or kinetic gas theory). While our ansatz is crude concerning the properties of ''real'' quarks and gluons, it nevertheless takes very serious the basic principles of quantum field theory for non-equilibrium states. It is found, that the thermalization time obtained from quantum transport theory is substantially longer than from kinetic theory. In our view this casts some doubts on scenarios which a priori assume a thermalized quark gluon plasma.
The elastic scattering of gqq, gqqbar and gqbarqbar and the thermalization of quark-gluon matter are studied. According to Feynman diagrams at the tree level, squared amplitudes for the elastic gqq scattering and the elastic gqqbar scattering are derived in perturbative QCD. Transport equations including the squared amplitudes for the elastic gqq, gqqbar and gqbarqbar scattering are established. Corresponding to anisotropic gluon and quark distributions created in central Au-Au collisions at RHIC, solutions of the transport equations show that thermalization time of quark matter can be shorten…
Using the AdS/CFT correspondence, we compute the medium-induced energy loss of a decelerating heavy quark moving through a strongly-coupled supersymmetric Yang Mills plasma. In the regime where the deceleration is small, a perturbative calculation is possible and we obtain the first two corrections to the energy-loss rate of a heavy quark with constant velocity. The thermalization of the heavy quark is also discussed.
We study the thermalization process of charm quarks in hot and dense matter. The diffusion of heavy quarks is calculated via a Langevin equation, both for a static medium as well as a QGP medium generated by a (3+1)D hydrodynamic model. We define two criteria for the thermalization of the heavy quarks, and observe thermalization times that are longer than the lifetime of the QGP phase for reasonable values of the diffusion constant.
Elastic parton-parton-parton scattering is briefly reviewed and is included in transport equations of quark-gluon matter. We solve the transport equations and get thermal states from initially produced quark-gluon matter. Both gluon matter and quark matter take early thermalization, but gloun matter has a shorter thermalization time than quark matter.
Kinetic equations are used to study thermalization of the anisotropic quark-gluon plasma produced by decays of color flux tubes possibly created at the very early stages of relativistic heavy-ion collisions. The decay rates of the initial color tubes are given by the Schwinger formula, while the collision terms are taken in the relaxation-time approximation. By connecting the relaxation time with viscosity we analyze production and thermalization processes in the plasma characterized by different values of the ratio of the shear viscosity to entropy density.
In this paper, we study the thermalization of gluons and N_f flavors of massless quarks and antiquarks in a spatially homogeneous system. First, two coupled transport equations for gluons and quarks (and antiquarks) are derived within the diffusion approximation of the Boltzmann equation, with only 2<-> 2 processes included in the collision term. Then, these transport equations are solved numerically in order to study the thermalization of the quark-gluon plasma. At initial time, we assume that no quarks or antiquarks are present and we choose the gluon distribution in the form f = f_0 theta (…
Elastic gluon-gluon-quark (gluon-gluon-antiquark) scattering is studied in perturbative QCD with 123 Feynman diagrams at the tree level. Individually squared amplitudes and interference terms of the Feynman diagrams are derived. With the elastic gluon-gluon-quark scattering and the elastic gluon-gluon-antiquark scattering transport equations are established. In the thermalization process of initially created quark-gluon matter, this matter is governed by elastic 2-to-2 scattering and elastic 3-to-3 scattering. Solutions of the transport equations show that initially created quark-gluon matter …
We study thermalization of strongly coupled gauge theory plasma in the presence of magnetic field using the AdS/CFT correspondence. We utilize the falling energy-shell model as a holographic description of gauge theory plasma undergoing thermalization, and find the effect of magnetic field on thermalization time in various space-time dimensions. Our results demonstrate that magnetic field universally hastens thermalization of strongly coupled gauge theory plasma.
We propose to measure azimuthal correlations of heavy-flavor hadrons to address the status of thermalization at the partonic stage of light quarks and gluons in high-energy nuclear collisions. In particular, we show that hadronic interactions at the late stage cannot significantly disturb the initial back-to-back azimuthal correlations of DDbar pairs. Thus, a decrease or the complete absence of these initial correlations does indicate frequent interactions of heavy-flavor quarks and also light partons in the partonic stage, which are essential for the early thermalization of light partons.
We discuss the role of elastic and inelastic collisions and their interplay in the thermalization of the quark-gluon plasma. We consider a simplified situation of a static plasma, spatially uniform and isotropic in momentum space. We focus on the small momentum region, which equilibrates first, and on a short time scale. We obtain a simple kinetic equation that allows for an analytic description of the most important regimes. The present analysis suggests that the formation of a Bose condensate, expected when only elastic collisions are present, is strongly hindered by the inelastic, radiative…
We estimate the ratio of the thermalization time over the freeze-out time using a holographic AdS-Vaidya model for quark-gluon plasma formed in the heavy ion collisions. In the model the process of thermalization is described as formation of the black hole in AdS space while dethermalization process, related with the freeze-out, as the black hole evaporation due to the Hawking radiation that is modeled by the Vaidya metric with a negative mass. In this model the thermalization takes place only at small scales and absent in the infrared region. At small scales the system tends towards a state o…
We treat heavy quark as an open quantum system in the hot medium and rederive the Stochastic Schrödinger Equation (SSE) from the full Schrödinger equation for both heavy quarks and the medium. We apply the SSE to the dynamical evolutions of heavy quarks (as a system) in the static hot medium (as an environment). Heavy quarks interact with the medium via random scatterings, which exchange the momentum and phase factor randomly between two wave functions of the system and the environment. The exchange of momentum and phase factor results in the transition between different eigenstates of the sys…
For an energetic jet propagating through a weakly-coupled quark-gluon plasma, we present the physical picture of jet quenching in longitudinal phase-space, as emerging from the interplay between the medium-induced, quasi-democratic, branchings and the elastic collisions responsible for the thermalization of the soft branching products.
Using the AdS/CFT correspondence, we compute the radiative energy loss of a slowly decelerating heavy quark with mass M moving through a supersymmetric Yang Mills (SYM) plasma at temperature T at large t'Hooft coupling λ. The calculation is carried out in terms of perturbation in \sqrtλT/M, and the rate of the energy loss is computed up to second order. We explain the physical meaning of each correction and estimate the thermalization time of a heavy quark moving in a strongly-coupled plasma.
Elastic scattering of charm (c) and bottom (b) quarks via D- and B-meson resonance states in an expanding, strongly interacting quark-gluon plasma is investigated. Drag and diffusion coefficients are calculated from an effective model based on chiral symmetry and heavy-quark effective theory, and utilized in a relativistic Langevin simulation to obtain transverse-momentum spectra and elliptic flow (v_2) of c- and b-quarks. The hadronization to D- and B-mesons is described by coalescence and fragmentation, and the resulting decay-electron spectra are compared to recent RHIC data.
We examine the possibility to utilize in-medium charmonium formation in heavy ion interactions at collider energy as a probe of the properties of the medium. This is possible because the formation process involves recombination of charm quarks which imprints a signal on the resulting normalized transverse momentum distribution containing information about the momentum distribution of the quarks. We have contrasted the transverse momentum spectra of J/Psi, characterized by <p_T^2>, which result from the formation process in which the charm quark distributions are taken at opposite limits with r…
We argue that isotropization and, consequently, thermalization of the system of gluons and quarks produced in an ultrarelativistic heavy ion collision does not follow from Feynman diagram analysis to any order in the coupling constant. We conclude that the apparent thermalization of quarks and gluons, leading to success of perfect fluid hydrodynamics in describing heavy ion collisions at RHIC, can only be attributed to the non-perturbative QCD effects not captured by Feynman diagrams. We proceed by modeling these non-pertrubative thermalization effects using viscous hydrodynamics. We point out…
Charm- and bottom-quark rescattering in a Quark-Gluon Plasma (QGP) is investigated with the objective of assessing the approach towards thermalization. Employing a Fokker-Planck equation to approximate the collision integral of the Boltzmann equation we augment earlier studies based on perturbative parton cross sections by introducing resonant heavy-light quark interactions. The latter are motivated by recent QCD lattice calculations which indicate the presence of "hadronic" states in the QGP. We model these states by colorless (pseudo-) scalar and (axial-) vector D- and B-mesons within a heav…
The thermalization rate of a heavy quark is related to its momentum diffusion coefficient. Starting from a Kubo relation and using the framework of the heavy quark effective theory, we argue that in the large-mass limit the momentum diffusion coefficient can be defined through a certain Euclidean correlation function, involving color-electric fields along a Polyakov loop. Furthermore, carrying out a perturbative computation, we demonstrate that the spectral function corresponding to this correlator is relatively flat at small frequencies. Therefore, unlike in the case of several other transpor…
In these lectures, I will attempt a pedagogical and qualitative introduction to the theory of equilibrium and thermalization of quark-gluon plasmas. I assume only that the reader is familiar with quantum field theory at zero temperature and with QCD as the theory of the strong interactions. I focus on the limit of small alpha_s, which in principle should be relevant at extremely high temperature because of asymptotic freedom, and in any case provides a clean theoretical context in which to discuss a variety of phenomena. Topics discussed include the basic equilibrium formalism for finite-tempe…
We calculate the medium dilepton yield from a quark-gluon plasma which has a time-dependent local momentum-space anisotropy. A phenomenological model for the hard momentum scale, p_hard(tau), and plasma anisotropy parameter, xi(tau), is constructed which interpolates between free streaming behavior at early times (tau << tau_iso) and ideal hydrodynamic behavior at late times (tau >> tau_iso). We show that high-energy dilepton production is sensitive to the assumed plasma isotropization time, tau_iso, and can therefore be used to experimentally determine the time of onset for hydrodynamic expan…
Hydrodynamical modeling of heavy ion collisions at RHIC suggests that the quark-gluon plasma (QGP) "thermalizes" in a remarkably short time scale, about 0.6 fm/c. We argue that this should be viewed as indicating fast isotropization, but not necessarily complete thermalization, of the non-equilibrium QGP. Non-Abelian plasma instabilities can drive local isotropization of an anisotropic QGP on a time scale which is faster than ordinary perturbative scattering processes. As a result, we argue that theoretical expectations based on weak coupling analysis are not necessarily in conflict with hydro…
We discuss dilepton production from a quark-gluon plasma which has a time-dependent anisotropy in momentum space. A phenomenological model for the hard momentum scale, p_hard(tau) and the plasma anisotropy parameter, xi(tau), is presented. The model interpolates between early-time 1+1 free streaming behavior (tau << tau_iso) and late-time ideal 1+1 hydrodynamical behavior (tau >> tau_iso). Using this model, we find that the dilepton rate arising from electromagnetic annihilations of quarks in the kinematic range 3 <p_T< 8 GeV is sensitive to the assumed isotropization time of the system, tau_i…
Early local equilibration of a hot medium created in high-energy heavy ion collisions has been one of the long standing issues in hadron physics. The glasma model predicts that the medium initially has a large amount of high-momentum gluons but few quarks. We develop a phenomenological model based on collinear splitting and recombination of quarks and gluons for a simplified description of thermalization and chemical equilibration. We find that both could be achieved in a short time but chemical equilibration is slower than thermalization.
Thermalization of a heavy quark near rest is controlled by the correlator of two electric fields along a temporal Wilson line. We address this correlator within real-time, classical lattice Yang-Mills theory, and elaborate on the analogies that exist with the dynamics of hot QCD. In the weak-coupling limit, it can be shown analytically that the dynamics on the two sides are closely related to each other. For intermediate couplings, we carry out non-perturbative simulations within the classical theory, showing that the leading term in the weak-coupling expansion significantly underestimates the…
We investigate decay modes of B mesons emitting two pseudoscalar (P) mesons in the Quark Diagram Scheme at SU(3) level. Several relations among the decay amplitudes are obtained and various branching ratios are predicted.
Screening effects from sea pairs on the quark-antiquark static potential are analyzed phenomenologically from the light-quark to the heavy-quark meson spectra. From the high excited light-quark meson spectrum a universal form for the screened static potential is proposed. This potential is then succesfully applied to heavy quarkonia. Our results suggest the assignment of X(4260) to the 4s state of charmonium and the possible existence of a 5s bottomonium resonance around 10748 MeV.
Exclusive semileptonic B meson decays to orbitally excited D mesons are investigated in the infinitely heavy quark limit in the framework of the relativistic quark model based on the quasipotential approach. The B\to D^{**}eνIsgur-Wise functions τ_{3/2}(w) and τ_{1/2}(w) are determined. It is found that the relativistic transformation of the meson wave functions (Wigner rotation of the light quark spin) contribute already at the leading order of the heavy quark expansion.
In order to investigate the tomographical structure of light pseudoscalar mesons, particularly, pion and kaon, we study the valence quark distribution function (PDF) and the generalized parton distributions (GPDs) using light-cone quark model (LCQM).
The harmonic quarks are applied to the analysis of quark structures of long-lived $D$-mesons and $ψ/J$. In the harmonic quark model the quarks of long-lived mesons ($π^0$, $π^\pm$, $K^\pm$, $K^0$, $B^0$, $B^\pm$) are weakly relativistic objects with the excess energy of valent quarks less than 7 MeV. In contrast to this, the long-lived $D$-mesons in two-quark standard have the apparent excess energies of a few hundred MeV. It was established that all long-lived $D$-mesons and $ψ/J$ have the six-quark structures. There are two valent quarks and two additional neutral quark-antiquark $u$-pairs. …
After describing the SU(2) linear sigma model (L$σ$M), we dynamically generate it using the B.W. Lee null tadpole sum (characterizing the true vacuum) together with the dimensional regularization lemma. Next we generate the chiral-limiting (CL) nonstrange and strange constituent quark masses ${\hat m}=325.7$ MeV; $m_s=486$ MeV away from the CL. Finally, we study vector meson dominance (VMD) and the pion, kaon charge radii and the loop-order $ρ\toπγ$, $π^0\toγγ$ amplitudes in the quark model. Lastly, we verify this procedure using tree-order VMD graphs.
The vacuum parton creation in quickly varying external fields is studied at the time scale of order 1 fm/$c$ typical for the quark-gluon plasma formation and thermalization. To describe the pre-equilibrium evolution of the system the transport kinetic equation is employed. It is shown that the dynamics of production process at times comparable with particle inverse masses can deviate considerably from that based on classical Schwinger-like estimates for homogeneous and constant fields. One of the effects caused by non-stationary chromoelectric fields is the enhancement of the yield of $s\bar{s…
We propose that there coexist two scalar mesons of different structures (a conventional meson and a four-quark meson) in the recently observed broad bumps just below the large peak of the tensor meson in the D-pi mass distribution. We base this proposal on the interpretation of the charm-strange scalar meson of mass 2317 MeV as a four-quark meson. The strange counterparts of these scalar mesons are also studied.
The contributions of one-loop diagrams with dynamical vector mesons to masses and decay constants of pseudoscalar mesons are determined. Hereby, a relativistic Lagrangian for both the pseudoscalar-meson octet and the vector-meson nonet is used. The vector mesons are given in the antisymmetric tensor representation. Both the differences between static and dynamical vector mesons and the differences between calculations with and without vector mesons are studied as functions of the light quark mass.
By assigning the narrow scalar resonance (which has been recently observed at the B-factories) to one of iso-triplet four-quark mesons containing a charm quark, two body decays of the four-quark mesons are studied. It is predicted that some of them can be observed as narrow resonances.
Semileptonic and nonleptonic decays of the B_c meson to B_s and B mesons, caused by the c\to s,d quark transitions, are studied in the framework of the relativistic quark model. The heavy quark expansion in inverse powers of the active c and spectator \bar b quark is used to simplify calculations while the final s and d quarks in the B_s and B mesons are treated relativistically. The decay form factors are explicitly expressed through the overlap integrals of the meson wave functions in the whole accessible kinematical range. The obtained results are compared with the predictions of other appr…
The physics of charm has become one of the best laboratories exposing the limitations of the naive constituent quark model and also giving hints into a more mature description of meson spectroscopy, beyond the simple quark--antiquark configurations. In this talk we review some recent studies of multiquark components in the charm sector and discuss in particular exotic and non-exotic four-quark systems.
We consider meson radiative decays within the framework of $U_0(1)\times U(1)\times SU(2)$ gauge symmetry. This approach is based on the linear sigma-model extended by the gauge and quark-meson interactions. Physical content and parameters of the model are discussed. Theoretical predictions for some radiative decays of vector mesons are in a good agreement with the experimental data.
We consider the quark antiquark potential of a quarkonium moving with velocity $v$ through a quark-gluon plasma at temperature T. An explicit, configuration-space expression is found for the screened interaction between the quarks constituting the meson. This potential is non-spherical, but axially symmetric about the direction of $v$.
Using the quark spectrum of the BCC Quark Model [1] and the phenomenological formula for the binding energies of the mesons, not only have we deduced the intrinsic quantum numbers (I, S, C, b, and Q) of all mesons as was done with the Quark Model [2], but also we deduced the meson mass spectrum in agreement with experimental results [3] that we could not deduce using the Quark Model. The experimental meson spectrum gives some evidence of the existence of the new quarks $q_S^*(1391)$, $q_S^*(2551)$ and $q_C^*(6591)$..., which are predicted by the BCC Quark Model. The meson $χ(1600)$ $[2^+(2^{++…
The present talk consists of two parts. The first one is allocated for consideration of the dimension of bilocal meson fields for quark-antiquark meson systems, which have been so far treated as the bosonic fields independent of constituent quark flavors, in the covariant oscillator quark model. Revisiting the electromagnetic currents of quark-antiquark meson systems, we show that the bilocal meson fields should be bosonic for light-quark meson systems, while fermionic for heavy-light and heavy-heavy meson systems. In the second part we apply the effective electromagnetic interactions of meson…
With usage of obvious mechanisms of quark currents the amplitudes of leptonic decaies of pseudoscalar mesons are investigated. The estimation for a constant of leptonic decay of the D+ meson is obtained, f_D+ ~ 0.23 GeV.
An effective potential in a meson-meson system is discussed based on the SU(3) chiral constituent quark model, and the analytic form of the potential is explicitly given. In addition, the effective potential is employed to study the bound state problem of $ωϕ$, which is related to the new resonance of $f_0(1810)$ observed in BESII very recently.
We present an exact calculation of $S$ and $P$ wave $QQ\bar n\bar n$ states using different standard nonrelativistic quark--quark potentials. We explore in detail the charm and bottom sectors looking for bound states that could be measured within existing facilities. Against the proliferation of four--quark states sometimes predicted in the literature, we found a small number of candidates to be stable. We analyze their properties in a trial to distinguish between compact and molecular states. Possible decay modes are discussed.
The calculation of the partial width of the rare t-quark decay into Upsilon-meson, W-boson and b-quark (t -> ΥW b) is presented. The branching ratio equals Br(t -> Upsilon W b) = 1.3 * 10^{-5} that make possible searches for this rare $t$-quark decay at LHC.
Using phenomenological formulae, we deduce the masses and quantum numbers of the quarks from two elementary quarks ($ε_{u}$ and $ε_{d}$) first. Then using the sum laws and a binding energy formula, in terms of the qqq baryon model and SU(4), we deduce the masses and quantum numbers of the important baryons from the deduced quarks. At the same time, using the sum laws and a binding energy formula, in terms of the quark-antiquark bound state meson model, we deduce the masses and quantum numbers of the mesons from the deduced quarks. The deduced masses of the baryons and mesons are 98% consistent…
The D-and F-wave quark-quark amplitudes are constructed in the framework of the dispersion N/D-method. The mass values of meson multiplets with $J^{PC}=1^{--},2^{--},2^{-+},3^{--}$ and $J^{PC}=2^{++},3^{++},3^{+-},4^{++}$ are calculated. The Regge trajectories of mesonic resonances with orbital numbers L=0,1,2,3 are obtained.
Temperature dependence of the quark condensate is studied in the Nambu--Jona-Lasinio model with meson loops. Substantial differences are found compared to the results with quark loops only.
