M. A. Durnev
Using the quark-antiquark interactions obtained in the framework of the bootstrap method we construct a potential model, investigate the possibility of describing of heavy quarkonia and calculate the bottomonium spectrum. The potential of the interaction was obtained as a nonrelativistic limit of the relativistic quark-antiquark amplitudes Q{\bar Q} -> Q\bar Q.
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We model the spectral effect of open flavor meson-meson thresholds in heavy quarkonia. The proposed energy dependent quark-antiquark static potential tries to incorporate in a quark model scheme the results from unquenched lattice calculations. A good qualitative and a reasonable quantitative description of charmonium and bottomonium, including the "new charmonium-like" states, is obtained.
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.
We calculate the spectra of charmonium and bottomium in an approximation scheme which treats hard gluons perturbatively while soft gluons are expanded in a set of localized wave functions. Quark-antiquark and quark-antiquark-gluon sectors are included. Reasonable agreement with 2 parameters only is found but the spectra are too coulombic. Despite large coupling constant the admixture of the quark-antiquark-gluon sector is found to be remarkably small.
The experiments at LHC have shown that the SUSY (exotic) bound states are likely to form bound states in an entirely similar fashion as ordinary quarks form bound states, i.e., quarkonium. Also, the interaction between two squarks is due to gluon exchange which is found to be very similar to that interaction between two ordinary quarks. This motivates us to solve the Schrödinger equation with a strictly phenomenological static quark-antiquark potential: $V(r)=-Ar^{-1}+κ\sqrt{r}+V_{0}$ using the shifted large $N$-expansion method to calculate the low-lying spectrum of a heavy quark with anti-sb…
Within the framework of nonrelativistic quark-antiquark Cornell potential model formalism, we study the annihilation of heavy quarkonia. We determine their annihilation widths resulting into digluon, dilepton, $3γ$, $3g$ and $γgg$ and compare our findings with the available theoretical results and experimental data. We also provide the charge radii and absolute square of radial Schrödinger wave function at zero quark-antiquark separation for heavy quarkonia and $B_c$ mesons.
We derive a light-front Schrodinger-type equation of motion for the quark-antiquark wave function of heavy quarkonia imposing constraints from the holographic soft-wall model.
Starting with two coupled Bethe-Salpeter equations for the quark-antiquark, and for the quark-glue-antiquark component of the quarkonium, we solve the bound state equations perturbatively. The resulting admixture of glue can be partially understood in a semiclassical way, one has, however, to take care of the different use of time ordered versus retarded Green functions. Subtle questions concerning the precise definition of the equal time wave function arise, because the wave function for the Coulomb gluon is discontinuous with respect to the relative time of the gluon. A striking feature is t…
We discuss systems containing a heavy quark and a heavy antiquark in the infinite mass limit of QCD. Studying the limit of equal velocities for both heavy particles, we formulate an effective theory approach to heavy quarkonia-like systems. The method is well suited to processes in which the two heavy quarks annihilate, such as electromagnetic and strong decays of charmonium and bottomonium and weak decays of $B_c$.
We solve the Bethe-Salpeter equation (BSE) for a system of a heavy quark-antiquark pair interacting with a Poincare invariant generalization of screened linear confining potential. In order to get reliable description the Lorentz scalar confining interaction is complemented by the effective one gluon exchange. Within presented model we reasonably reproduce all known radial excitations of the vector charmonia. We have found that $J/Ψ$ is the only charmonium left bellow naive quark-antiquark threshold $2m_c$, while the all excited states are situated above this threshold. We develop a method whi…
We calculate the NLO corrections for the gluon fragmentation functions to a heavy quark-antiquark pair in ${^{1}\hspace{-0.6mm}S_{0}^{[1]}}$ or ${^{1}\hspace{-0.6mm}S_{0}^{[8]}}$ state within NRQCD factorization. We use integration-by-parts reduction to reduce the original expression to simpler master integrals (MIs), and then set up differential equations for these MIs. After calculating the boundary conditions, MIs can be obtained by solving the differential equations numerically. Our results are expressed in terms of asymptotic expansions at singular points of $z$ (light-cone momentum fract…
A chiral invariant Lagrangian describing the tetraquark-quarkonia interaction is considered at the leading and subleading order in the large-$N_{c}$ expansion. Spontaneous chiral symmetry breaking generates mixing of scalar tetraquark and quarkonia states and non-vanishing tetraquark condensates. In particular, the mixing strength is related to the decay strengths of tetraquark states into pseudoscalar mesons. The results show that scalar states below 1 GeV are mainly four-quark states and the scalars between 1 and 2 GeV quark-antiquark states, probably mixed with the scalar glueball in the is…
Production of heavy quark antiquark systems in high energy heavy ion collisions must involve relativistic momentum components in a quantum mechanical approach. If the color forces are screened in a deconfining medium, one can define the analog of a formation or separation time by an overlap integral in the nonrelativistic bound state rest frame. This time parameter has some interesting properties which depend on the momentum spectrum of the initial quarks. Consequences of these properties for the phenomenology of deconfinement signals are discussed.
We have investigated the spectra of light-heavy quarkonia with the use of a quantum-chromodynamic potential model which is similar to that used earlier for the heavy quarkonia. An essential feature of our treatment is the inclusion of the one-loop radiative corrections to the quark-antiquark potential, which contribute significantly to the spin-splittings among the quarkonium energy levels. Unlike $c\bar{c}$ and $b\bar{b}$, the potential for a light-heavy system has a complicated dependence on the light and heavy quark masses $m$ and $M$, and it contains a spin-orbit mixing term. We have obtai…
We have investigated the spectra of light-heavy quarkonia with the use of a quantum-chromodynamic potential model which is similar to that used earlier for the heavy quarkonia. An essential feature of our treatment is the inclusion of the one-loop radiative corrections to the quark-antiquark potential, which contribute significantly to the spin-splittings among the quarkonium energy levels. Unlike $c\bar{c}$ and $b\bar{b}$, the potential for a light-heavy system has a complicated dependence on the light and heavy quark masses $m$ and $M$, and it contains a spin-orbit mixing term. We have obtai…
Valuable data on quarkonia (the bound states of a heavy quark Q=c,b and the corresponding antiquark) have recently been provided by a variety of sources, mainly e+ e- collisions, but also hadronic interactions. This permits a thorough updating of the experimental and theoretical status of electromagnetic and strong transitions in quarkonia. We discuss QQbar transitions to other QQbar states, with some reference to processes involving QQbar annihilation.
Quenched lattice data for the quark-antiquark interaction (in terms of heavy quark free energies) in the color singlet channel at finite temperatures are fitted and used within the nonrelativistic Schroedinger equation formalism to obtain binding energies and scattering phase shifts for the lowest eigenstates in the charmonium and bottomonium systems in a hot gluon plasma. The partial dissociation rate due to the Bhanot-Peskin process is calculated using different assumptions for the gluon distribution function, including free massless gluons, massive gluons, and massive damped gluons. It is d…
This is the first of a sequence of papers that address the non-perturbative origin of the central, and spin-dependent forces between quarks. Its main thrust is a focus on meson spectroscopy in the center of mass frame. We suggest a "dense instanton ensemble" model for the QCD vacuum, to explain the interquark forces in mesons, from quarkonia to heavy-light and light-light ones, to the extent it is possible. The sequels will show how to export these interactions to the light front, and derive the corresponding Hamiltonians and mesonic wavefunctions.
Based on the two Higgs doublet model, we study the effect of Higgs-boson exchange on the (super)heavy quarkonium \bar QQ, which induces a strong attractive force between a (super)heavy quark Q and an antiquark \bar Q. An interesting application is the decay of (super)heavy quarkonia \bar QQ into a Higgs boson associated with gauge bosons. The criterion for making the \bar QQ bound state is studied. We also show that non-perturbative effects due to gluonic field fluctuations are rather small in such a heavy quark sector. Possible enhancement for productions and decays of \bar QQ bound states ma…
We study quarkonium correlators and spectral functions at zero and finite temperature in QCD with only heavy quarks using potential models combined with perturbative QCD. First, we show that this approach can describe the quarkonium correlation function at zero temperature. Using a class of screened potentials based on lattice calculations of the static quark-antiquark free energy we calculate spectral functions at finite temperature. We find that all quarkonium states, with the exception of the $1S$ bottomonium, dissolve in the deconfined phase at temperatures smaller than $1.5T_c$, in contra…
The heavy quark potential and particularly the one proposed by Richardson to incorporate both asymptotic freedom and linear confinement is analyzed in terms of a generalized Borel Transform recently proposed. We were able to obtain, in the range of physical interest, an approximate analytical expression for the potential in coordinate space valid even for intermediate distances. The deviation between our approximate potential and the numerical evaluation of the Richardson's one is much smaller than $Λ$ of QCD. The $c\overline{c}$ and $b\overline{b}$ quarkonia energy levels agree reasonably wel…
Heavy flavor correlations and Quarkonia production in high energy pp collisions in the EPOS4 framework
本研究利用EPOS4事例产生器分析高能pp碰撞，揭示重味夸克关联如何反映重夸克对产生机制并影响夸克偶素的横动量分布。
Quark Gluon Plasma transport coefficients for heavy quarks and quark-antiquark pairs are computed through an extension of the results obtained for a hot QED plasma by describing the heavy-quark propagation in the eikonal approximation and by weighting the gauge field configurations with the Hard Thermal Loop effective action. It is shown that such a model allows to correctly reproduce, at leading logarithmic accuracy, the results obtained by other independent approaches. The results are then inserted into a relativistic Langevin equation allowing to follow the evolution of the heavy-quark mome…
Quarkonium suppression is one of the most investigated probes of the medium produced in heavy-ion collisions. In this thesis we extend the well-established and successful zero temperature framework of Non-Relativistic (NR) Effective Field Theories (EFTs) (NRQCD, pNRQCD) for the study of heavy quarkonia (production, spectroscopy, decays, ...) to finite temperatures. This is achieved by integrating out in sequence the scales that characterize a NR bound state and those that are typical of a thermal medium, in the possible hierarchies that are relevant for quarkonia in the quark-gluon plasma. Wit…
A formula for an improved spin--dependent potential between a heavy quark and a heavy antiquark was developed using Heavy Quark Effective Theory techniques. The leading logarithmic quark mass terms emerging from loop contributions were explicitly extracted and summed up. There is no renormalization scale dependence in this new formula and it includes both the Eichten--Feinberg formula as well as the one--loop QCD result as special cases. The hyperfine splittings were calculated using the spin--spin part of this improved formula. For charmonium the $J/ψ$-$η_c$ $S$-wave splitting agrees well wit…
Decay rates of quarkonia are studied within the framework of NRQCD formalism. The basic parameters of the formalism have been obtained from different potential schemes studied for the spectra of quarkonia. We estimate the heavy quarkonia mass spectra, radiative and leptonic widths and compare them with other contemporary theoretical approaches and experimental results.
We discuss S-wave quarkonia correlators and spectral function using the Wong-potential, and show that these do not agree with the lattice results.
Master equations of the Lindblad type have recently been derived to describe the dynamics of quarkonium states in the quark-gluon plasma. Because their full resolution in three dimensions is very challenging, the equations are often reduced to one dimension. The main ingredient of these equations is the complex potential that describes the binding of the heavy quark-antiquark pairs and their interactions with the medium. In this work, we propose a one-dimensional complex potential parameterized to reproduce at best two key properties -- the temperature-dependent masses of the eigenstates and t…
recently proposed strictly phenomenological static quark-antiquark potential belonging to the generality $V(r)=-Ar^{-α}+κr^β+V_{0}$ is tested with heavy quarkonia in the context of the shifted large N-expansion method. This nonrelativistic potential model fits the spin-averaged mass spectra of the $c\bar{c},$ $b\bar{b}$ and $c% \bar{b}$ quarkonia within a few ${\rm MeV}$ and also the five experimentally known leptonic decay widths of the $c\bar{c}$ and $b% \bar{b}$ vector states. Further, we compute the hyperfine splittings of the bottomonium spectrum as well as the fine and hyperfine splittin…
Rigorous QCD predictions for decay rates of the P-wave states of heavy quarkonia are presented. They are based on a new factorization theorem which is valid to leading order in the heavy quark velocity and to all orders in the running coupling constant of QCD. The decay rates for all four P states into light hadronic or electromagnetic final states are expressed in terms of two phenomenological parameters, whose coefficients are perturbatively calculable. Logarithms of the binding energy encountered in previous perturbative calculations of P-wave decays are factored into a phenomenological par…
n this paper I discuss what we can learn about quarkonium dissociation from lattice-potential based models. Special emphasis is given to results obtained in agreement by different models, and to the relevance of lattice QCD for potential models. Future directions are also discussed.
We study the quarkonia correlators above deconfinement using the potential model with screened temperature-dependent potentials. We find that while the qualitative features of the spectral functions, such as the survival of the 1S state, can be reproduced by potential models, the temperature dependence of the correlators disagree with the recent lattice data.
The melting of a heavy quark-antiquark bound state depends on the screening phenomena associated with the binding energy, as well as scattering phenomena associated with the imaginary part of the potential. We study the imaginary part of the static potential of heavy quarkonia moving in the strongly coupled plasma. The imaginary potential dependence on the velocity of the traveling bound states is calculated. Non-zero velocity leads to increase of the absolute value of the imaginary potential. The enhancement is stronger when the quarkonia move orthogonal to the quark-gluon plasma maximizing t…
We investigate the influence of a homogeneus and constant strong external magnetic field on the heavy-meson spectrum. Quarkonium states $c\bar{c}$ and $b\bar{b}$ are described within a non-relativistic framework and by means of a suitable potential model based on the Cornell parametrization. In particular, in this work we propose a model which takes into account the possible anisotropies emerging at the level of the static quark-antiquark potential, as observed in recent lattice studies. The investigation is perfomed both with and without taking into account the anisotropy of the static potent…
Exotic states in the charmonium family are systematically treated in the framework of simplest model with an effective coulomb-like interaction of heavy quark and antiquark in the presence of static excitation of quark-gluon modes responsible for a nonperturbative term of potential, which provides with the confinement of quarks, in terms of bag over the threshold in the excitation spectrum of vacuum fields. Once the spectrum has got quite a wide mass gap, it allows us to approximate the bag contribution into the potential by a constant value of bag mass at low distances less than the bag size.…
Rapid thermalization in ultra-relativistic heavy-ion collisions leads to fast changing potential between a heavy quark and antiquark from zero temperature potential to the finite temperature one. Time dependent perturbation theory can then be used to calculate the survival probability of the initial quarkonium state. In view of very short time scales of thermalization at RHIC and LHC energies, we calculate the survival probability of $J/ψ$ and $Υ$ using sudden approximation. Our results show that quarkonium decay may be significant even when temperature of QGP remains low enough so that the co…
Here I review the temperature-dependence of heavy quarkonia correlators in potential models with three different screened potentials, and compare these to the results from lattice QCD. None of the potentials investigated yield results consistent with the lattice data, indicating that screening is likely not the mechanism for heavy quarkonia suppression. I also discuss a simple toy model, not based on temperature-dependent screening, that can reproduce the lattice results.
The mass spectra and decay properties of heavy quarkonia are computed in nonrelativistic quark-antiquark Cornell potential model. We have employed the numerical solution of Schrödinger equation to obtain their mass spectra using only four parameters namely quark mass ($m_c$, $m_b$) and confinement strength ($A_{c\bar c}$, $A_{b\bar b}$). The spin hyperfine, spin-orbit and tensor components of the one gluon exchange interaction are computed perturbatively to determine the mass spectra of excited $S$, $P$, $D$ and $F$ states. Digamma, digluon and dilepton decays of these mesons are computed usin…
We study the diffractive electroproduction of quarkonia from quark-antiquark-gluon states in the photon wave function. We show that these states contribute to the leading-power and leading-logarithm level. We suggest the measurement of J/psi production via inelastic diffraction to study color-transparency and color-opacity effects in the diffractive gluon distribution.
A systematic study of a wide class of nonrelativistic models of $b\overline{b}$ quarkonia is described. It is found that the potential $V(r) = 0.706380(\sqrt{r} - \frac{0.460442}{r}) + 8.81715$ (all in GeV) with the $b$-quark mass $m_b = 4.80303$ GeV gives a satisfactory description of the experimental data below the threshold for strong decays ($ χ^2/DF = 6.5/7$). Limitations and implications of this observation are discussed.
Some of the non-relativistic QQ/bar interaction potentials and its isospectral partner-potentials have been employed to evaluate the masses and leptonic decay widths of Charmonium and Upsilon states. An attempt has been made to develop a prescription to provide a simultaneous fit to Masses and leptonic decay widths of Quarkonia. Preliminary calculation shows that the class of isospectral-potentials corresponding to: V(r)= -(alphas/r)+ar^n appears to yield the desired results. The various associated theoretical and phenomenological issues are discussed in light of recent data. The possible rela…
We review non-perturbative static potentials commonly used in potential models for quarkonia at finite T. Potentials derived from Polyakov loop correlators are shown to be inappropriate for this purpose. The q\bar{q} free energy is physical but has the wrong spatial decay and perturbative limit. The so-called singlet free energy is gauge dependent and unphysical. An appropriate static real time potential can be defined through a generalisation of pNRQCD to finite T. In perturbation theory, its real part reproduces the Debye-screened potential, its imaginary part accounts for Landau damping. Po…
We update our recent calculation of quarkonium Euclidean correlators at finite temperatures in a potential model by including the effect of zero modes in the lattice spectral functions. These contributions cure most of the previously observed discrepancies with lattice calculations, supporting the use of potential models at finite temperature as an important tool to complement lattice studies.
Truncation of the Radial Ladder in Heavy Quarkonia
本研究针对重夸克偶素径向激发阶梯是否有限截断的问题，用高斯展开法求解屏蔽Godfrey--Isgur哈密顿量，首次定量给出粲偶素和底偶素的径向激发上限，且该判据可通过未来实验数据检验。
Heavy quarkonia in QGP medium in an arbitrary magnetic field
本文利用Schwinger固有时方法计算任意磁场下QGP中的重夸克偶素复势，揭示其各向异性，并评估磁场对偶极取向、热宽度及强场近似的影响。
We examine to what extent several recently discovered narrow resonances can be interpreted as conventional $c\bar{c}$ bound states describable using a potential model. In doing so, we use a semirelativistic approach, which includes both the $v^2/c^2$ and QCD one-loop corrections to the short distance potential and a long range linear potential together with its scalar and vector $v^2/c^2$ spin-dependent terms.
We compute derived quantities for various values of the model parameter of the Cornell potential model for the S-wave heavy quarkonia with radial quantum numbers n=1, 2, and 3. Our results can be used to determine leading and relative-order-v^2 nonrelativistic quantum chromodynamics matrix elements for S-wave charmonia and bottomonia such as psi(2S), eta_c(2S), and Upsilon(nS) for n=1, 2, and 3. These matrix elements will be essential ingredients for resumming relativistic corrections to processes involving those S-wave heavy quarkonium states.
We present a more general form of the Schrödinger equation in curvilinear space that is exposed to external fields. Thereby, we solve the wave equation with the Cornell plus harmonic potentials (CHP) under the influence of the magnetic and Aharonov-Bohm (AB) flux fields using curvilinear coordinates system in such space. With this requirement, the energy spectrum and the corresponding wave functions are calculated by means of the series method. The mass spectrum of both charmonium and bottomonium states consisting of quark and antiquark are calculated. In addition, the main thermodynamic funct…
The N-dimensional radial Schrödinger equation has been solved using the analytical exact iteration method (AEIM), in which the Cornell potential is generalized to finite temperature and chemical potential. The energy eigenvalues have been calculated in the N-dimensional space for any state (n, l). The present results have been applied for studying quarkonium properties such as charmonium and bottomonium masses. The binding energies and the mass spectra of heavy quarkonia are studied in the N-dimensional space. The dissociation temperatures for different states of heavy quarkonia are calculated…
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.
Heavy $c\bar c$ and $b\bar b $ quarkonia are considered as systems confined within a hard-wall potential shaped after a linear combination of a cotangent-- with a square co-secant function. Wave functions and energy spectra are then obtained in closed forms in solving by the Nikiforov-Uvarov method the associated radial Schrödinger equation in the presence of a centrifugal term. The interest in this potential is that in one parametrization it can account for a conformal symmetry of the strong interaction, and in another for its perturbation, a reason for which we here employ it to study status…
The $Q \bar{Q}$ semirelativistic interaction in QCD can be expressed in terms of the Wilson loop and its functional derivatives. In this framework we discuss the complete (velocity and spin dependent) $1/m^2$ potential in the stochastic vacuum model and in the dual theory.
Heavy quarkonia, Bc-meson, and CS-meson masses are calculated within the framework of the N-dimensional radial Schrodinger equation. The Cornell potential is extended by including the harmonic oscillator potential. The energy eigenvalues and the corresponding wave functions are calculated in the N-dimensional space using the Nikiforov-Uvarov (NV) method. The energy eigenvalues are obtained in the three-dimensional space. The mass of spectra of charmonium, bottomonium, and mesons are calculated. The effect of dimensionality number on the mass of quarkonium is investigated. A comparison with oth…
Heavy quarkonia and new hadrons with two heavy quarks
本文教学式综述重夸克偶素及含两个重夸克的奇特强子，重点讨论违背夸克模型的XYZ态及其对非微扰QCD和夸克禁闭研究的挑战。
We investigate the Mott effect for heavy quarkonia due to Debye screening of the heavy quark potential in a plasma of massless quarks and antiquarks. The influence of residual color correlation is investigated by coupling the light quark sector to a temporal gauge field driven by the Polyakov loop potential. This leads to an increase of the Mott dissociation temperatures for quarkonia states which stabilizes in particular the excited states, but has marginal effect on the ground states.
We solve the Bethe-Salpeter equation for a system of a heavy quark-antiquark pair interacting with a screened linear confining potential. First we show the spinless QFT model is inadequate and fail to describe even gross feature of the quarkonia spectrum. In order to get reliable description the spine degrees of freedom has to be considered. Within the approximation employed we reasonably reproduce known radial excitation of vector charmonium. The BSE favors relatively large string breaking scale $μ\simeq 350MeV$ . Using free charm quark propagators we observe that $J/Ψ$ is the only charmonium…
Decay rates of $c\bar c$ and $b\bar b$ mesons have been studied within the NRQCD formalism. The basic parameters of the formalism have been obtained from different potential schemes studied for the quarkonia spectra. The present results are compared with other potential model results with and without correction terms proposed through hard gluon processes involved in the decay.
This is the third paper on hadronic light front wave functions (LFWFs). We derive a light front Hamiltonian from first principles using the key features of the QCD vacuum at low resolution. In the first approximation, it gives transverse oscillator and longitudinal harmonic modes and yields the correct Regge trajectories. For heavy quarkonia, we compare its spectrum to that obtained from the usual Schroedinger equation in the rest frame. We use the same approach for light quarks, and investigate the role of confinement and chiral symmetry breaking in the quark-antiquark sector. We then study s…
Experimental data for $b\bar{b}$ quarkonia have been compared with the predictions of a variety of nonrelativistic quark models. It is found that a potential $a\sqrt{r} - b/r +$ const gives good agreement, while many others do not. Some implications of this observation are discussed.
We investigate the effects of including the full three-loop QCD correction to the static short distance $1/r$ potential on the spectroscopy and decays in the charmonium and upsilon systems. We use a variational technique with the full three-loop corrected potential to determine a set of unperturbed trial wave functions and treat the relativistic and one-loop corrections as perturbations. The perturbed results are compared to the subset of the charmonium and upsilon spectra using a $χ^2$ test. This approach results in more accurate descriptions of the hyperfine splittings in both the $b\bar{b}$…
In the high-temperature quark-gluon plasma and its subsequent hadronic matter created in a high-energy nucleus-nucleus collision, the quark-antiquark potential depends on the temperature. The temperature-dependent potential is expected to be derived from the free energy obtained in lattice gauge theory calculations. This requires one to study the relation between the quark-antiquark potential and the quark-antiquark free energy. When the system's temperature is above the critical temperature, the potential of a heavy quark and a heavy antiquark almost equals the free energy, but the potential …
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