We study the charmonium spectrum using a complete one gluon exchange approach based on a phenomenological relativistic $q\bar{q}$ potential model with Dirac spinors in momentum space. We use phenomenological screening factors to include vacuum quantum effects. Our formulation does not rely on nonrelativistic approximations. We fit the lowest-lying charmonia (below the $D\bar{D}$ threshold) and predict the higher-lying resonances of the spectrum. In general, we reproduce the overall structure of the charmonium spectrum and, in particular, we can reasonably describe the $X(3872)$ resonance mass as (mostly) a $c\bar{c}$ state. The numerical values of the free parameters of the model are determined taking into account also the experimental uncertainties of the resonance energies. In this way, we are able to obtain the uncertainties of the theoretical resonance masses and the correlation among the free parameters of the model.
Charmonia produced in initial hard parton scatterings during heavy ion collisions move with respect to the medium rather than flow with the medium. Lattice studies suggest that charmonium bound states at the rest are dissociated at $T\gtrsim 1.5 T_c$. We present results on momentum dependences of charmonium properties in a hot medium from lattice QCD Monte Carlo simulations. The dispersion relation of the screening mass and the change of correlation and spectral functions at various temperatures and momenta are discussed.
We investigate charmonium production in the hot medium created by heavy-ion collisions by setting up a framework in which in-medium charmonium properties are constrained by thermal lattice QCD (lQCD) and subsequently implemented into kinetic approaches. A Boltzmann transport equation is employed to describe the time evolution of the charmonium phase space distribution with the loss and gain term accounting for charmonium dissociation and regeneration (from charm quarks), respectively. The momentum dependence of the charmonium dissociation rate is worked out. The dominant process for in-medium …
Transport and Langevin equations are employed to study hadronic medium effects on charmonium elliptic flows in heavy-ion collisions. In Pb-Pb collisions, the anisotropic energy density of the quark-gluon plasma (QGP) in the transverse plane is transformed into hadron momentum anisotropy after the phase transition. Charmonia with high transverse momentum $p_T$ are produced via the primordial hard process and undergo different degrees of dissociation along different paths in the QGP. They then scatter with light hadrons in the hadron phase. Both contributions to the charmonium elliptic flows are…
We compute correlators and spectral functions for J/psi and eta_c mesons at nonzero momentum on anisotropic lattices with Nf=2. We find no evidence of significant momentum dependence at the current level of precision. In the pseudoscalar channel, the ground state appears to survive up to T~450MeV or 2.1T_c. In the vector channel, medium modifications may occur at lower temperatures.
We analyze the transverse momentum distribution of $J/ψ$ mesons produced in Au + Au collisions at the top RHIC energy within a blast-wave model that accounts for a possible inhomogeneity of the charmonium distribution and/or flow fluctuations. The results imply that the transverse momentum spectra of$J/ψ$, $ϕ$ and $Ω$ hadrons measured at the RHIC can be described well if kinetic freeze-out takes place just after chemical freeze-out for these particles.
In this paper we have solved the nonrelativistic form of the Lippmann-Schwinger equation in the momentum-helicity space by inserting a spin-dependent quark-antiquark potential model numerically. To this end, we have used the momentum-helicity basis states for describing a nonrelativistic reduction of one gluon exchange potential. Then we have calculated the mass spectrum of the charmonium $ψ(c\bar{c})$, and finally we have compared the results with the another theoretical results and experimental data.
A collision of a light meson and a charmonium produces quarks and antiquarks first, then the charm quark fragments into a charmed hadron, and finally three or more mesons are produced. This is the mechanism that we consider and propose to understand the prompt-J/psi nuclear modification factor in the range of J/psi transverse momentum from 10 GeV/c to 18 GeV/c, as measured by the CMS Collaboration and the ATLAS Collaboration. Unpolarized cross sections are derived and calculated for the reactions pion+charmonium ->H_c+X with H_c being a charmed meson. Numerical cross sections are parametrized …
We study the properties of charmonium in a strongly coupled QCD-like plasma at finite momentum. As a basis for this study, a "bottom-up" holographic model is used which has been previously shown to reproduce charmonium phenomenology in vacuum and give a reasonable dissociation temperature at zero momentum. The finite momentum spectral functions are presented and found to be consistent with recent lattice results. The in-medium dispersion relation and momentum dependence of decay width of J/Psi have also been studied. We find no signature of a subluminal limiting velocity from the dispersion re…
We propose the study of unpolarized transverse momentum dependent gluon parton distributions as well as the effect of linearly polarized gluons on transverse momentum and rapidity distributions of $J/ψ$ and $Υ$ production within the framework of transverse momentum dependent factorization employing color evaporation model (CEM) in unpolarized proton-proton collision. We estimate the transverse momentum and rapidity distributions of $J/ψ$ and $Υ$ at LHCb, RHIC and AFTER energies using TMD evolution formalism.
We calculate the double charmonium production cross section within the framework of $4\times 4$ Bethe-Salpeter Equation in the electron-positron annihilation, at center of mass energy $\sqrt{s}= 10.6$GeV, that proceeds through the exchange of a single virtual photon. In this calculation, we make use of the full Dirac structure of 4D BS wave functions of these charmonia, with the incorporation of all the Dirac covariants (both leading and sub-leading). The calculated cross-sections for the double charmonium productions for final states, ($J/Ψ, η_c$); ($Ψ',η_c$) ; ($J/Ψ, η_c'$); and ($Ψ',η_c'$) …
The elaborate analysis of spectrum of charmonium states and charmed hybrids in the mass region over DD-threshold is given. The combined approach based on the potential model and relativistic spherical symmetric top model for decay products has been proposed. The experimental data from different collaborations were analyzed. Especial attention was given to the new states with the hidden charm discovered recently. Eight of these states may be interpreted as higher laying radial excited charmoniumstates. Butmuchmore data on different decay modes are needed for deeper analysis. These data can be d…
Lorentz scalar and mass interactions are studied in more detail in the framework of a reduced Dirac equation for heavy quark-antiquark mesons. A microscopic model for these interactions is proposed and analyzed. The charmonium mass spectrum is reproduced by means of two free parameters; a third parameter is fixed by means of a phenomenological hypothesis in accordance with the model.
A previously introduced reduction of the Dirac equation is used to study the Charmonium spectrum. A regularized vector potential that only depends on the coupling constant and on the regularization radius is adopted, considering the interacting quark as an extended source of the Chromo-electric field. A scalar interaction is also introduced with some constraints for its parameters. A good description of the structure of the Charmonium spectrum is obtained with only three free parameters.
We study the possibility to probe the unpolarized and linearly polarized transverse momentum- dependent gluon distributions in unpolarized pp collision in charmonium and bottomonium produc- tion, employing non-relativistic QCD (NRQCD) based color octet model within transverse momentum dependent (TMD) factorization framework. The transverse momentum (p T ) and rapidity distributions of J/ψ and Υ(1S) at LHCb, RHIC and AFTER energies are estimated. Significant modulations in transverse momentum spectrum of quarkonium in the low p T region is obtained when contributions of linearly polarized gluon…
We calculate the production of large-pTcharmonium and narrow resonance state (exotic charmonium) in proton-proton, proton-nucleus, and nucleus-nucleus collisions with the semi-coherent two-photon interactions at Relativistic Heavy Ion Collider (RHIC), Large Hadron Collider (LHC), and Future Circular Collider (FCC) energies. Using the large quasi-real photon fluxes, we present the γγ->H differential cross section for charmonium and narrow resonance state production at large transverse momentum in ultra-peripheral heavy ion collisions. The numerical results demonstrate that the experimental stud…
A charmonium produced in heavy ion collisions at RHIC and LHC propagates through a dense co-moving matter with a rather high relative momentum, <p_T^2>=4-10GeV^2. In spite of Debye screening of the binding potential, the charmonium survives with a substantial probability, even if the c-cbar potential is completely screened in the hot environment. In addition, the color-exchange interaction with the medium is another important source of charmonium suppression. Attenuation in a hot medium caused by both effects is evaluated by means of the path integral technique, which requires ability of boost…
$J/ψ$ observables of p+p collisions at $\sqrt{s}=$ 200 GeV and 2.76 TeV are calculated using the PYTHIA event generator for the production of $c$ and $\bar c$ and the Wigner density formalism. The charm quark momentum from PYTHIA is tuned in such a way that the transverse momentum and rapidity distribution correspond to the Fixed-Order Next-to-Leading Logarithm (FONLL) calculations and hence to the experimental data for open charm mesons. Using the Wigner density of the charmonium wave function we calculate for each charm quark pair the probability to form a charmonium. As a result, the experi…
The phenomenological analysis of various characteristics of $J/ψ$ and $D$ meson production in PbPb collisions at the center-of-mass energy 2.76 TeV per nucleon pair is presented. The data on momentum spectra and elliptic flow are reproduced by two-component model HYDJET++ including thermal and non-thermal charm production mechanisms. The significant part of $D$-mesons is found to be in a kinetic equilibrium with the created medium, while $J/ψ$-mesons are characterized by earlier (as compared to light hadrons) freeze-out.
Starting from the Feynman diagram representation of multiple scattering we consider the polarized $χ_c$(1P)-charmonia production in antiproton-nucleus reactions close to the threshold ($p_{\rm lab}=5-7$ GeV/c). The rescattering and absorption of the incoming antiproton and outgoing charmonium on nucleons are taken into account, including the possibility of the elastic and nondiagonal (flavor-conserving) scattering $χ_{cJ} N \to χ_{cJ^\prime} N$, $J,J^\prime=0,1,2$. The elementary amplitudes of the latter processes are evaluated by expanding the physical $χ_c$-states in the Clebsch-Gordan serie…
We calculate the decay widths of the charmonium states, $J/ψ$, $ψ(3686)$ and $ψ(3770)$, to $D\bar D$ pairs, as well as the decay width of $D^* \rightarrow Dπ$, in isospin asymmetric strange hadronic matter, using a field theoretical model for composite hadrons with quark constituents. For this purpose we use the quark antiquark pair creation term of the free Dirac Hamiltonian written in terms of the constituent quark field operators, and use explicit charmonium, $D$, $\bar {D}$, $D^*$ and $π$ states to evaluate the matrix elements for the charmonium as well as $D^*$ decay amplitudes. The mediu…
Recently it has been put forward that linearly polarized gluons inside unpolarized protons affect the transverse momentum distribution of final state particles in hadronic collisions. They lead to a characteristic modulation of the differential cross section in Higgs production and to azimuthal asymmetries in, for instance, heavy quark pair production. Here we study the effect on charmonium and bottomonium production in hadronic collisions, such as at LHCb and at the proposed fixed target experiment AFTER at LHC. We focus mainly on the scalar and pseudoscalar quarkonia, eta_c, chi_{c0}, eta_b,…
The mass spectra of charmonium are investigated using a Coulomb plus linear (Cornell) potential. Gaussian wave function in position space as well as in momentum space are employed to calculate the expectation value of potential and kinetic energy respectively. Various experimental states ($X(4660)(5^{3}S_{1})$, $X(3872)(2^{3}P_{1})$, $X(3900)(2^{1}P_{1})$, $X(3915)(2^{3}P_{0})$ and $X(4274)(3^{3}P_{1})$ etc.) are assigned as charmonium states. We also study the Regge trajectories, pseudoscalar and vector decay constants, the Electric and Magnetic dipole transition rates and the annihilation de…
Confinement indicates an asymptotic quark state not observable except its energy is zero. Unitarity indicates that the total probability of a definite state of quark system to transit to any final state is exactly one. This talk reviews some important conclusions/predictions from the basic properties like unitarity of the combination model, as addressed by the title. We also in the Postscript section address the bottom quark energy loss. In the discussions around the dinner table in the Rencontre, the author combined the large transverse momentum J/Psi suppression and the contribution to J/Psi…
The total cross section of the process $e^+e^- \to Λ\barΛ$ is calculated within the energy range close to the mass of $ψ(3770)$ charmonium state. Two different contributions were considered: the $D$-meson loop and the three gluon charmonium annihilation one. Both of them contribute noticeably and in sum fairly reproduce the data. Large relative phase for these contributions are generated with respect to the pure electromagnetic mechanism. As a by product the fit for the electromagnetic form factor of $Λ$-hyperon is obtained for the large momentum transferred region.
The decay widths of the charmonium states to $D\bar D$ in isospin asymmetric nuclear matter in the presence of a magnetic field are studied, using a field theoretical model for composite hadrons with quark/antiquark constituents. The medium modifications of these partial decay widths arise due to the changes in the masses of the decaying charmonium state and the produced $D$ and $\bar D$ mesons in the magnetized hadronic matter, calculated within a chiral effective model. The decay widths are computed using the light quark--antiquark pair creation term of the free Dirac Hamiltonian in terms of…
Central and spin-spin potentials for charmonium, constructed from Nambu-Bethe-Salpeter amplitudes in lattice simulations of full QCD, are matched with results from perturbative QCD at an appropriate distance scale. This matching is made possible by defining the perturbative potentials through Fourier transforms with a low-momentum cutoff. The central (spin-independent) potential is compared with potentials derived from an expansion in powers of the inverse quark mass. A well-controlled continuation of the charmonium spin-spin potential from lattice QCD to short distances is performed. The mass…
We calculate the combined angular distribution functions of the polarized photons ($γ_1$ and $γ_2$) and electron ($e^-$) produced in the cascade process $\bar{p}p\rightarrow$ $^3D_3\rightarrow$ $^3P_2+γ_1\rightarrow$ $(ψ+γ_2)+γ_1\rightarrow(e^++e^-)+γ_1+γ_2$, when the colliding $\bar{p}$ and $p$ are unpolarized. Our results are independent of any dynamical models and are expressed in terms of the spherical harmonics whose coefficients are functions of the angular-momentum helicity amplitudes of the individual processes. Once the joint angular distribution of ($γ_1$, $γ_2$) and that of ($γ_2$, …
Momenta of charmonia created in Pb-Pb collisions at the Large Hadron Collider are so large that three or more mesons may be produced when the charmonia collide with light mesons in hadronic matter. We study the meson-charmonium collision in a mechanism where the collision produces two quarks and two antiquarks, the charm quark then fragmenting into charmed mesons, and the other three constituents as well as quarks and antiquarks created from vacuum give rise to two or more mesons. The absolute square of the transition amplitude for the production of two quarks and two antiquarks is derived fro…
In this work, we calculate the total cross sections and the center-of-mass frame angular distributions of the charmonium production plus a light meson by the low energy $p\bar{p}$ interaction. The results of $p\bar{p}\to π^0 Ψ$ with and without form factor (FF) indicate that the FF contribution in the calculation cannot be ignored. The obtained cross section of $p\bar{p}\to π^0 J/ψ$ with FF can fit the E760 data well. We also predict the total cross sections and the center-of-mass frame angular distributions of $p\bar{p}\to ωΨ$, which show that these physical quantities are dependent on Pauli …
Many mesons with properties incompatible with a $\bar cc$ structure have already been discovered, e.g. the $Z_c$ mesons with isospin 1. We investigate the spectrum of exotic charmonium-like mesons using lattice QCD. The focus is on $\bar cc \bar qq$ states with $J^{PC}=1^{+\pm}$ and isospin 1. This is the first study of four-quark states with these quantum numbers, a non-zero total momentum and two different lattice volumes. We extract the energy levels and determine the scattering length for $D\bar D^*$ scattering close to the threshold using Lüscher's formalism. Our preliminary results show …
In this work we calculate the mass spectrum, weak decay constants, two photon decay widths, and two gluon decay widths of ground (1S), and radially excited (2S,3S,...) states of pseudoscalar charmoniuum and bottomonium such as $η_{c}$ and $η_{b}$, as well as the mass spectrum and leptonic decay constants of ground state (1S), excited (2S,1D,3S,2D,4S,and 3D) states of vector charmonium and bottomonium such as $J/ψ$, and $Υ$, using the formulation of Bethe-Salpeter equation under covariant Instantaneous Ansatz (CIA). Our results are in good agreement with data (where ever available) and other mo…
A Crucial Test for Color-Octet Production Mechanism in Z^0 Decays
计算了$Z^0$衰变过程中$D$波charmonia的直接产生率.与其他$D$波粲偶素产生机制相比，色八隅体产生过程$Z^0\rightarrow ^3D_J(c\bar c) q\bar q$具有明显的大分支比，与$J/ψ$产生过程具有相同的数量级。这可能是测试色八重态机制以及观察$Z^0$衰变中$D$波粲偶素态的一个关键通道。此外，在Tevatron上，还应该观察到与$J/ψ$或$ψ^\prime$一样强的$^3D_J$粲偶素的信号，其具有大的横向动量。
We present a method for the measurement of parameters of elastic and inelastic interactions of charmonium with hadrons. In this technique, we use femtoscopic analysis of charmonium-hadron correlations at low relative momentum and the Lednicky-Lyuboshitz analytical model to extract the interaction parameters. We argue that such a study is already feasible in the LHCb experiment at the LHC, and we discuss the prospects for studies in the STAR at RHIC and other experiments at the LHC.
The potential between charm and anti-charm quarks is calculated non-perturbatively using physical, rather than static quarks at temperatures on both sides of the deconfinement transition $T_{\rm C}$, using a lattice simulation with 2+1 dynamical quark flavours. We used the HAL QCD time-dependent method, originally developed for inter-nucleon potentials. Our lattices are anisotropic, with temporal lattice spacing less than the spatial one which enhances the information content of our correlators at each temperature. Local-extended charmonium correlators were calculated efficiently by contractin…
