We compare the results of a numerical lattice QCD calculation of the charmonium spectrum with the structure of a general non-relativistic potential model. To achieve this we form the non-relativistic reduction of derivative-based fermion bilinear interpolating fields used in lattice QCD calculations and compute their overlap with c-cbar meson states at rest constructed in the non-relativistic quark model, providing a bound-state model interpretation for the lattice data. Essential gluonic components in the bound-states, usually called hybrids, are identified by considering interpolating fields that involve the gluonic field-strength tensor and which have zero overlap onto simple c-cbar model states.
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 extend the formalism based on perturbative QCD that was developed in our previous work, and compute the hyperfine splittings of the bottomonium spectrum as well as the fine and hyperfine splittings of the charmonium spectrum. All the corrections up to O(alpha_s^5 m) are included in the computations. We find agreement (with respect to theoretical uncertainties) with the experimental values whenever available and give predictions for not yet observed splittings.
The ground and first excited states of the hybrid charmonium ${\bar c} c g$, with non-exotic quantum numbers $J^{PC}=0^{-+}$, $1^{--}$ and $1^{++}$ are investigated using quenched lattice QCD. They are completely ignored in the literature, only because their ground states are degenerate with $η_c$, $J/ψ$, and $χ_{c1}$, and are difficult to be distinguished from these conventional charmonium mesons in experiment. However, we observe strong gluonic radial excitations in the first excited states; We predict that their masses are 4.352(225)GeV, 4.379(149)GeV and 7.315(257)GeV, completely different…
We present both spin-independent and -dependent parts of a central interquark potential for charmonium states, which is calculated in 2+1 flavor dynamical lattice QCD using the PACS-CS gauge configurations with a lattice cutoff of a^{-1}~2.2 GeV. Our simulations are performed with a relativistic heavy quark action for the charm quark at the lightest pion mass, M_π=156(7) MeV, in a spatial volume of 3fm^3. We observe that the spin-independent charmonium potential obtained from lattice QCD with almost physical quark masses is quite similar to the Conrnell potential used in non-relativistic poten…
Charmonium properties at high temperatures from lattice QCD
Fakultät für Physik, Universität Bielefeld（比勒费尔德大学物理系）；Physics Department, Brookhaven National Laboratory（布鲁克海文国家实验室物理系）；Institut für Kernphysik, Technische Universität Darmstadt（达姆施塔特工业大学核物理研究所）；Werner-Heisenberg-Gymnasium Bad Dürkheim（巴特迪尔凯姆维尔纳·海森堡中学）
We report on a study of charmonium at high temperature in 2-flavour QCD. This is the first such study with dynamical fermions. Using an improved anisotropic lattice action, spectral functions are extracted from correlators in the vector and pseudoscalar channels. No signs of medium-induced suppression of the ground states are seen for temperatures up to 1.5T_c, while at T~2T_c there are clear signs of modifications. The current systematic and statistical uncertainties in our data, in particular the relatively coarse lattice and small volume, do not allow us to draw a firm conclusion at this st…
We study spatial correlation functions of charmonium in 2+1 flavor QCD using an improved staggered formulation. Contrary to the temporal correlation functions the spatial correlation functions exhibit a strong temperature dependence above the QCD transition temperature. Above this temperature they are sensitive to temporal boundary conditions. Both features become significant at a temperature close to 1.5 Tc and suggest corresponding modifications of charmonium spectral functions.
We present a study for charmonium radiative transitions: $J/ψ\rightarrowη_cγ$, $χ_{c0}\rightarrow J/Ψγ$ and $h_c\rightarrowη_cγ$ using $N_f=2$ twisted mass lattice QCD gauge configurations. The single-quark vector form factors for $η_c$ and $χ_{c0}$ are also determined. The simulation is performed at a lattice spacing of $a= 0.06666$ fm and the lattice size is $32^3\times 64$. After extrapolation of lattice data at nonzero $Q^2$ to 0, we compare our results with previous quenched lattice results and the available experimental values.
We present spin-independent and spin-spin interquark potentials for charmonium states, that are calculated using a relativistic heavy quark action for charm quarks on the PACS-CS gauge configurations generated with the Iwasaki gauge action and 2+1 flavors of Wilson clover quark. The interquark potential with finite quark masses is defined through the equal-time Bethe-Salpeter amplitude. The light and strange quark masses are close to the physical point where the pion mass corresponds to $M_π\approx 156(7)$ MeV, and charm quark mass is tuned to reproduce the experimental values of $η_c$ and $J/…
We compute charmonium spectral functions in 2-flavor QCD on anisotropic lattices using the maximum entropy method. Our results suggest that the S-waves (J/psi and eta_c) survive up to temperatures close to 2Tc, while the P-waves (chi_c0 and chi_c1) melt away below 1.2Tc.
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 study the properties of charmonium states at finite temperature in quenched lattice QCD on large and fine isotropic lattices. We perform a detailed analysis of charmonium correlation and spectral functions both below and above Tc. Our analysis suggests that the S wave states disappear at about 1.5 Tc. The charm diffusion coefficient is estimated and found to be approximately 1/πT at 1.5Tc {\leq} T {\leq} 3Tc.
I briefly review Non-Relativistic QCD and related effective theories, and discuss applications to heavy quarkonium decay, and production in electron-positron colliders.
We perform an exploratory lattice QCD simulation of $D \bar D$ scattering, aimed at determining the masses as well as the decay widths of charmonium resonances above open charm threshold. Neglecting coupling to other channels, the resulting phase shift for $D \bar D$ scattering in p-wave yields the well-known vector resonance $ψ(3770)$. For $m_π= 156$ MeV, the extracted resonance mass and the decay width agree with experiment within large statistical uncertainty. The scalar charmonium resonances present a puzzle, since only the ground state $χ_{c0}(1P)$ is well understood, while there is no co…
We present a spectrum of highly excited charmonium mesons up to around 4.5 GeV calculated using dynamical lattice QCD. Employing novel computational techniques and the variational method with a large basis of carefully constructed operators, we extract and reliably identify the continuum spin of an extensive set of excited states, states with exotic quantum numbers (0+-, 1-+, 2+-) and states with high spin. Calculations are performed on two lattice volumes with pion mass approximately 400 MeV and the mass determinations have high statistical precision even for excited states. We discuss the re…
We study the charmonium spectrum including higher spin and gluonic excitations. We determine an upper limit on the mixing of the eta_c ground state with light pseudoscalar flavour-singlet mesons and investigate the mixing of charmonia near open charm thresholds with pairs of (excited) D and anti-D mesons. For charm and light valence quarks and nF=2 sea quarks, we employ the non-perturbatively improved Sheikholeslami-Wohlert (clover) action. Excited states are accessed using the variational technique, starting from a basis of suitably optimised operators. For some aspects of this study, the use…
We compute charmonium spectral functions in 2-flavour QCD using the maximum entropy method and anisotropic lattices. We find that the S-waves (J/psi and eta_c) survive up to temperatures close to 2T_c, while the P-waves (chi_c0 and chi_c1) melt away below 1.3T_c.
We present highly-excited charmonium, $D_s$ and $D$ meson spectra from dynamical lattice QCD calculations with light quarks corresponding to $M_π \sim 240$ MeV and compare these to previous results with $M_π \sim 400$ MeV. Utilising the distillation framework, large bases of carefully constructed interpolating operators and a variational procedure, we extract and reliably identify the continuum spin of an extensive set of excited mesons. These include states with exotic quantum numbers which, along with a number with non-exotic quantum numbers, we identify as having excited gluonic degrees of …
We show that both hard perturbative and soft non-perturbative QCD effects are important in hadroproduction of charmonium. Observed $x_F$ and $p_\perp$ distributions of J/psi in fixed target experiments can be well described by our Monte Carlo model based on perturbative QCD and the Color Evaporation Model.
We review selected lattice results on the charmonium spectrum and first attempts to search for the existence of exotic states. The hadro-quarkonium model was proposed to interpret some of the exotic states as a quarkonium core inside a hadron. We present a lattice study of the hadro-quarkonium model in the limit of static quarks. The charm quark decouples in low energy observables and binding energies of charmonium. In a model calculation we are able to evaluate the corrections to decoupling of the charm quark in the continuum.
The charmonium mass spectrum is considered in the framework of the constituent quark model with the relativistic treatment of the c quark. The obtained masses are in good agreement with the existing experimental data including the mass of eta_c(2S).
We study the properties of charmonium states at finite temperature in quenched QCD on large and fine isotropic lattices. We perform a detailed analysis of charmonium correlation and spectral functions both below and above $T_c$. Our analysis suggests that both S wave states ($J/ψ$ and $η_c$) and P wave states ($χ_{c0}$ and $χ_{c1}$) disappear already at about $1.5 T_c$. The charm diffusion coefficient is estimated through the Kubo formula and found to be compatible with zero below $T_c$ and approximately $1/πT$ at $1.5 T_c\lesssim T\lesssim 3 T_c$.
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.
Axial vector $(J^{PC}=1^{++})$ charmonium and bottomonium hybrid masses are determined via QCD Laplace sum-rules. Previous sum-rule studies in this channel did not incorporate the dimension-six gluon condensate, which has been shown to be important for $1^{--}$ and $0^{-+}$ heavy quark hybrids. An updated analysis of axial vector charmonium and bottomonium hybrids is presented, including the effects of the dimension-six gluon condensate. The axial vector charmonium and bottomonium hybrid masses are predicted to be 5.13 GeV and 11.32 GeV, respectively. We discuss the implications of this result…
Charmonium is an attractive system for the application of lattice QCD methods. While the sub-threshold spectrum has been considered in some detail in previous works, it is only very recently that excited and higher-spin states and further properties such as radiative transitions and two-photon decays have come to be calculated. I report on this recent progress with reference to work done at Jefferson Lab.
We compute, for the first time using lattice QCD methods, radiative transition rates involving excited charmonium states, states of high spin and exotics. Utilizing a large basis of interpolating fields we are able to project out various excited state contributions to three-point correlators computed on quenched anisotropic lattices. In the first lattice QCD calculation of the exotic 1-+ eta_c1 radiative decay, we find a large partial width Gamma(eta_c1 -> J/psi gamma) ~ 100 keV. We find clear signals for electric dipole and magnetic quadrupole transition form factors in chi_c2 -> J/psi gamma,…
Working with a large basis of covariant derivative-based meson interpolating fields we demonstrate the feasibility of reliably extracting multiple excited states using a variational method. The study is performed on quenched anisotropic lattices with clover quarks at the charm mass. We demonstrate how a knowledge of the continuum limit of a lattice interpolating field can give additional spin-assignment information, even at a single lattice spacing, via the overlap factors of interpolating field and state. Excited state masses are systematically high with respect to quark potential model predi…
Hard and soft QCD dynamics are both important in charmonium hadroproduction, as presented here through a next-to-leading order QCD matrix element calculation combined with the colour evaporation model. Observed $x_F$ and $p_\perp$ distributions of $J/ψ$ in hadroproduction are reproduced. Quite similar results can also be obtained with a Monte Carlo event generator where \ccbar pairs are instead produced through leading order matrix elements and the parton shower approximation of higher order processes. The soft dynamics may alternatively be described by the soft colour interaction model. We al…
Radiative transitions between charmonium states offer an insight into the internal structure of heavy-quark bound states within QCD. We compute, for the first time within lattice QCD, the transition form-factors of various multipolarities between the lightest few charmonium states. In addition, we compute the experimentally unobservable, but physically interesting vector form-factors of the $η_c, J/ψ$ and $χ_{c0}$. To this end we apply an ambitious combination of lattice techniques, computing three-point functions with heavy domain wall fermions on an anisotropic lattice within the quenched ap…
We calculate the next-to-leading order (NLO) quantum chromodynamics (QCD) corrections to inclusive processes $W^+\to J/ψ(η_c)+c+\bar{s}+X$ and $W^+\to B_c(B_c^{*})+b+\bar{s}+X$ in the framework of nonrelativistic QCD (NRQCD) factorization formalism. Result indicates that the NLO corrections are significant, and the uncertainties in theoretical predictions with NLO corrections are greatly reduced. The charmonium and $B_c$ meson yielding rates at the Large Hadron Collider (LHC) are given.
We formulate a general scheme to improve the truncated perturbative expansion in alpha_s by means of the renormalization group in QCD for the single-scale quantities. The procedure is used for the evaluation of hadronic decay rates of tau-lepton and eta_c-charmonium. The scale dependence of result for eta_c is studied in the scheme of fixed value for the MS-bar mass of charmed quark.
It is shown that the nuclear shadowing of charmonium due to the modification of the nuclear parton distribution is similar in the factorization approach based on non relativistic QCD and in the color evaporation model. In the first model, a separate study of the color octet and color singlet contributions to the yields of the various charmonium states as well as the contributions of these states to the total $J/Ψ$ production is performed. It is found a clear $x_F$ dependence of these contributions which can reproduce experimental data for moderate $x_F$.
We consider the non-relativistic limit of the QCD Hamiltonian in the Coulomb gauge, to describe radiative transitions between conventional charmonium states and from the lowest multiplet of $c\bar{c}$ hybrids to charmonium mesons. The results are compared to potential quark models and lattices calculations.
We investigated the form factors of the $B_{c}$ meson into $P$-wave orbitally excited charmonium using the nonrelativistic QCD effective theory. Through the analytic computation, the next-to-leading order relativistic corrections to the form factors were obtained, and the asymptotic expressions were studied in the infinite bottom quark mass limit. Employing the general form factors, we discussed the exclusive decays of the $B_{c}$ meson into $P$-wave orbitally excited charmonium and a light meson. We found that the relativistic corrections lead to a large correction for the form factors, which…
In this work, the charm quark mass is obtained from a QCD sum rule analysis of the charmonium system. In our investigation we include results from nonrelativistic QCD at next-to-next-to-leading order. Using the pole mass scheme, we obtain a value of $M_c=1.70\pm 0.13$ GeV for the charm pole mass. The introduction of a potential-subtracted mass leads to an improved scale dependence. The running ${\rm \bar{MS}}$-mass is then determined to be $m_c(m_c) = 1.23 \pm 0.09$ GeV.
We address the problem of observed charmonium decays which should be forbidden in perturbative QCD. We examine the model in which these decays proceed through a gluonic component of the $J/Ψ$ and the $η_c$, arising from a mixing of $(c\bar c)$ and glueball states. We give some bounds on the values of the mixing angles and propose the study of the $p \bar{p} \to ϕϕ$ reaction, at $\sqrt{s} \simeq 3$ GeV, as an independent test of the model.
The interquark potential in charmonium states is calculated for the first time in both the zero and non-zero temperature phases from a first-principles lattice QCD calculation. Simulations with two dynamical quark flavours were used with temperatures T in the range 0.4 T_c \lesssim T \lesssim 1.7 T_c, where T_c is the deconfining temperature. The correlators of point-split operators were analysed to gain spatial information about the charmonium states. A method, introduced by the HAL QCD collaboration and based on the Schroedinger equation, was applied to obtain the interquark potential. We fi…
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 calculate the nonperturbative $J/Ψ-N$ and $Ψ'-N$ cross sections with the model of the stochastic vacuum which has been succesfully applied in many high energy reactions. We also give a quantitative discussion of pre-resonance formation and medium effects.
Both hard and soft QCD dynamics are important in charmonium production, as presented here through a next-to-leading order QCD matrix element calculation combined with the colour evaporation model. Observed $x_F$ and $p_\perp$ distributions of $J/ψ$ in hadroproduction at fixed target and $p\bar{p}$ collider energies are reproduced. Quite similar results can also be obtained in a more phenomenologically useful Monte Carlo event generator where the perturbative production of \ccbar pairs is instead obtained through leading order matrix elements and the parton shower approximation of the higher or…
The recently obtained solutions of the Dirac equation in the confining SU(3)-Yang-Mills field in Minkowski spacetime are applied to describe the energy spectrum of charmonium. The nonrelativistic limit is considered for the relativistic effects to be estimated in a self-consistent way and it is shown that the given effects could be extremely important for both the energy spectrum and the confinement mechanism.
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.
Masses of the pseudoscalar $(J^{PC}=0^{-+})$ charmonium and bottomonium hybrids are determined using QCD Laplace sum-rules. The effects of the dimension-six gluon condensate are included in our analysis and result in a stable sum-rule analysis, whereas previous studies of these states were unable to optimize mass predictions. The pseudoscalar charmonium hybrid is predicted to have a mass of approximately 3.8 GeV and the corresponding bottomonium prediction is 10.6 GeV. Calculating the full correlation function, rather than only the imaginary part, is shown to be necessary for accurate formulat…
The $B_c(^1S_0)$ meson to S-wave Charmonia transition form factors are calculated in next-to-leading order(NLO) accuracy of Quantum Chromodynamics(QCD). Our results indicate that the higher order corrections to these form factors are remarkable, and hence are important to the phenomenological study of the corresponding processes. For the convenience of comparison and use, the relevant expressions in asymptotic form at the limit of $m_c\rightarrow0$ for the radiative corrections are presented.
In this work, the charm quark mass is obtained from a QCD sum rule analysis of the charmonium system. In our investigation we include results from non-relativistic QCD at next-to-next-to-leading order. Using the pole mass scheme, we obtain a value of $M_c=1.70\pm 0.13$ GeV for the charm pole mass. The introduction of a potential-subtracted mass leads to an improved scale dependence. The running ${\rm \MSb}$-mass is then determined to be $m_{c}(m_{c}) = 1.23 \pm 0.09$ GeV.
We study an interquark QQ^bar potential for the charmonium system, that is determined from the the equal-time and Coulomb gauge QQ^bar Bethe-Salpeter (BS) wavefunction through the effective Schrödinger equation. This novel approach enables us to evaluate a kinetic heavy quark mass m_Q and a proper interquark potential at finite quark mass m_Q, which receives all orders of 1/m_Q corrections on the static QQ^bar potential from Wilson loops, simultaneously. Precise information of the interquark potential for both charmonium and bottomonium states directly from lattice QCD provides us a chance to …
We present results for charmonium-nucleon potential $V_{c\bar{c}-N}(r)$ from quenched lattice QCD, which is calculated from the equal-time Bethe-Salpeter amplitude through the effective Schrödinger equation. Detail information of the low-energy interaction between the nucleon and charmonia ($η_c$ and $J/ψ$) is indispensable for exploring the formation of charmonium bound to nuclei. Our simulations are performed at a lattice cutoff of $1/a\approx 2.1$ GeV in a spatial volume of $(3 fm)^3$ with the nonperturbatively $O(a)$ improved Wilson action for the light quarks and a relativistic heavy quar…
Semileptonic and nonleptonic decays of the B_c meson to charmonium and D mesons are studied in the framework of the relativistic quark model. The decay form factors are explicitly expressed through the overlap integrals of the meson wave functions in the whole accessible kinematical range. The relativistic meson wave functions are used for the calculation of the decay rates. The obtained results are compared with the predictions of other approaches.
We present the semileptonic decay of $B_{c}$ meson in a QCD potential model with the coulombic part of the Cornell potential $-\frac{4α_{S}}{3r}+br+c$ as perturbation. Computing the slope and curvature of Isgur Wise function in this approach, we study the pseudoscalar and vector form factors for the transition of $B_{c}$ meson to its S wave charmonium $c\bar{c}$ states. Numerical estimates of widths for the transitions of $B_{c}\rightarrow J/ψ(η_{c})lν_{l}$ are presented. The results are found to be in good agreement with other theoretical values.
We present a next-to-leading order (NLO) QCD corrections to $B_c\to η_c$ and $B_c\to J/ψ$ tensor form factors within nonrelativistic QCD (NRQCD) framework. The full analytical results for $B_c$ to S-wave charmonium tensor form factors are obtained. We also studied the asymptotic behaviours of tensor form factors in hierarchy heavy quark limit, i.e. $m_b\to\infty,~ m_c\to\infty, ~\mathrm{and }~m_c/m_b\to0$. A compact expression for tensor form factors are given analytically in the hierarchy heavy quark limit. The relation among different form factors is also analyzed especially at large momentu…
Charmonia spectral functions at finite temperature are studied using QCD sum rules in combination with the maximum entropy method. This approach enables us to directly obtain the spectral function from the sum rules, without having to introduce any specific assumption about its functional form. As a result, it is found that while J/psi and eta_c manifest themselves as significant peaks in the spectral function below the deconfinement temperature T_c, they quickly dissolve into the continuum and almost completely disappear at temperatures between 1.0 T_c and 1.1 T_c.
We determine the MS-bar charm quark mass from a charmonium QCD sum rules analysis. On the theoretical side we use input from perturbation theory at O(alpha_s^3). Improvements with respect to previous O(alpha_s^3) analyses include (1) an account of all available e+e- hadronic cross section data and (2) a thorough analysis of perturbative uncertainties. Using a data clustering method to combine hadronic cross section data sets from different measurements we demonstrate that using all available experimental data up to c.m. energies of 10.538 GeV allows for determinations of experimental moments a…
Rare decay process of the Higgs boson into a pair of $J/Ψ$ and $Υ$ particles is studied within perturbative Standard Model and relativistic quark model. The relativistic corrections connected with the relative motion of quarks are calculated in the production amplitude and the wave functions of the bound states. Numerical values of the decay widths of the Higgs boson are obtained, which can be used for comparison with experimental data.
New evaluation of the relativistic effects in the double production of $S$-wave charmonium states is performed on the basis of perturbative QCD and the relativistic quark model. The main improvement consists in the exact account of properties of the relativistic meson wave functions. For the gluon and quark propagators entering the production vertex function we use a truncated expansion in the ratio of the relative quark momenta to the center-of-mass energy $\sqrt{s}$ up to the second order. The exact relativistic treatment of the wave functions makes all such second order terms convergent, th…
We compute masses of $D$ mesons, $D_s$ mesons and charmonium states using Wilson twisted mass lattice QCD. We present results for spin $J = 0,1,2,3$, parity $\mathcal{P} = -,+$ and in case of charmonium also charge conjugation $\mathcal{C} = -,+$. Computations are based on quark-antiquark creation operators and performed at three different unphysically heavy $u/d$ quark masses allowing an extrapolation to the physical $u/d$ quark mass. Within combined statistical and systematic errors, which are around $2 \% \ldots 3 \%$, our results agree with available experimental results. Particular focus …
