We report preliminary 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. Our simulations are performed at a lattice cutoff of $1/a$=2.0 GeV in a spatial volume of $(3\;\text{fm})^3$ with the nonperturbatively $O(a)$ improved Wilson action for the light quarks and a relativistic heavy quark action for the charm quark. We have found that the potential $V_{c\bar{c} N}(r)$ is weakly attractive at short distance and exponentially screened at long distance.
The charmonium-nucleon effective central interactions have been computed by the time-dependent HAL QCD method. This gives an updated result of a previous study based on the time-independent method, which is now known to be problematic because of the difficulty in achieving the ground-state saturation. We discuss that the result is consistent with the heavy quark symmetry. No bound state is observed from the analysis of the scattering phase shift; however, this shall lead to a future search of the hidden-charm pentaquarks by considering channel-coupling effects.
Detailed information of the low-energy interaction between the charmonia (ηc and J/ψ) and the nucleon is indispensable for exploring the formation of charmonium bound to nuclei. In order to investigate the charmonium-nucleon interactions at low energies, we adopt two essentially different approaches in lattice QCD simulations. The charmonium-nucleon potential can be calculated from the equal-time Bethe-Salpeter amplitude through the effective Schrödinger equation. This novel method is based on the same idea originally applied for the nucleon force by Aoki- Hatsuda-Ishii. Another approach is to…
Lattice QCD results on the spectroscopy of charmonium(like) states and open charm mesons are reviewed. Near-threshold states X(3872) and D_{s0}^*(2317) were treated rigorously for the first time and the searches for Z_c^+(3900), X(4140) and $cc\bar u\bar d$ were carried out. The first simulations of the resonances with charm quarks have been performed, including the determination of their strong decay widths. Spectroscopy of highly excited charmed, charmonium and hybrid states has been calculated.
The charmonium potential at non-zero temperature has been studied using gauge configurations with anisotropic lattices and 2+1 dynamical flavors of light sea quarks. We use the HAL QCD time-dependent method developed for the study of nucleon-nucleon potentials. To serve as in-put, local-extended charmonium correlators were calculated. The results are consistent with the expectation that the potential between heavy quarks should become deconfining at high temperatures.
We study hadron properties near the deconfining transition in the finite temperature lattice QCD. This paper focus on the heavy quarkonium states, such as $J/ψ$ meson. We compare the meson correlators above and below $T_c$ and discuss the possibility of the $c\bar{c}$ bound state by observing the wave function.
We report here our lattice simulation on the charmonium spectra in the quenched approximation. Because the full adjustment on the nonperturbative parameters such as $C_E$, $C_B$, $m_0a_s$ and $r_s$ needs many calculation time, we only adjust two of them, $m_0a_s$ and $r_s$($ξ_3$ plays this role in the paper) but with some rescale for mass splitting. After the rescale, we find that our results are in agreement with the experiment ones.
The charmonium-nucleon interaction is studied by the time-dependent HAL QCD method. We use a larger lattice volume and the relativistic heavy quark action for charm quark to obtain less systematic errors than those in our previous study. As a result, the sizable J/$ψ$N hyperfine splitting is observed, indicating that the spin-spin interaction is important to understand this system quantitatively. No J/$ψ$N or $η_c$N bound state is observed below the thresholds as in the previous results.
We use the dynamical gluon configurations provided by the MILC collaboration in a study of the charmonium spectrum and psi leptonic width. We examine sea quark effects on mass splitting and on the leptonic decay matrix element for light masses as low as m_s/5, while keeping the strange quark mass fixed and the lattice spacing nearly constant.
Charmonium systems in two-flavour QCD at non-zero temperature are studied at, and above the deconfining transition. Using anisotropic lattices the MEM approach is used to extract spectral functions for these channels. By carefully varying some of the irrelevant parameters in the MEM procedure, we confirm that our systematic effects are under control. The eta_c and J/psi states are found to persist at temperatures >~ 1.3 T_c in agreement with our previous dynamical studies.
We present results for Charmonium spectroscopy using Non-Relativistic QCD (NRQCD). For the NRQCD action the leading order spin-dependent and next to leading order spin-independent interactions have been included with tadpole-improved coefficients. We use multi-exponential fits to multiple correlation functions to extract ground and excited $S$ states. Splittings between the lowest $S$, $P$ and $D$ states are given and we have accurate values for the $S$ state hyperfine splitting and the $χ_c$ fine structure. Agreement with experiment is good - the remaining systematic errors are discussed.
We present preliminary results using overlap fermions for the charmonium spectrum, in particular for hyperfine splitting. Simulations are performed on $16^3 \times 72$ lattices, with Wilson gauge action at $β=6.3345$. Depending on how the scale is set, we obtain 104(5) MeV (using $1\bar{P}-1\bar{S}$) or 88(4) MeV (using $r_0$=0.5 fm) for the hyperfine splitting.
Dissociation temperatures of J/ψ, ψ', and χ_c states play key roles in the sequential J/ψsuppression scenario for high energy heavy ion collisions. We report on a study of charmonium dissociation temperatures in quenched lattice QCD. On anisotropic lattices, we first subtract the effects of the constant mode in finite temperature meson correlators, which have lead to unphysical results in previous studies. We then extract ground and first exited state masses by diagonalizing correlation functions among different source and sink operators. To distinguish bound states from scattering states, we …
We present the first study of the charmonium spectrum using overlap fermions, on quenched configurations. Simulations are performed on $16^3 \times 72$ lattices, with Wilson gauge action at $β$ = 6.3345. We demonstrate that we have discretization errors under control at about 5%. We obtain 88(4) MeV for hyperfine splitting using the $r_0$ scale, and 121(6) MeV using the ($1\bar{P}-1\bar{S}$) scale. This paper raises the possibility that the discrepancy between the lattice results and the experimental value for charmonium hyperfine splitting can be resolved using overlap fermions to simulate th…
We present our final results of the charmonium spectrum in quenched QCD on anisotropic lattices. Simulations are made with the plaquette gauge action and a tadpole improved clover quark action employing $ξ= a_s/a_t = 3$. We calculate the spectrum of S- and P-states and their excitation, and study the scaling behavior of mass splittings. Comparison is made with the experiment and previous lattice results. The issue of hyperfine splitting for different choices of the clover coefficients obtained by Klassen is discussed.
Charmonium dissociation temperatures are studied in a quenched anisotropic lattice QCD with standard plaquette gauge action and O(a) improved Wilson fermion action. Simulations are carried out at temperatures in the range 0.88T_c to 2.3T_c. From the meson correlators, we first subtract the contribution of constant mode, which was reported to mislead the analysis of, in particular, P wave signals. We then calculate effective masses and Bethe-Salpeter wave functions for ground (1S, 1P) and excited states (2S, 2P) using the multi-state variational analysis. To distinguish between bound states and…
We study charmonium correlators at finite temperature using quenched lattice QCD simulations. Two analysis procedures are applied to extract information on the spectral function: the maximum entropy method, and the $χ^2$ fit analyses including the constrained curve fitting. We focus on the low energy structure of the spectral function by applying the smearing technique. We first discuss the applicability of these methods to the finite temperatures by analyzing the data at T=0 with restricted numbers of degrees of freedom. Then we apply these methods to the correlators at $T>0$. We find no indi…
Sparse modeling study of extracting charmonium spectral functions from lattice QCD at finite temperature
Meteorological College, Japan Meteorological Agency（日本气象厅气象大学校）；Center for Computational Sciences, University of Tsukuba（筑波大学计算科学中心）；Department of Information and Mathematical Sciences, Division of Mathematical Sciences, Tokyo Women’s Christian University（东京女子基督教大学数学科学系信息数学科学部）；RIKEN Center for Computational Science（理化学研究所计算科学中心）；Department of Physics, Kyoto University（京都大学物理学系）
The $J/ψ$-nucleon interaction is studied by lattice QCD calculations. At the leading order of the derivative expansion, the interaction consists of four terms: the central, the spin-spin, and two types of tensor forces. We determine these spin-dependent forces quantitatively by using the time-dependent HAL QCD method. We find that the spin-spin force is the main cause of the hyperfine splitting between the $J=1/2$ and the $J=3/2$ states, while the two tensor forces have much smaller effects on the S-wave scattering processes.
I will describe recent results from the HPQCD collaboration using a new very accurate method for charm quarks in lattice QCD, that we have used in calculations including the full effect of u, d and s sea quarks. Multiple values of the lattice spacing and of the u, d and s sea quark masses allow us to extrapolate reliably, with a full error budget, to the real world. This opens up the field of charm physics to precision lattice QCD tests. So far we have calculated the D and D_s meson masses to 6 MeV, having fixed the charm quark mass from the eta_c meson. Our D and D_s decay constants (determin…
Finite temperature charmonium spectral functions in the pseudoscalar and vector channels are studied in lattice QCD with 2+1 flavours of dynamical Wilson quarks, on fine isotropic lattices (with a lattice spacing of 0.057 fm), with a non-physical pion mass of $m_π \approx$ 545 MeV. The highest temperature studied is approximately $1.4 T_c$. Up to this temperature no significant variation of the spectral function is seen in the pseudoscalar channel. The vector channel shows some temperature dependence, which seems to be consistent with a temperature dependent low frequency peak related to heavy…
We present spin-independent and spin-spin interquark potentials for the charmonium and charmed-strange mesons, which are calculated in 2+1 flavor lattice QCD simulations using the PACS-CS gauge configurations generated at the lightest pion mass ($M_π\approx 156(7)$~MeV) with a lattice cutoff of $a^{-1}\approx 2.2$ GeV and a spatial volume of $(3~{\rm fm})^3$. For the charm quark, we use a relativistic heavy quark (RHQ) action with fine tuned RHQ parameters, which closely reproduce both the experimental spin-averaged mass and hyper-fine splitting of the $1S$ charmonium. The interquark potential…
Charmonium spectroscopy with Kogut-Susskind valence quarks are carried out for quenched QCD at $β=6.0$ and for two-flavor full QCD at $β=5.7$. Results for 1P--1S mass splitting and estimates of $α^{(5)}_{\overline{MS}}(m_Z)$ are reported. Problems associated with flavor breaking effects and finite size effects of $1P$ states are discussed.
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…
The spectral functions of QCD can give us insight into properties of hadrons, and they are useful in probing the QCD vacuum. I will discuss the correlators and spectral functions of charmonium in high temperature two flavour QCD. The spectral functions have been obtained using the Maximum Entropy Method from anisotropic lattice data using the conserved vector current. This work has been done as part of the FASTSUM collaboration. We find that the spectral functions for zero momentum are stable. At non-zero momentum the spectral functions are less stable but still produce resonance and transport…
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…
We study the charmonium spectral functions at finite momentum and the dispersion relation of $η_c$ at finite temperature. For the analysis of the spectral function, we use an extended maximum entropy method (MEM). We perform the MEM analysis for the product space of Euclidean correlators in different channels or momenta to incorporate information encoded in correlations among the Euclidean correlators in MEM. We find that this method can improve the error of the reconstructed spectral images. To study the dispersion relation, we introduce a definition of the peak position in the spectral image…
Lattice QCD studies on charmonium at finite temperature are presented After a discussion about problems for the Maximum Entropy Method applied to finite temperature lattice QCD, I show several results on charmonium spectral functions. The ``wave function'' of charmonium is also discussed to study the spatial correlation between quark and anti-quark in deconfinement phase.
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 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.
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…
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 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.
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…
We present the first set of results for Charmonium Spectroscopy using Non-Relativistic QCD (NRQCD). For the NRQCD action the leading order spin-dependent and next to leading order spin-independent interactions have been included. Clear signals for the s and p hyperfine splittings have been observed as well as various orbital states.
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.
Recent studies on the spectral function of charmonium in lattice QCD suggest survival of $J/ψ$ state in the deconfinement phase till relatively high temperature. Based on the studies, different scenarios of $J/ψ$ suppression are discussed to understand experimental results in the Heavy Ion Collision experiments. The scenarios require the information on the dissociation temperatures of $χ_c$ and $ψ'$ as well as that of $J/ψ$. In order to investigate these states in finite temperature lattice QCD, we have to consider an effect of a characteristic constant mode in the correlators. As a result of …
We propose a method to evaluate spectral functions on the lattice based on a variational method. On a lattice with a finite spatial extent, spectral functions consist of discrete spectra only. Adopting a variational method, we calculate the locations and the heights of spectral functions at low-lying discrete spectra. We first test the method in the case of analytically solvable free Wilson quarks at zero and finite temperatures and confirm that the method well reproduces the analytic results for low-lying spectra. We find that we can systematically improve the results by increasing the number…
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 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.
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 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 estimate the effects on the decay constants of charmonium and on heavy meson masses due to the charm quark in the sea. Our goal is to understand whether for these quantities $N_f=2+1$ lattice QCD simulations provide results that can be compared with experiments or whether $N_f=2+1+1$ QCD including the charm quark in the sea needs to be simulated. We consider two theories, $N_f=0$ QCD and QCD with $N_f=2$ charm quarks in the sea. The charm sea effects (due to two charm quarks) are estimated comparing the results obtained in these two theories, after matching them and taking the continuum lim…
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 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 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 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…
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.
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 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 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 …
