We present the scale setting for a new set of gauge configurations generated with $N_f=3+1$ Wilson quarks with a non-perturbatively determined clover coefficient in a massive O($a$) improvement scheme. The three light quarks are degenerate, with the sum of their masses being equal to its value in nature and the charm quark has its physical mass. We use open boundary conditions in time direction to avoid the problem of topological freezing at small lattice spacings and twisted-mass reweighting for improved stability of the simulations. The decoupling of charm at low energy allows us to set the scale by measuring the value of the low-energy quantity $t_0^\star/a^2$, which is the flow scale $t_0$ at our mass point, and comparing it to an $N_f=2+1$ result in physical units. We present the details of the algorithmic setup and tuning procedure and give the bare parameters of ensembles with two lattice spacings a=0.054 fm and a=0.043 fm. We discuss finite volume effects and lattice artifacts and present physical results for the charmonium spectrum. In particular the hyperfine splitting between the $η_c$ and $J/ψ$ mesons agrees very well with its physical value.
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.
Recent lattice QCD results on charmonium properties are reviewed. I comment on molecules and hybrid states as well as on future studies of states near strong decay thresholds.
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…
We present a study of the effect of charm quarks on the QCD equation of state using partially-quenched p4 charm quarks on a dynamically generated 2+1 flavor background, at zero chemical potential. We show preliminary results for the charm quark contribution to the energy density and pressure in the high temperature region ($T_c < T < 4 T_c$) and compare it to the free-field calculation. The charm quark mass is determined by measuring the charmonium spectrum.
We present preliminary results of an ongoing lattice QCD computation of the spectrum of $D$ mesons and $D_s$ mesons and of charmonium using 2+1+1 flavors of twisted mass sea and valence quarks.
The current correlator method has been shown to be a practical tool to extract the charm quark mass and strong coupling constant from Lattice QCD data as an alternative to the sum rule approach using experimental electron-positron annihilation cross section data. We report on the progress of an investigation of charm current-current correlators in N_f=2 Twisted Mass Lattice QCD. Upon determining the temporal moments of the current correlators we compare to the low-energy expansion of the moments in perturbative QCD and calculate the charm quark mass and strong coupling constant and in case of …
We present first results of a 2+1+1 flavor twisted mass lattice QCD computation of strange and charm meson masses. We focus on D and D_s mesons with spin J = 0,1 and parity P = -,+.
We compute the mass of the charm quark using both quenched and dynamical lattice QCD calculations. We examine the effects of mass dependent lattice artifacts by comparing two different formalisms for the heavy quarks. We take the continuum limit of the charm mass in quenched QCD by extrapolating from three different lattice spacings. At a fixed lattice spacing, the mass of the charm quark is compared between quenched QCD and dynamical QCD with a sea quark mass around strange. In the continuum limit of quenched QCD, we find m_c(m_c)=1.29(7)(13) GeV. No evidence was seen for unquenching.
We investigate the influence of dynamical charm quarks on observables that depend explicitly on the charm quark fields, like the pseudo-scalar and vector masses $m_{η_c}$ and $m_{J/ψ}$, the hyperfine splitting $(m_{J/ψ}-m_{η_c})/m_{η_c}$, the charm quark mass and the meson decay constants. For this purpose, instead of working in full QCD we study a simplified setup. We simulate two theories: $N_f= 0$ QCD and QCD with $N_f= 2$ dynamical quarks at the charm mass. The absence of light quarks allows us to reach extremely fine lattice spacings (0.02 fm < a < 0.05 fm) which are crucial for reliable …
In recent years, several charmed baryons have been discovered, with more states likely to be found in the future. We investigate the spectra of singly and doubly charmed baryons on the lattice. The spin J=1/2 and J=3/2 states are calculated for both positive and negative parity.
We study the effects of the addition of the charm quark on the QCD equation of state at zero and nonzero chemical potential on lattices with $N_t=6$. Our ensembles are quenched with respect to charm and the charm quark is a valence staggered quark. Along the trajectory of constant physics the ratio $m_s/m_c$ is kept constant after tuning the charm quark mass at a lattice spacing of about 0.09 fm. We find that the charm quark has a significant contribution to the equation of state at zero chemical potential already at temperatures between about $1.2T_c$ and $2T_c$. The additional contribution a…
The charmed-strange meson masses are calculated on a quenched lattice QCD. The charm and strange quark propagators are calculated on the same lattice with the overlap fermion. $16^3\times 72$ lattice with Wilson gauge action at $β=0.6345$ are used. The charm and strange quark masses are determined by fitting the $J/ψ$ and $ϕ$ masses respectively. The charmed strange meson spectrum for the scalar, axial, pseudoscalar and vector channels are calculated. They agree with experiments. In particular, we find the scalar meson mass to be 2248(78)MeV which is in agreement with that of D_{s0}^*(2317).
We present results for the mass spectrum of charm and bottom heavy baryons, using MILC coarse lattice configurations with 2+1 flavors. Clover heavy quark propagators with the Fermilab interpretation and improved staggered light quark propagators are used to construct two point functions with local operators for different flavor and spin states.
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.
The correlator of heavy-quark currents is calculated in quenched Lattice QCD on a $16^3 \times 32$-lattice for $β= { 6, 6.3 }$. The renormalized charmed quark mass is extracted from the short-distance part of that correlator: $m_c^{\overline{MS}}(m_c) = 1.22(5) GeV$. We study the sensitivity of our data to the strong coupling constant.
We present an update on the QCD equation of state of the Wuppertal-Budapest Collaboration, extending our previous studies [JHEP 0601 (2006) 089, JHEP 1011 (2010) 077]. A Symanzik improved gauge and a stout-link improved staggered fermion action is utilized. We discuss partial quenching and present preliminary results for the fully dynamical charmed equation of state.
We investigate the charm quark system on 2+1 flavor PACS-CS configurations. Calculations are performed at the lattice spacing $a^{-1}=2.194(10)$ GeV and the spatial extent $L=2.9$ fm with O(a)-improved Wilson fermions for the light quarks and the relativistic heavy fermion for the charm quark. Our dynamical $ud$ and strange quark masses and valence charm quark mass are set to their physical values. A comparison of the mass spectrum and decay constants with experiments is presented. Our results for the charm quark mass and CKM matrix elements are also reported.
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…
Using the high statistics datasets of the HotQCD Collaboration, generated with the HISQ (2+1)-flavor action for light and strange quarks, and treating the charm sector in the quenched approximation, we analyze the second and fourth order cumulants of charm fluctuations and the correlations of charm with lighter conserved flavor quantum numbers. We can make use of a factor 100 larger statistics on ${N_τ=8}$ lattices which never have been used in studies of charm fluctuations. Analyzing correlations of charm fluctuations with baryon number and electric charge fluctuations we can project onto cha…
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.
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…
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 a preliminary calculation of the charmed meson spectrum using the 2+1 flavor domain wall fermion lattice configurations currently being generated by the RBC and UKQCD collaborations. The calculation is performed using the 3-parameter, relativistic heavy quark action with nonperturbatively determined coefficients. We will also demonstrate a step-scaling procedure for determining these coefficients nonperturbatively using a series of quenched, gauge field ensembles generated for three different lattice spacings.
We investigate the charmed baryon mass spectrum using the relativistic heavy quark action on 2+1 flavor PACS-CS configurations previously generated on $32^3 \times 64$ lattice. The dynamical up-down and strange quark masses are set to the physical values by using the technique of reweighting to shift the quark hopping parameters from the values employed in the configuration generation. At the physical point, the lattice spacing equals $a^{-1}=2.194(10)$ GeV and the spatial extent $L=2.88(1)$ fm. Our results for the charmed baryon masses are consistent with experiments except for $Ξ_{cc}$, whic…
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.
We investigate the anisotropic lattice with $O(a)$ improved quark action as a candidate of framework in which we can treat both the heavy and light quark region in the same manner and systematically reduce the systematic uncertainties. To examine applicability of anisotropic lattice, we calculate the charmed meson spectrum and decay constants in quenched approximation. We find consistent result with most advanced results on isotropic lattices.
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 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.
We compute the mass spectrum for strange/charmed baryons in the partially quenched approach using N_f=2 twisted mass QCD configurations. We investigate two main issues: the size of lattice artefacts using three values of the lattice spacing (the smallest of which is approximately 0.05 fm) and the dependence of baryon masses on meson (or quark) masses. We thus perform a global fit in order to extrapolate simultaneously to the continuum limit and to the physical point. We estimate the masses of Omega_{sss}, Xi_{dss}, Lambda_{uds}, Omega_{ccc}, Xi_{dcc}, Lambda_{udc}.
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 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.
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 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 results for masses of spin-1/2 and spin-3/2 double-charm baryons in quenched lattice QCD, from an exploratory study using a non-perturbatively improved clover action at beta=6.2. We have studied local operators and we observe, after appropriate projections, a good signal for the ground states. We also present results for single-charmed baryons and spin-splittings for both double- and single-charmed states.
As a continuation of our recent work on the electromagnetic properties of the doubly charmed $Ξ_{cc}$ baryon, we compute the charge radii and the magnetic moments of the singly charmed $Σ_c$, $Ω_c$ and the doubly charmed $Ω_{cc}$ baryons in 2+1 flavor Lattice QCD. In general, the charmed baryons are found to be compact as compared to the proton. The charm quark acts to decrease the size of the baryons to smaller values. We discuss the mechanism behind the dependence of the charge radii on the light valence- and sea-quark masses. The magnetic moments are found to be almost stable with respect t…
Masses of singly and doubly charmed baryons are calculated in quenched lattice QCD using an improved action of the D234 type on an anisotropic lattice. The mass differences between spin 3/2 and spin 1/2 baryon states are calculated and compared to mass differences between vector and pseudoscalar mesons. The suppression of spin splittings in mesons containing heavy quarks, characteristic of quenched QCD simulations, is not observed in the baryon sector. The mass dependence of color hyperfine effects is discussed within the context of the quark model and heavy quark effective theory.
We present highly excited spectra of charmonium, charm-light and charm-strange mesons using the dynamical anisotropic lattices of the Hadron Spectrum Collaboration. The use of novel techniques has allowed us to extract these spectra with a high degree of statistical precision, while also enabling us to observe states as high as spin-4, states with exotic quantum numbers and candidate gluonic excitations. We discuss the phenomenology of these spectra, and also present preliminary results of Dπ scattering considering only the lowest partial wave in the isospin-3/2 channel.
We discuss the status of current dynamical lattice QCD simulations in connection to the emerging results on the strange and charmed baryon spectrum, excited states of the nucleon and the investigation of the structure of scalar mesons.
We make the first calculation in lattice QCD of two-photon decays of mesons. Working in the charmonium sector, using the LSZ reduction to relate a photon to a sum of hadronic vector eigenstates, we compute form-factors in both the space-like and time-like domains for the transitions $η_c \to γ^* γ^*$ and $χ_{c0} \to γ^* γ^*$. At the on-shell point we find approximate agreement with experimental world-average values.
We determine the mass of the charm quark ($m_c$) from lattice QCD with two flavors of dynamical quarks with a mass around the strange quark. We compare this to a determination in quenched QCD which has the same lattice spacing (0.1 fm). We investigate different formulations of the quark mass, based on the Vector Ward Identity, PCAC relation and the FNAL heavy quark formalism. Based on these preliminary results we find no effects due to sea quarks with a mass around strange.
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 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…
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 compute the electromagnetic properties of Ξ_cc baryons in 2+1 flavor Lattice QCD. By measuring the electric charge and magnetic form factors of Ξ_cc baryons, we extract the magnetic moments, charge and magnetic radii as well as the Ξ_cc Ξ_cc ρcoupling constant, which provide important information to understand the size, shape and couplings of the doubly charmed baryons. We find that the two heavy charm quarks drive the charge radii and the magnetic moment of Ξ_cc to smaller values as compared to those of, e.g., the proton.
We study the light quark-mass dependence of charmed baryon masses as measured by various QCD lattice collaborations. A global fit to such data based on the chiral SU(3) Lagrangian is reported on. All low-energy constants that are relevant at next-to-next-to-next-to-leading order (N$^3$LO) are determined from the lattice data sets where constraints from sum rules as they follow from large-Nc QCD at subleading order are considered. The expected hierarchy for the low-energy constants in the 1/Nc expansion is confirmed by our global fits to the lattice data. With our results the low-energy interac…
The precision of lattice QCD calculations has been steadily improving for some time and is now approaching, or has surpassed, the 1% level for multiple quantities. At this level QED effects, i.e. the fact that quarks carry electric as well as color charge, come into play. In this report we will summarise results from the first lattice QCD+QED computations of the properties of ground-state charmonium and bottomonium mesons by the HPQCD Collaboration.
We present the energy spectra of the low lying doubly-charmed baryons using lattice quantum chromodynamics. We precisely predict the ground state mass of the charmed-strange Omega(cc) (1/2+) baryon to be 3712(11)(12) MeV which could well be the next doubly-charmed baryon to be discovered at the LHCb experiment at CERN. We also predict masses of other doubly-charmed strange baryons with quantum numbers 3/2+, 1/2-, and 3/2-.
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.
We compute temporal correlators and spectral functions for light, open charm and charmonium mesons in the pseudoscalar and vector channel for a range of temperatures below and above the deconfinement transition. The study is carried out using anisotropic lattice QCD with 2+1 dynamical flavours, $a_s=0.123\,$fm and $a_s/a_τ=3.5$. The high-temperature results are benchmarked by comparing them to reconstructed correlators obtained by direct summation of the zero temperature correlator. We use two Bayesian methods to reconstruct the spectral functions: the maximum entropy method and the more recen…
We compute the hadronic light-by-light scattering contribution to the muon $g-2$ from the charm quark using lattice QCD. The calculation is performed on ensembles generated with dynamical $(u,d,s)$ quarks at the SU(3)$_{\rm f}$ symmetric point with degenerate pion and kaon masses of around 415 MeV. It includes the connected charm contribution, as well as the leading disconnected Wick contraction, involving the correlation between a charm and a light-quark loop. Cutoff effects turn out to be sizeable, which leads us to use lighter-than-physical charm masses, to employ a broad range of lattice s…
We compute the leading-order low-energy constants of the DeltaS=1 effective weak Hamiltonian in the quenched approximation of QCD with up, down, strange, and charm quarks degenerate and light. They are extracted by comparing the predictions of finite volume chiral perturbation theory with lattice QCD computations of suitable correlation functions carried out with quark masses ranging from a few MeV up to half of the physical strange mass. We observe a large DeltaI=1/2 enhancement in this corner of the parameter space of the theory. Although matching with the experimental result is not observed…
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.
