Charm Mass Determination from QCD Charmonium Sum Rules at Order alpha_s^3
Bahman Dehnadi, Andre H. Hoang, Vicent Mateu, S. Mohammad Zebarjad
备注：
56 pages, 16 figures. Updated experimental input and treatment of correlations. Added results on higher moment mass determinations. Slight modification of final result. Conclusions unchanged
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 and their correlations with small errors and that there is no need to rely on theoretical input above the charmonium resonances. We also show that good convergence properties of the perturbative series for the theoretical sum rule moments need to be considered with some care when extracting the charm mass and demonstrate how to set up a suitable set of scale variations to obtain a proper estimate of the perturbative uncertainty. As the final outcome of our analysis we obtain m_c(m_c) = 1.282 \pm 0.006_stat \pm 0.009_syst \pm 0.019)_pert \pm 0.010_alpha \pm 0.002_GG GeV. The perturbative error is an order of magnitude larger than the one obtained in previous O(alpha_s^3) sum rule analyses.
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.
In calculations of the hyperfine splitting in charmonium, the contributions of the disconnected diagrams are considered small and are typically ignored. We aim to estimate nonperturbatively the size of the resulting correction, which may eventually be needed in high precision calculations of the charmonium spectrum. We study this problem in the quenched and unquenched QCD cases. On dynamical ensembles the disconnected charmonium propagators contain light modes which complicate the extraction of the signal at large distances. In the fully quenched case, where there are no such light modes, the …
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.
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 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/…
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 review the current theoretical situation with regard to the anomalously large cross section for exclusive J/psi + eta_c production in e^+ e^- annihilation, as measured by BELLE Collaboration.
Based on the updated data of charmoniumlike state $Y(4220)$ reported in the hidden-charm %and open-charm channels of the $e^+e^-$ annihilation, we propose a $4S$-$3D$ mixing scheme to categorize $Y(4220)$ into the $J/ψ$ family. We find that the present experimental data can support this charmonium assignment to $Y(4220)$. Thus, $Y(4220)$ plays a role of a scaling point in constructing higher charmonia above 4 GeV. To further test this scenario, we provide more abundant information on the decay properties of $Y(4220)$, and predict its charmonium partner $ψ(4380)$, whose evidence is found by ana…
This report discusses some recent investigations of the heavy hadron spectra using lattice QCD. The first half addresses multiple precision determinations of the masses of charm (and bottom) baryons. Recent lattice results in the tetraquark and the dibaryon sectors are also presented. The second half focuses on new exploratory studies of the excited charmonium spectra in the vector and scalar channels. Along the way, lattice results are compared with the experimental results, wherever they are available.
The cross section value of doubly charmonium production in e+e- annihilations have been estimated at interaction energy 10.6 GeV. The quarkonium wave function shape, as well as the nonzero value of charm quark have been taken into account.
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 analyze the singlet $P$--wave charmonium production at $e^+ e^-$ colliders within the framework of unconstrained supersymmetry. We show that the CP--violating transitions, dominated by the gluino exchange, are typically four orders of magnitude larger than the CP--conserving ones, and former is generated by the electric dipole moment of the charm quark. Our results can be directly tested via the charmonium searches at the CLEO--c experiment.
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.
This contribution briefly discusses some new theoretical results for the properties of charmonium, especially the "higher charmonium" states above open-charm threshold. In particular we discuss the spectrum of states, open-flavor strong decays, and the surprisingly large effects of virtual decay loops of charmed meson pairs.
In this study, the properties of the $J^{PC}=1^{++}$ hidden charm poles are analyzed under the variation of the bare 2P charmonium mass within the effective field theory proposed in Ref.[1]. The main focus of the current work is on the pole trajectory of the $χ_{c1}(2P)$ charmonium dressed by the $D \bar{D}^*$ meson loops. It is shown that the trajectories of the pole change radically for values of the bare charmonium mass above a certain value and also depending on how close the pole is to the threshold.
This talk summarizes the status of the charmonium system, with particular emphasis on outstanding problems in QCD spectroscopy which a tau-charm factory can address.
Recent theoretical progress in calculations of the spectrum and decays of charmonium is reviewed. Traditionally, our understanding of charmonium was based on potential models. This is now being replaced by first principles.
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…
Topics in the description of the properties of charmonium states are reviewed with an emphasis on specific theoretical ideas and methods of relating those properties to the underlying theory of Quantum Chromodynamics.
In decays of the $Z^0$, the dominant mechanism for the direct production of charmonium states is the decay of the $Z^0$ into a charm quark or antiquark followed by its fragmentation into the charmonium state. We calculate the fragmentation functions describing the splitting of charm quarks into S-wave charmonium states to leading order in the QCD coupling constant. Leading logarithms of $M_Z/m_c$ are summed up using Altarelli-Parisi evolution equations. Our analytic result agrees with the complete leading order calculation of the rate for $Z^0 \rightarrow ψc {\bar c}$. We also use our fragment…
We perform numerical comparison of the fragmentation mechanism of charmonium production ($g\,g\to c\,\bar{c}$ followed by $c\toψ\,c$) with the full leading order calculation ($g\,g\toψ\,c\,\bar{c}$ at $Ø (α_s^4)$). We conclude that the non-fragmentation contributions remain important up to $J/ψ$ transverse momenta about as large as 50 GeV, thus making questionable the applicability of the fragmentation approximation at smaller transverse momenta.
Caution is suggested on the comparison of the spin-singlet charmonium P-state with the centre of gravity of triplet states, when the mass splitting is of the order of a few MeV. The physics of new hidden-charm states X and Y is briefly reviewed. Perspectives for producing double-charm baryons and double-charm exotic mesons are discussed.
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).
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.
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…
We review recent results on the production of prompt charmonium in association with a hadron jet or a prompt photon in two-photon collisions at next-to-leading order in the factorization framework of nonrelativistic quantum chromodynamics.
In statistical QCD, color deconfinement and the properties of the quark-gluon plasma determine the in-medium behavior of heavy quark bound states. In high energy nuclear collisions, charmonia probe the partonic medium produced in the early stages of the interaction. We survey the present theoretical status and provide a critical evaluation of the charmonium production measurements in experiments at the CERN-SPS and the BNL-RHIC.
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…
If the $X(3872)$ is described by the picture as a mixture of the charmonium and molecular $D^{\ast} D$ states; $Y(3940)$ as a mixture of the $χ_{c0}$ and $D^\ast D^\ast$ states; and $X(4260)$ as a mixture of the tetra-quark and charmonium sates, their orthogonal combinations should also exist. We estimate the mass and residues of the states within the QCD sum rules method. We find that the mass splitting among $X$, $Y$ and their orthogonal states is at most $200MeV$. Experimental search of these new states can play critical role for establishing the nature of the new charmonium states.
The production of charmonium in heavy-ion collisions is investigated based on Boltzmann-type transport model for charmonium evolution and langevin equation for charm quark evolution. Charmonium suppression and regeneration in both quark-gluon plasma (QGP) and hadron phase are considered. Charm quarks are far from thermalization, and regeneration of charmonium in QGP and hadron gas is neglectable at SPS and FAIR. At peripheral collisions, charmonium suppression with hadron gas explains the experimental data well. But at central collisions, additional suppression from deconfined matter (QGP) is …
The theoretical explanations about the ``Rho-pi puzzle'' in charmonium decays are reviewed extensively, and the comparison of theoretical predications with experimental data is made whenever possible. Three methods to estimate the ratio of the branching fractions of J/psi and psi' decays are also discussed. It is pointed out that in order to understand the Rho-pi puzzle, and the dynamics of charmonium decays, systematic studies should be made in theory, phenomenology and experiment aspects.
I briefly review Non-Relativistic QCD and related effective theories, and discuss applications to heavy quarkonium decay, and production in electron-positron colliders.
We present a detailed investigation of the quark mass-dependence of charmonium correlators in Euclidean-time obtained using a potential model, as well as the comparison with results on isotropic lattice calculations performed at several lattice spacings.
Many new states in the charmonium and bottomonium mass region were recently discovered by the BaBar, Belle and CDF Collaborations. We use the QCD Sum Rule approach to study the possible structure of some of these states. In particular we identify the recently observed bottomonium-like resonance $Z_b^+(10610)$ with the first excitation of the tetraquark $X_b(1^{++})$, the analogue of the X(3872) state in the charm sector.
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 …
We study the effect of thermal charm production on charmonium regeneration in high energy nuclear collisions. By solving the kinetic equations for charm quark and charmonium distributions in Pb+Pb collisions, we calculate the global and differential nuclear modification factors $R_{AA}(N_{part})$ and $R{AA}(p_t)$ for $J/Ψ$s. Due to the thermal charm production in hot medium, the charmonium production source changes from the initially created charm quarks at SPS, RHIC and LHC to the thermally produced charm quarks at Future Circular Collider (FCC), and the $J/Ψ$ suppression ($R_{AA}<1$) observe…
In this paper we confront both the hadronic molecule and the hadro-charmonium interpretations of the $\y$ with the experimental data currently available. We conclude that the data support the $\y$ being dominantly a $D_1\bar D+c.c.$ hadronic molecule while they challenge the hadro-charmonium interpretation. However, additional data is necessary to allow for stronger conclusions.
Recent data on charmonium production in B-meson decays suggest that charmonium hybrid mesons with mass ~4 GeV may be produced in B-decay via c\bar{c} colour octet operators. Some of these states are likely to be narrow with clean signatures to J/ψpi^+ pi^- final states. Experimental signatures and search strategies for existing B-factories are described.
The open-charm strong decays of higher charmonium states up to the mass of the $6P$ multiplet are systematically studied in the $^3P_0$ model. The wave functions of the initial charmonium states are calculated in the linear potential (LP) and screened potential (SP) quark model. The decay widths for most of the well-established charmonium states above the open-charm thresholds can be reasonably described. By comparing our quark model calculations with the experimental observations we also discuss the nature of some of the newly observed charmonium-like states. It is found that (i) the $ψ(4415)…
The analysis of the mass spectrum and the calculation of the strong decay of P-wave charmonium states strongly support to explain the newly observed X(3915) and X(4350) as new members in P-wave charmonium family, i.e., $χ_{c0}^\prime$ for X(3915) and $χ_{c2}^{\prime\prime}$ for X(4350). Under the P-wave charmonium assignment to X(3915) and X(4350), the $J^{PC}$ quantum numbers of X(3915) and X(4350) must be $0^{++}$ and $2^{++}$ respectively, which provide the important criterion to test P-wave charmonium explanation for X(3915) and X(4350) proposed by this letter. The decay behavior of the re…
We propose the initial single chiral particle emission mechanism, with which the hidden-charm di-kaon decays of higher charmonia and charmonium-like states are studied. Calculating the distributions of differential decay width, we obtain the line shape of the $J/ψK^+$ invariant mass spectrum of $ψ_i\to J/ψK^+K^-$, where $ψ_i=ψ(4415), Y(4660)$, and $ψ(4790)$. Our numerical results show that there exist enhancement structures with both hidden-charm and open-strange decays, which are near the $D\bar{D}_s^*/D^*\bar{D}_s$ and $D^*\bar{D}_s^*/\bar{D}^*{D}_s^*$ thresholds. These charged charmonium-li…
In this work, we predict two charged charmonium-like structures close to the $D^\ast\bar{D}$ and $D^\ast\bar{D}^\ast$ thresholds, where the Initial Single Pion Emission mechanism is introduced in the hidden-charm dipion decays of higher charmonia $ψ(4040)$, $ψ(4160)$, $ψ(4415)$ and charmonium-like state Y(4260). We suggest BESIII to search for these structures in the $J/ψπ^+$, $ψ(2S)π^+$ and $h_b(1P)π^+$ invariant mass spectra of the $ψ(4040)$ decays into $J/ψπ^+π^-$, $ψ(2S)π^+π^-$ and $h_b(1P)π^+π^-$. In addition, the experimental search for these structures in the $J/ψπ^+$, $ψ(2S)π^+$ and $h…
