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, thus allowing the reliable calculation of their contributions to the production cross section. Compared to the nonrelativistic calculation we obtain a significant increase of the cross sections for the $S$-wave double charmonium production. This brings new theoretical results in good agreement with the available experimental data.
In this paper initial state radiation corrections to double production of charmonium mesons on one-photon electron-positron annihilation at center of mass energy $\sqrt{s}=10.6\GeV$ are studied. It is shown, that these corrections have noticeable effect and must be taken into consideration.
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 the charmonium production in $e^+e^-$ annihilation at $\sqrt{s}=10.6GeV$. NRQCD predictions for the $J/ψ$ production are compared with the recent measurements by BaBar and Belle. A NRQCD calculation for the $D$-wave charmonium production is reported to further test the color-octet mechanism and detect the $J^{PC}=2^{--}$ state. The issue of double $c \bar c$ production in $e^+e^-$ annihilation observed by Belle is also discussed.
In this paper the production of excited vector and pseudoscalar charmonium mesons in $\epem$ annihilation is analyzed in the framework of light cone. In particular the cross sections $\epem \to ψ(2S)η_c(1S), ψ(1S)η_c(2S),ψ(2S)η_c(2S)$ have been calculated. It is shown, that contrary to NRQCD the cross sections calculated in the framework of light cone agree with experimental data.
In this paper we study inclusive production of vector charmonium states $J/ψ$ or $ψ(2S)$ in two-photon $\epem$-annihilation at $\sqrt s=10.6 \rm GeV$ using color-singlet model. Analytic expressions for differential cross sections, numerical values of total cross sections and plots of different distributions are presented. These distributions differ significantly from the one-photon case so these modes can be easily separated.
The production cross sections of $J/ψ~η_b$, $Υ\;η_c$ pairs in a single boson $e^+e^-$ annihilation have been studied in a wide range of energies, which will be achieved at future $e^+e^-$ colliders. The main color singlet contributions to the production processes are taken into account, including the one loop QCD contribution.
We calculate the double charmonium production cross section within the framework of $4\times 4$ Bethe-Salpeter Equation in the electron-positron annihilation, at center of mass energy $\sqrt{s}= 10.6$GeV, that proceeds through the exchange of a single virtual photon. In this calculation, we make use of the full Dirac structure of 4D BS wave functions of these charmonia, with the incorporation of all the Dirac covariants (both leading and sub-leading). The calculated cross-sections for the double charmonium productions for final states, ($J/Ψ, η_c$); ($Ψ',η_c$) ; ($J/Ψ, η_c'$); and ($Ψ',η_c'$) …
We suggest searching for excited charmonium states in $e^+e^-$ annihilation via double charmonium production at $\sqrt{s}=10.6$ GeV with $B$ factories, based on a more complete leading order calculation including both QCD and QED contributions for various processes. In particular, for the C=+ states, the $χ_{c0}(nP)$ (n=2,3) and $η_c(mS)$ (m=3,4) may have appreciable potentials to be observed; while for the C=- states, the $η_ch_c$ production and especially the $χ_{c1}h_c$ production might provide opportunities for observing the $h_c$ with higher statistics in the future. A brief discussion fo…
Recent measurements of the Belle Collaboration of the exclusive production of two charmonia in the $e^+e^-$ annihilation differ substantially from theoretical predictions. Recently it was suggested that a significant part of this discrepancy can be explained by the process $e^2e^- --> 2J/psi$ and value for its cross-section was published. In this paper it is shown, that these results are incorrect and the values for the cross-sections of the production of different vector charmonia are presented.
Two-photon annihilation rates of $2^+$ tensor charmonium and bottomonium up to third radial excited states are estimated in the relativistic Salpeter method. Full Salpeter equation for $2^+$ tensor state is solved with a well defined relativistic wave function and we calculated the annihilation amplitude using the Mandelstam formalism. Our estimates of the decay widths are: $Γ(χ_{c2} \to 2γ)=501$ eV, $Γ(χ'_{c2} \to 2γ)=534$ eV, $Γ(χ_{b2} \to 2γ)=7.4$ eV and $Γ(χ'_{b2} \to 2γ)=7.7$ eV. We also give total decay widths of the lowest states estimated by the two-gluon decay rates, and the results a…
We calculate the D-wave charmonium production in $e^+e^-$ annihilation at BELLE and BABAR at $\sqrt{s}=10.6$ GeV using the nonrelativistic QCD factorization formalism, including color singlet and color octet contributions. We analyze the contributions of various processes for $δ_J(J=1,2)$ production. We find that both the color singlet and color octet channels may give substantial contributions, and the production rates are estimated to be $σ(δ_1)\simeq 0.043-0.16pb$ and $σ(δ_2)\simeq 0.094-0.29pb$, which, however, are very sensitive to the choice of the color octet matrix elements of the D-wa…
Inspired by the observation of charmoniumlike $Z(4200)$, we explore the discovery potential of the neutral $Z^{0}(4200)$ production by antiproton-proton annihilation with an effective Lagrangian approach. By investigating the $\bar{p}p\rightarrow J/ψπ^{0}$ process including the $Z^{0}(4200)$ signal and background contributions, it is found that the center of mass energy $E_{c.m.}\simeq 4.0-4.5$ GeV is the best energy window for searching the neutral $Z^{0}(4200)$, where the signal can be clearly distinguished from background. The relevant calculations is not only helpful to search for the neut…
The associated production of a $J/ψ$ and a $π$-meson in antiproton-nucleon annihilation is studied in the framework of QCD collinear factorization. In this approach, a hard subprocess responsible for the production of the heavy quark-antiquark pair factorizes from soft hadronic matrix elements, such as the antiproton (nucleon) distribution amplitude and the nucleon-to-pion (antiproton-to-pion) transition distribution amplitude. This reaction mechanism should dominate the forward and backward kinematical regions, where the cross sections are expected to be measurable in the set-up of the PANDA …
We calculate the exclusive cross sections for e^+ e^- annihilation into two charmonium states through a virtual photon. Purely electromagnetic contributions are surprisingly large, changing the cross sections by as much as 21%. The predicted cross section for J/psi + eta_c is about an order of magnitude smaller than a recent measurement by the BELLE Collaboration, although part of the discrepancy can be attributed to large relativistic corrections. The cross sections for S-wave + P-wave, P-wave + P-wave, and S-wave + D-wave charmonium states are also calculated. It may be possible to discover …
In this paper we summarize our recent results for low energy associated charmonium production cross sections, using 1) crossing symmetry, and 2) an explicit hadronic model. These predictions are of relevance to the planned charmonium and charmonium hybrid production experiment PANDA at GSI.
In this work we study the process $e^{+}+e^{-}\longrightarrow J/Ψ+η_{c} $ at energy $\sqrt{s}= 10.6 GeV$ observed recently at B-factories whose measurements were made by Babar and Belle groups. We calculate the cross section for this process in the Bethe-salpeter formalism under Covariant Instantaneous Anstaz (CIA). To simplify our calculation, the heavy quark approximation $(q<<M, P M)$ is employed in the quark and gluon propagators. In the exclusive process of $e^{+}e^{-}$ annihilation into two heavy quarkonia, the cross section calculated in this scenario is compatible with the experimental…
We calculate the contributions from QED processes involving two virtual photons to the cross sections for e^+ e^- annihilation into two charmonium states with the same C-parity. Generically, the cross sections are three orders of magnitude smaller than those for charmonia with opposite C-parity because they are suppressed by a factor of alpha^2/alpha_s^2. However, if both charmonia have quantum numbers J^{PC} = 1^{--}, then there is a contribution to the cross section that involves the fragmentation of each photon into a charmonium. The fragmentation contribution is enhanced by powers of E_{be…
In this paper, we present a new analysis on the $P$-wave charmonium annihilation into two photons up to next-to-next-to-leading order (NNLO) QCD corrections by using the principle of maximum conformality (PMC). The conventional perturbative QCD prediction shows strong scale dependence and deviates largely from the BESIII measurements. After applying the PMC, we obtain a more precise scale-invariant pQCD prediction, which also agrees with the BESIII measurements within errors, i.e. $R={Γ_{γγ}(χ_{c2})} /{Γ_{γγ}(χ_{c0})}=0.246\pm0.013$, where the error is for $Δα_s(M_τ)=\pm0.016$. By further cons…
The vector glueball $O$, made of 3 valence gluons, is expected to be ``clean": it mixes less with quarkonia, but mediates OZI violations. The recent $0^{++} $ glueball candidate and the persistence of the $J/ψ, ψ' \to ρπ$ puzzle suggest $m_O\simeq m_{J/ψ}$, with mixing angle $\sim 2^\circ - 4^\circ$, hence $Γ(O\to ρπ$, $K^+K^-$, $e^+e^-) \sim$ MeV, few keV, few eV. Lower and upper bounds on $Γ_O$ can be argued from $e^+e^- \to ρπ$ energy scan data and the condition $B(O\to ρπ) > B(J/ψ\to ρπ)$. $O$ dominance may explain the ``large" OZI violation in $^1S_0(\bar pp)\to ϕγ$ vs. $ωγ$.
We calculate the form factor and cross section of the excited charmonium production process $e^{+}+e^{-}\rightarrow ψ\left ( 2S \right )+η_{c}$ by light-cone sum rules. In our method, the form factor depends on the distribution amplitude of $η_{c}$ meson. Experimentally, the energy scale of $e^{+}+e^{-}\rightarrow ψ\left ( 2S \right )+η_{c}$ process is much larger than the initial energy scale of $η_{c}$ meson in our BHL model. Therefore, we further consider the evolution of the distribution amplitude with the energy scale, and select the distribution amplitude as our input parameter when the …
The cross sections for the charmonium production processes p pbar -> m Psi, where m is a light meson and Psi is a charmonium state, are of great interest for the planned p-pbar experiment PANDA. In this paper we estimate these cross sections using known results for the decays Psi -> m p pbar which are related to these reactions by crossing. In lieu of detailed experimental data on the decay Dalitz plots, we assume a constant amplitude as a first approximation; this implies a simple relation between the cross sections and decay widths. The single measured exclusive cross section of this type is…
On the basis of perturbative QCD and the relativistic quark model we calculate relativistic and bound state corrections in the production processes of a pair of P-wave charmonium states. Relativistic factors in the production amplitude connected with the relative motion of heavy quarks and the transformation law of the bound state wave function to the reference frame of the moving P-wave mesons are taken into account. 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 s…
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).
I briefly review Non-Relativistic QCD and related effective theories, and discuss applications to heavy quarkonium decay, and production in electron-positron colliders.
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 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.
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.
The QCD mechanisms underlying the exclusive strong decays and hadronic production amplitudes of charmonium remain poorly understood, despite decades of study and an increasingly detaled body of experimental information. One set of hadronic channels of special interest are those that include baryon-antibaryon states. These are being investigated experimentally at BES and CLEO-c in terms of their baryon resonance content, and are also of interest for the future PANDA experiment, in which charmonium and charmonium hybrids will be produced in p-pbar annihilation in association with light mesons. I…
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.
On the basis of perturbative QCD and the relativistic quark model we calculate relativistic and bound state corrections in the production processes of a pair of S-wave and P-wave charmonium states. Relativistic factors in the production amplitude connected with the relative motion of heavy quarks and the transformation law of the bound state wave function to the reference frame of the moving S- and P-wave mesons are taken into account. 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 cente…
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.
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.
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.
The $1^1D_2 (c\bar c)$ state is the ground state of spin-singlet D-wave charmonia. Although it has not been found yet, the experimental data accumulate rapidly. This charmonium attracts more and more attention, especially when the BaBar Collaboration finds that the X(3872) particle has negative parity. In this paper we calculate the double-gamma and double-gluon annihilation processes of $^1D_2$ charmonia and bottomonia by using the instantaneous Bethe-Salpeter method. We find the relativistic corrections make the decay widths of $1^1D_2 (c\bar c)$ 2$\sim$5 times smaller than the non-relativis…
Motivated by the recent observation of double charm quark pair production by the Belle Collaboration, we calculate the complete ${\cal O}(α_{s}^{2})$ inclusive production cross sections for $η_{c}$, $J/ψ$, and $χ_{cJ}$(J=0, 1, 2) plus $c\bar{c}$ in $e^+ e^-$ annihilation through a virtual photon. We consider both color-singlet and color-octet contributions, and give the analytical expressions for these cross sections. The complete color-singlet calculations are compared with the approximate fragmentation calculations as functions of the center-of-mass energy $\sqrt{s}$. We find that most of th…
Within the nonrelativistic quantum chromodynamics (NRQCD) factorization formalism, we compute the relativistic corrections to the exclusive decays of bottomonia with even charge conjugation parity into $S$-wave charmonium pairs at leading order in the strong coupling constant. Relativistic corrections are resummed for a class of color-singlet contributions to all orders in the charm-quark velocity $v_c$ in the charmonium rest frame. Almost every process that we consider in this work has negative relativistic corrections ranging from -20 to -35,%. Among the various processes, the relativistic c…
We make a comparative and comprehensive study on the charmonium exclusive productions at the $e^+e^-$ collider with the collision energy either round the $Z^0$-boson mass for a super $Z$ factory or equals to 10.6 GeV for the $B$ factories as Belle and BABAR. We study the total cross sections for the charmonium production via the exclusive processes $e^+e^- \to γ^*/Z^0 \to H_{1}+H_{2}$ and $e^+e^- \to γ^*/Z^0 \to H_{1} +γ$, where $H_{1}$ and $H_{2}$ represent the dominant color-singlet $S$-wave and $P$-wave charmonium states respectively. Total cross sections versus the $e^+e^-$ collision energ…
On the basis of pertubative QCD and the relativistic quark model we calculate relativistic corrections to the process of pair $J/ψ$ production in proton-proton collisions at LHC energy $\sqrt S=7$ TeV. Relativistic terms in the production amplitude connected with the relative motion of heavy quarks and the transformation law of the bound state wave functions to the reference frame of moving $J/ψ$ mesons are taken into account. For the gluon and quark propagators entering the amplitude we use a truncated expansion in relative quark momenta up to the second order. Relativistic corrections to the…
Relativistic effects are important in the rigorous study of heavy quarks. In this paper, we study the relativistic corrections of semileptonic $B_c$ decays to charmonium with the instantaneous Bethe-Salpeter method. Within the Bethe-Salpeter framework, we use two methods to study the relativistic effects. One of them is to expand the transition amplitude in powers of $\vec{q}$ which is the relative momentum between the quark and antiquark, and the other is to expand the amplitude base on the wave functions. In the level of decay width, the results show that, for the transition of $B_c\to η_c$,…
Charmonium production in association with a forward or backward pion in nucleon-antinucleon annihilation is one of the most promising reaction to access nucleon-to-pion transition distribution amplitudes (TDAs) at PANDA. We briefly review the description of this reaction in terms of πN TDAs within the collinear factorization approach and present the first results of dedicated feasibility studies for the PANDA experimental setup.
We use the framework of a relativistic constituent quark model to study the semileptonic transitions of the Bc meson into CCbar charmonium states where CCbar = etaC (1S0), J/psi (3S1), chiC0 (3P0), chiC1 (3P1), hc (1P1), chiC2 (3P2), psi (3D2). We compute the q^2-dependence of all relevant form factors and give predictions for their semileptonic Bc decay modes including also their tau-modes. We derive a formula for the polar angle distribution of the charged lepton in the (l nu) c.m. frame and compute the partial helicity rates that multiply the angular factors in the decay distribution. For t…
We consider the charmonium production in thermalized hadronic medium created in ultrarelativistic heavy ion collisions at LHC energy. The calculations for the secondary $J/ψ$ and $ψ^,$ production by $D\bar D$ annihilation are performed within a kinetic model taking into account the space-time evolution of a longitudinally and transversely expanding medium. We show that the secondary charmonium production appears almost entirely during the mixed phase and it is very sensitive to the charmonium dissociation cross section with co-moving hadrons. Within the most likely scenario for the dissociatio…
Cross section of the process $e^+ + e^- \to Ξ^0 + \barΞ^0$ in the vicinity of charmonium $ψ(3770)$ and in the charmonium (-like) state including the $D$-meson loop and three-gluon contributions
Institute of Physics, Ministry of Science and Education（阿塞拜疆教育与科学部物理研究所）；Bogoliubov Laboratory of Theoretical Physics, JINR（俄罗斯杜布纳联合核子研究所鲍戈留博夫理论物理实验室）
In the framework of quark-hadron duality, the cross section values of charmonium and doubly charmed baryon production in $e^+e^-$-annihilations have been estimated at interaction energy $\sqrt{s}=10.6$ GeV. It has been shown that the approach under discussion allows to resolve some contradictions between the experimental data and pQCD predictions.
We calculate the cross section for the exclusive production of J^{PC}=0^{++} glueballs G_0 in association with the J/psi in e^+e^- annihilation using the pQCD factorization formalism. The required long-distance matrix element for the glueball is bounded by CUSB data from a search for resonances in radiative Upsilon decay. The cross section for e^+e^- -> J/psi+ G_0 at sqrt{s}=10.6 GeV is similar to exclusive charmonium-pair production e^+e^- -> J/psi+h for h=eta_c and chi_{c0}, and is larger by a factor 2 than that for h=eta_{c}(2S). As the subprocesses gamma^* -> (c c-bar) (c c-bar) and gamma^…
The strong coupling constant $α_s(μ)$ is extracted from the fits to charmonium spectrum and fine structure splittings. The relativistic kinematics is taken into account and relativistic corrections are shown to increase the matrix elements defining spin effects up to 40%. The value of $α_s(μ)$ at low-energy scale $μ=1.0 \pm 0.2 GeV$ was found to be $α_s(μ) = 0.38 \pm 0.03 (exp.) + 0.04 (theor.)$ which is about 50% lower than standard perturbative two-loop approximation and is in good agreement with the freezing $α_s$ behaviour.
By solving the covariant relativistic Schrödinger equations for a pair of heavy quarks, we obtained the wave functions for the ground and excited quarkonium states at finite temperature. In comparison with the non-relativistic calculation, the $J/ψ$ dissociation temperature determined by the infinity size or zero binding energy of the system increases $7%-13%$, when the central potential varies between the free energy and internal energy.
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…
In this paper, Schrodinger equation is numerically applied through non-relativistic potential model for deriving Spectrum, radial wave functions at origin, decay constants, lepton and photon decay widths for radial and orbital excited conventional as well as hybrid charmonium mesons. These calculated results are found in agreement with others theoretical results and with the experimental observations.
The $P$-wave charmonium decays $h_{c}\rightarrowγη^{(\prime)}$ are revisited by taking into account relativistic corrections. The decay amplitudes are derived in the Bethe-Salpeter formalism, in which the involved one-loop integrals are evaluated analytically. Intriguingly, from both the quark-antiquark content and the gluonic content of $η^{(\prime)}$, the relativistic corrections make significant contributions to the decay rates of $h_{c}\rightarrowγη^{(\prime)}$. By comparison with the leading-order contributions from the quark-antiquark content (one-loop level), the ones from the gluonic c…
Pion exchange in S-wave between hadrons that are themselves in a relative S-wave is shown to shift energies by hundreds of MeV, leading to deeply bound quasi-molecular states. In the case of charmed mesons $D^*,D_1$ a spectroscopy arises consistent with enigmatic charmonium states observed above 4 GeV in $e^+e^-$ annihilation. A possible explanation of $Y(4260)\to ψππ$ and $Y(4360) \to ψ'ππ$ is found. We give results for all isospin and charge-conjugation combinations, and comment on flavor exotic doubly charmed states and bottomonium analogs. A search in $D\bar{D}3π$ is recommended to test th…
We calculate the centrality dependence for coherent photoproduction of very low-$p_{T}$ $J/ψ$ at Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC) energies within the impact parameter dependent saturated color dipole model. By using the large equivalent photon fluxes, we present the differential cross section of very low-$p_{T}$ $J/ψ$ produced by coherent photonuclear in peripheral heavy-ion collisions. The numerical results demonstrate that our calculation are agree with $J/ψ$ data in peripheral heavy ion collisions at Relativistic Heavy Ion Collider (RHIC) energies.
We study the unpolarised and polarised hadro-production of charmonium in non-relativistic QCD (NRQCD) at low transverse momentum, including sufficiently higher orders in the relative velocity, $v$, so as to study the ratio of $χ_{c1}$ and $χ_{c2}$ production rates.
We study the nuclear medium effects on the $c\bar{c}$ time evolution and charmonium production, in a relativistic proton-nucleus collision. In particular, we focus on the fragmentation region of the nucleus where the formation length of the charmonium mesons is shorter than the size of the nucleus. Little is known on the nuclear effects in this region. We use a quantum-mechanical model which includes a realistic potential for the $c\bar{c}$ system and an imaginary potential to describe the collisions of the $c\bar{c}$ with the nucleons. The imaginary potential introduces a transition amplitude…
