We revisit earlier calculations of leptonic decay constants of vector charmonia and present and illustrate our decomposition of the corresponding covariant Bethe-Salpeter amplitudes in terms of orbital angular momentum as interpreted in the meson's rest frame. Our results confirm our previous conclusions drawn from the magnitudes of vector-meson leptonic decay constants, identifying the Psi(3770) and Psi(4160) as D-wave states in our setup.
Inspired by the recent observations of the vector charmonium-like states at BES III Collaboration and $ψ(3842)$ at LHCb Collaboration, we comb the $D$ wave charmonium state in the present work. We first evaluate the possibility of $Y(4320)$ as $ψ(3^3D_1)$ by investigating its open charm decays in quark-pair creation model and we find the width of $Y(4320)$ can be reproduced in a reasonable parameter range. Moreover, we take $ψ(3770)$, $ψ(4160)$ and $Y(4320)$ as the scale of $1D$, $2D$ and $3D$ charmonia to estimate the open charm decays of other $D$ wave charmonia. The total and partial widths…
We show that the newly measured branching ratios of vector charmonia ($J/ψ$, $ψ^\prime$ and $ψ(3770))$ into $γP$, where $P$ stands for light pseudoscalar mesons $π^0$, $η$, and $η^\prime$, can be well understood in the framework of vector meson dominance (VMD) in association with the $η_c$-$η(η^\prime)$ mixings due to the axial gluonic anomaly. These two mechanisms behave differently in $J/ψ$ and $ψ^\prime\to γP$. A coherent understanding of the branching ratio patterns observed in $J/ψ(ψ^\prime)\to γP$ can be achieved by self-consistently including those transition mechanisms at hadronic leve…
We study the semileptonic differential decay rates of $B_c$ meson to S-wave charmonia, $η_c$ and $J/Ψ$, at the next-to-leading order accuracy in the framework of NRQCD. In the heavy quark limit, $m_b \to \infty$, we obtain analytically the asymptotic expression for the ratio of NLO form factor to LO form factor. Numerical results show that the convergence of the ratio is perfect. At the maximum recoil region, we analyze the differential decay rates in detail with various input parameters and polarizations of $J/ψ$, which can now be checked in the LHCb experiment. Phenomenologically, the form f…
Solved is a new puzzle raised by the observation of an enhancement structure Z(3930) in $γγ\to D\bar{D}$. If categorizing Z(3930) as $χ_{c2}(2P)$ suggested by Belle and BaBar, we must explain why $χ_{c0}(2P)$ dominantly decaying into $D\bar{D}$ is missing in the $D\bar{D}$ invariant mass spectrum. In this work, we propose that the Z(3930) enhancement structure may contain two $P$-wave higher charmonia {$χ_{c0}(2P)$} and $χ_{c2}(2P)$. We show that this assumption is supported by our analysis of the $D\bar{D}$ invariant mass spectrum and $\cosθ^\ast$ distribution of $γγ\to D\bar{D}$. This observ…
We investigate the ground-state heavy quarkonium $χ_{c1}(1P)$ and its first excited state $χ_{c1}(2P)$ with quantum numbers $J^{PC}=1^{++}$. The masses and decay constants of these charmonium states are computed using two-point QCD sum rule method by including quark, gluon and mixed condensates up to dimension-8. We compare our numerical results with the available experimental data as well as existing theoretical predictions in the literature.
B_c mesons are laboratories for probing heavy quark physics. Furthermore, they decay into charmonia and hence their decays can be used to analyze possible exotic charmonium. In this work, the semileptonic decays of B_c mesons into P wave charmonia are analysed using light cone QCD sum rules (LCSR). The distributions amplitudes for the charmonia are taken from a quark model computation. The obtained decay rates for the ground state and excited charmonia are compared with the results found in the literature.
We consider exclusive double diffractive production of polarised axial-vector $χ_c(1^+)$ and tensor $χ_c(2^+)$ charmonia in proton-(anti)proton collisions at Tevatron energy. The corresponding amplitudes for these processes are derived within the $k_t$-factorisation approach. Contributions from different polarisation states of axial-vector and tensor charmonia are quantified. Corresponding experimental consequences are discussed.
The importance of the color octet component in P-wave charmonia is discussed in the context of exclusive decay processes. It is vital to include this contribution already at the level of the two-body decay channels. The ππand proton-antiproton channels are used as examples.
The mass spectrum and the two-body open-charm decays of the $J^{PC}=1^{--}$ charmonium states are studied with the coupled-channel effects taken into account. The coupled-channel-induced mixing effects among the excited vector charmonia are studied. Based on our calculations of the masses and the decay widths, we find that the tension between the observed properties of $Y(4260)/Y(4360)$ and their conventional charmonia interpretations could be softened.
Under the aegis of isospin conservation, the amplitudes in Born approximation, i.e., considering the only one-photon-exchange mechanism, of the decay $ψ\to Λ\overline Σ^0+{\rm c.c.}$, where $ψ$ is a vector charmonium, and of the reaction $e^+e^- \to Λ\overline Σ^0+{\rm c.c.}$ at the $ψ$ mass, are parametrized by the same electromagnetic coupling. It follows that, the modulus of such a coupling can be extracted the data on the two observables: the decay branching fraction and the annihilation cross section. By considering the first two vector charmonia, $J/ψ$ and $ψ(2S)$, it is found that, espe…
The masses of charmonium s and p-states, pseudoscalar and vector decay constants, leptonic, hadronic as well as radiative decay widths for charmonia have been computed in the framework of extended harmonic confinement model without any additional parameters. The outcome in comparison with other contemporary theoretical and experimental results is presented.
We study the semi-leptonic and non-leptonic decays of $B_c$ meson to $D$-wave charmonia, namely, $η_{c2}(1^1\!D_2)$, $ψ_2(1^3\!D_2)$, and $ψ_3(1^3\!D_3)$. In our calculations, the instantaneous Bethe-Salpeter method is applied to achieve the hadronic matrix elements. This method includes relativistic corrections which are important especially for the higher orbital excited states. For the semi-leptonic decay channels with electron as the final lepton, we get the branching ratios $\mathcal{B}[B_c \rightarrow η_{c2}e\barν_e] = 5.9^{-0.8}_{+1.0}\times 10^{-4}$, $\mathcal{B}[B_c \rightarrow ψ_2e\b…
In the framework of QCD factorization, we study the $B$ meson exclusive decays $B\to χ_{cJ}K$ where the spin-triplet P-wave charmonium states $χ_{cJ}(J=0,1,2)$ are described by the color-singlet non-relativistic wave functions. We find that for these decays (except $χ_{c1}$) there are infrared divergences arising from nonfactorizable vertex corrections as well as logarithmic end-point singularities arising from nonfactorizable spectator interactions at leading-twist order. The infrared divergences due to vertex corrections will explicitly break down QCD factorization within the color-singlet m…
We discuss the possibilities of producing the X(3872), which is assumed to be a D \bar D^* bound state, in radiative decays of charmonia. We argue that the ideal energy regions to observe the X(3872) associated with a photon in e^+e^- annihilations are around the Y(4260) mass and around 4.45 GeV, due to the presence of the S-wave D \bar D_1(2420) and D^* \bar D_1(2420) threshold, respectively. Especially, if the Y(4260) is dominantly a D \bar D_1 molecule and the X(3872) a D \bar D^* molecule, the radiative transition strength will be quite large.
For the flavour-singlet heavy quark system of charmonia, we compute the masses of the ground state mesons in four different channels: pseudo-scalar ($η_c(1S)$), vector ($J/Ψ(1S)$), scalar ($χ_{c_0}(1P)$) and axial vector ($χ_{c_{1}}(1P)$), as well as the weak decay constants of the $η_c(1S)$ and $J/Ψ(1S)$ and the charge radius of $η_c(1S)$. The framework for this analysis is provided by a symmetry-preserving Schwinger-Dyson equation (SDEs) treatment of a vector$\times$vector contact interaction (CI). The results found for the meson masses and the weak decay constants, for the spin-spin combina…
In this work, we investigate the $X(3915)$ and $Z(3930)$ decays into $J/ψω$ with the $χ_{c0}^\prime(2P)$ and $χ_{c2}^\prime (2P)$ assignments to $X(3915)$ and $Z(3930)$, respectively. The results show that the decay width of $Z(3930)\to J/ψω$ is at least one order smaller than that of $X(3915)\to J/ψω$. This observation explains why only one structure $X(3915)$ has been observed in the $J/ψω$ invariant mass spectrum for the process $γγ\to J/ψω$.
Adding to the long standing "rho-pi puzzle" in psi(3686) and J/psi decays, recently BES reported the branching ratio of psi(3686) -> Kshort Klong which is enhanced relative to the pQCD " 12% rule" expectation from the branching ratio of J/psi -> Kshort Klong. If the enhancement is due to the mixing of the S- and D-wave charmonium states as in the rho-pi case, the newly measured branching ratio of psi(3686) -> Kshort Klong gives a constraint on the psi(3770) -> Kshort Klong. It serves as a good test for the scenario of the S- and D-wave mixing in the psi(3686) and psi(3770).
The form factors of the semileptonic $B_c\to S(AV)\ellν$ $(\ell=τ, μ, e)$ transitions, where S and AV denote the scalar $X_{c0}$ and axial vector $(X_{c1}, h_{c})$ mesons, are calculated within the framework of the three-point QCD sum rules. The heavy quark effective theory limit of the form factors are also obtained and compared with the values of the original transition form factors. The results of form factors are used to estimate the total decay widths and branching ratios of these transitions. A comparison of our results on branching ratios with the predictions of other approaches is also…
How to hunt for higher $P$-wave states of charmonium is still an open topic when $2P$ charmonia were identified. {In this work, we present an unquenched quark model calculation to illustrate the spectroscopy behavior of these $3P$, $4P$ and $5P$ states in charmonium family.} For the $3P$ charmonia, the predicted masses are around 4.2 GeV and their two-body open-charm decay behaviors were given, by which we propose that searching for these $3P$ states via their open-charm decay channels from $γγ$ fusion and $B$ decay can be accessible at future experiment like LHCb and Belle II. We continue to …
QCD string model is employed to calculate the masses and spin splittings of lowest charmonium hybrid states with a magnetic gluon. Relative decay rates into various S- and P-wave D-meson pairs are calculated for these hybrids.
In the covariant light-front quark model, we investigate the $B_c\to h_c, χ_{c0,1,2}$ form factors. The form factors are evaluated in space-like kinematic region and are recasted to the physical region by adopting the exponential parametrization. We also study the semileptonic $B_c$ decays and find that branching fractions for the $B_c\to (h_c,χ_{c0,1,2})l\barν(l=e,μ)$ decays have the order $10^{-3}$ while branching fractions for $B_c\to (h_c,χ_{c0,1,2})τ\barν_τ$ are suppressed by one order. These predictions will be tested at the forthcoming hadron colliders.
We investigate the charmless decays of excited $P$-wave charmonia $χ_{c1}^\prime \to VV$ and $χ_{c2}^\prime \to VP$ via intermediate charmed meson loops, where $V$ and $P$ denote the light vector and pseudoscalar mesons, respectively. Within the model parameters, the charmed meson loop contributions are evaluated by using the effective Lagrangian approach. For $χ_{c1}^\prime \to VV$, the partial widths of the $ρρ$, $ωω$, and $K^*{\bar K}^*$ channels can reach to the order of MeV, while the partial width of the $ϕϕ$ channel is very small and in the order of keV. For $χ_{c2}^\prime \to V P$, the…
We show that the twist-2 light-cone wave-functions of eta_c and J/ψcan be factorized with nonrelativistic QCD(NRQCD) at one-loop level, where the nonperturbative effects are represented by NRQCD matrix elements. The factorization is achieved by expanding the small velocity v, which the c- or \bar c- quark moves inside a rest quarkonium with. At leading order of v the twist-2 light-cone wave-functions of eta_c and J/ψcan be factorized as the product of a perturbative function and a NRQCD matrix element. The perturbative function is calculated at one-loop level and free from any soft divergence.…
We study strong decays of the possible fully-charm tetraquarks recently observed by LHCb, and calculate their relative branching ratios through the Fierz rearrangement. Together with our previous QCD sum rule study [Phys. Lett. B 773, 247 (2017)], our results suggest that the broad structure around $6.2$-$6.8$ GeV can be interpreted as an $S$-wave $cc\bar c \bar c$ tetraquark state with $J^{PC} = 0^{++}$ or $2^{++}$, and the narrow structure around 6.9 GeV can be interpreted as a $P$-wave one with $J^{PC} = 0^{-+}$ or $1^{-+}$. These structures were observed in the di-$J/ψ$ invariant mass spec…
The presented paper is devoted to theoretical analysis of charmonium mesons $η_c$, $J/ψ$, $χ_{c0,1,2}$, and $h_c$ production in exclusive radiative $Z$ boson decays in the frameworks of Nonrelativistic Chromodynamic and amplitude expansion on the light-cone. In the framework of light-cone expansion amplitudes and widths of all processes are described with one universal relation. It is interesting to note that from this relation it follows automatically which component of $Z$ boson (either vector or axial) gives contribution to the width of the particular decay. It is shown that the effect of i…
In this work, the decays of $B_s$ mesons to a charmonium state and a $K^+K^-$ pair are carefully investigated in the perturbative QCD approach. Following the latest fit from the LHCb experiment, we restrict ourselves to the case where the produced $K^+K^-$ pair interact in isospin zero $S$, $P$, and $D$ wave resonances in the kinematically allowed mass window. Besides the dominant contributions of the $ϕ(1020)$ resonance in the $P$-wave and $f_2'(1525)$ in the $D$-wave, other resonant structures in the high mass region as well as the $S$-wave components are also included. The invariant mass sp…
We present lattice QCD results for the screening masses of light mesons and charmonia. The lattice computations were performed with 2+1 flavors of improved staggered quarks using quark masses which correspond to realistic pion and kaon masses at zero temperature. For the light quark sector we have found that the screening masses in the pseudo-scalar and the isovector scalar channels do not become degenerate at the chiral crossover temperature indicating an effective non-restoration of the axial symmetry. Also the splitting between the vector and the pseudo-scalar screening masses persists even…
We investigate two exclusive processes, e+ e- -> eta_c + gamma and e+ e- -> J/psi + J/psi, at the center-of-momentum energy sqrt{s}=10.58 GeV within the framework of the nonrelativistic QCD factorization approach. A class of relativistic corrections is resummed to all orders in the heavy-quark velocity v and the corrections are large negative. We further improve the prediction by including available QCD next-to-leading-order corrections and the interference between the QCD and relativistic corrections. The prediction for sigma[e+ e- -> eta_c + gamma] is about 50 fb. In the case of e+ e- -> J/p…
Motivated by the experimental findings of some new exotic states decaying into channels like $J/ψϕ$, we investigate the formation of resonances/bound states in the $D^*_s\bar D^*_s$ system using QCD sum rules. To do this we start with a current of the type vector times vector and use spin projectors to separate the spin 0, 1 and 2 contributions to the correlation function. We find three states with isospin 0, nearly spin degenerate, with a mass around 4.1 GeV. We have also investigated the decay of these states to $J/ψϕ$ and provide the corresponding partial widths. Such information should be …
We investigate the two-photon transitions $H_{c\bar c} \to γ^*γ$ of the charmonium system in light-front dynamics. The light-front wave functions were obtained from solving the effective Hamiltonian based on light-front holography and one-gluon exchange interaction within the basis light-front quantization approach. We compute the two-photon transition form factors as well as the two-photon decay widths for S- and P-wave charmonia, $η_c$ and $χ_{cJ}$ and their excitations. Without introducing any free parameters, our predictions are in good agreement with the recent experimental measurements b…
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.
Within the framework of nonrelativisitic QCD factorization formalism, we present the next-to-leading-order relativistic corrections to $Υ$ exclusive decay into $η_c$ plus $J/ψ$. The double charmonia can be produced through several immediate channels, i.e. $Υ\to g^*g^*g^*\to η_c+J/ψ$, $Υ\to g^*g^*γ^*\to η_c+J/ψ$, and $Υ\to γ^*\to η_c+J/ψ$. The amplitudes of these three channels are obtained accurate up to ${\cal O}(α_s^3 v^2)$, ${\cal O}(αα_s^2 v^2)$, and ${\cal O}(αα_s^2 v^2)$ respectively, where $v$ indicates the typical heavy quark velocity in bottomonium and/or charmonium rest frame. The de…
In this work, we investigate the spectroscopy and decay rates of charmonia within the framework of non-relativistic Schrödinger equation by employing an approximate inter quark-antiquark potential. The spin hyperfine, spin-orbit and tensor components of the one gluon exchange interaction are employed to compute the spectroscopy of the excited S states and few low-lying P and D waves. The resultant wave functions at zero inter quark separation as well as some finite separation are employed to predict the di-gamma, di-leptonic and di-gluon decay rates of charmonia states by using the conventiona…
We investigate the changes of the masses and widths of $χ_{c0}$ and $χ_{c1}$ in hot gluonic matter near $T_c$ and in nuclear medium using QCD sum rules. As in the previous works for the $J/ψ$ and $η_c$, in-medium effects are incorporated through the changes of gluon condensates. Twist-2 terms for the $^3 P_0 (χ_{c0})$ and $^3 P_1 (χ_{c1})$ are also included for the first time. The results show that larger mass shifts and width broadenings take place as compared to the $S$-wave states. As the critical change take place near $T_c$, related measurements can reveal critical phenomenon in QCD.
This paper is devoted to the study of the leading twist distribution amplitudes of P-wave nonrelativistic mesons. It is shown that at the leading order approximation in relative velocity of quark-antiquark pair inside the mesons these distribution amplitudes can be expressed through one universal function. As an example, the distribution amplitudes of the P-wave charmonia mesons are considered. Within QCD sum rules the model for the universal function of P-wave charmonia mesons is built. In addition, it is found the relations between the moments of the universal function and the nonrelativisti…
We propose a new model to create a light meson in the heavy quarkonium transition, which is inspired by the Nambu$-$Jona-Lasinio (NJL) model. Hadronic transitions of $J^{PC}=1^{--}$ higher charmonia with the emission of an $η$ meson are studied in the framework of the proposed model. The model shows its potential to reproduce the observed decay widths and make predictions for the unobserved channels. We present our predictions for the decay width of $Ψ\to J/ψη$ and $Ψ\to h_{c}(1P)η$, where $Ψ$ are higher $S$ and $D$ wave vector charmonia, which provide useful references to search for higher ch…
Based on a general form of the effective vertex functions for the decays of P-wave charmonia $\chicj$, angular distribution formulas for the subsequent decays $\chicj\rightarrow \jpsi γ$ and $\jpsi \to μ^+μ^-$ are derived. The formulas are the same as those obtained in a different approach in the literature. Our formulas are expressed in a more general form, including parity violation effects and the full angular dependence of $\jpsi$ and muon in the cascade decay $\chicj\to\jpsiγ\toμ^+μ^-γ$. The $\chicj$ polarization observables are expressed in terms of rational functions of the spin density…
The quark potential model for mesons and its extension for hybrid mesons are used to study the effects of radial excitations on the masses, sizes and radial wave functions at the origin for conventional and hybrid charmonium mesons. These results can help in experimentally recognizing hybrid mesons. The properties of conventional and hybrid charmonium mesons are calculated for the ground and radially excited states using the shooting method to numerically solve the required Schrodinger equation for the radial wave functions. We compare our results with the experimentally observed masses and t…
Disentangling isospin violation in charmonia decaying into $Ξ\overline Ξ$ pairs
State Key Laboratory of Heavy Ion Science and Technology, Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所重离子物理与加速器大科学装置全国重点实验室）；School of Nuclear Sciences and Technology, University of Chinese Academy of Sciences（中国科学院大学核科学与技术学院）；Department of Physics, Yunnan University（云南大学物理系）；Research Center for Hadron and CSR Physics, Lanzhou University and Institute of Modern Physics of CAS（兰州大学与中科院近代物理所强子物理与重离子加速器物理研究中心）
We indicated in our previous work that for QED the contributions of the scalar potential which appears at the loop level is much smaller than that of the vector potential and in fact negligible. But the situation may be different for QCD, one reason is that the loop effects are more significant because $α_s$ is much larger than $α$, and secondly the non-perturbative QCD effects may induce the scalar potential. In this work, we phenomenologically study the contribution of the scalar potential to the spectra of charmonia. Taking into account both vector and scalar potentials, by fitting the well…
This paper gives results for the spectrum, all allowed E1 radiative partial widths (and some important M1 widths) and all open-charm strong decay amplitudes of all 40 c-cbar states expected up to the mass of the 4S multiplet, just above 4.4 GeV. The spectrum and radiative widths are evaluated using two models, the relativized Godfrey-Isgur model and a nonrelativistic potential model. The electromagnetic transitions are evaluated using Coulomb plus linear plus smeared hyperfine wavefunctions, both in a nonrelativistic potential model and in the Godfrey-Isgur model. The open-flavor strong decay …
We investigate the properties of charmonia in a thermal medium, showing that with increasing temperature the decay widths of these mesons behave in a non-trivial way. Employing a potential model with interaction potential extracted from thermal lattice QCD calculations of the free-energy of a static quark-antiquark pair, we study some decay processes in the crossover region. We find that at temperatures $T \sim T_c$ the decay widths of the $J/Ψ$ that depend on the value of the wave function at the origin are enhanced with respect to the values in vacuum. In the same temperature range the decay…
We examine the status of charmonia like states by looking into the behaviour of the energy level differences and regularity in the behaviour of the leptonic decay widths of the excited charmonia states. The spectroscopic states are studied using a phenomenological Martin-like confinement potential and their radial wave functions are employed to compute the di-leptonic decay widths. Their deviations from the expected behaviour provide a clue to consider them as admixtures of the nearby S and D states. The present analysis strongly favour \$$\backslash$psi \$ (3686) as admixture of $c \bar{c}$ (…
In this work, we investigate the open-charm decay process $ψ\toΛ_c\barΛ_c$ via the hadronic loop mechanism for vector charmonia above $Λ_c\barΛ_c$ threshold. The branching ratios of these vector charmonium states to $Λ_c\barΛ_c$ are estimated. The charmonium explanation of the $Y(4630)$ observed in $e^+e^- \to Λ_c\barΛ_c$ is tested. Furthermore, for the predicted higher vector charmonia above 4.7 GeV, the branching ratios $\mathcal{B}[ψ(nS)\toΛ_c\barΛ_c]$ with $n=7,8,9$ are found to be of the order of magnitude of $10^{-4}-10^{-3}$ while $\mathcal{B}[ψ(mD)\toΛ_c\barΛ_c]$ with $m=6,7,8$ are of …
