We study the fine structure in the spectrum of known and predicted negative-parity hidden-charm exotic meson states, which comprise the lowest $P$-wave multiplet in the dynamical diquark model. Starting with a form previously shown to successfully describe the $S$-wave states, we develop a 5-parameter Hamiltonian that includes spin-orbit and tensor terms. After discussing the experimental status of the observed $J^{PC} = 1^{--}$ states $Y$ with respect to masses and decay modes (classified by eigenvalues of heavy-quark spin), we note a number of inconsistencies between measurements from different experiments that complicate a unique determination of the spectrum. Outlining a variety of scenarios for interpreting the $Y$ data, we perform fits to each one, obtaining results that demonstrate differing possibilities for the $P$-wave spectra. Choosing one of these fits for illustration, we predict masses for all 28 isomultiplets in this $1P$ multiplet, compare the results to tantalizing hints in the data, and discuss the rich discovery potential for new states.
The $J/ψp$ signals at 4380 MeV and 4450 MeV which were seen by the LHCb collaboration in the decay $Λ^0_b\to K^-J/ψp$ are discussed following the hypothesis of the existence of diquark-diquark-antiquark composite states. The discussed problems concern: (i) estimation of masses and mass splittings for low-lying states, (ii) determination of decay modes in the quark recombination scheme, (iii) unitarity and analyticity constrains for pentaquark propagators, (iv) hadronic deuteron-like components in the diquark-diquark-antiquark multiplet.
Some features and predictions of a recently proposed model based on diquark-antidiquark bound states are illustrated. Its ability in accomodating newly discovered charmed resonances around 4 GeV is discussed.
The yield of doubly charmed baryons with excited heavy diquark in $S$ wave and $P$ wave states has been estimated at LHC energies. The observation possibility of such baryons is discussed.
A diquark model is used to investigate single charmed baryons. In this model, baryon is composed of two diquarks and an antiquark. Masses of lowest lying states with $J^P= 1/2 ^ \pm$ are obtained. Some masses are smaller than other theoretic predictions which indicates that these baryons of pentaquark structure could be relatively stable. The results also show that $Λ(2882)$ may be a pentaquark with $J^P=1/2^-$ and $Ξ(3125)$ may be a pentaquark with $J^P=1/2^+$.
This is a conference mostly devoted to diquarks. Although an exotic meson can in principle be composed of a diquark and an antidiquark, such an exotic is unlikely to be experimentally observable in the near future. The reason, according to the model, is that diquark-antidiquark exotics have masses well above the threshold for decay into two mesons, and are likely to have widths too large to make them observable. A possible exception is a $ u d \bar b \bar b$ exotic, but it will be a long time before such a state can be observed even if it is stable against strong decay.
The masses of the excited heavy tetraquarks with hidden charm are calculated within the relativistic diquark-antidiquark picture. The dynamics of the light quark in a heavy-light diquark is treated completely relativistically. The diquark structure is taken into account by calculating the diquark-gluon form factor. New experimental data on charmonium-like states above open charm threshold are discussed. The obtained results indicate that X(3872), Y(4260), Y(4360), Z(4248), Z(4433) and Y(4660) could be tetraquark states with hidden charm.
The finite size of doubly heavy diquark gives a positive correction to the masses of baryons calculated in the local diquark approximation. We evaluate this correction for the basic states of doubly charmed baryons to give quite accurate predictions actual for current searches of those baryons at LHCb: $m[{Ξ_{cc}^{1/2}}^{+}]\approx m[{Ξ_{cc}^{1/2}}^{++}]=3615\pm 55$ MeV and $m[{Ξ_{cc}^{3/2}}^{+}]\approx m[{Ξ_{cc}^{3/2}}^{++}]=3747\pm 55$ MeV.
We discuss the quantum state structure on the basis of $SU(3)_c$ for some known exotic quark systems using a model which describes these particular states as highly correlated diquarks and antidiquarks. We are then able to calculate for a single colored diquark a finite von Neumann entropy from the quantum reduced density matrix, from which we explicitly evaluate the likelihood of certain arrangements of quark flavors in a given diquark. These results can be related to some recently experimentally found pentaquark systems as well as a possible model for the scalar mesons.
The properties of the Theta^{+} and Xi^{--}_{3/2} exotic baryons have been investigated in the framework of diquark- diquark-antiquark system. A model for diquark suggested in an analogy with the quasi-particle in a crystal lattice has been used. The mass of the exotics have been computed. The Decay width of the Theta^{+} has been estimated to be ~ 11 MeV using effective diquark theory. The radius of the Xi^{--}_{3/2} has been extracted as 0.94fm using the experimental value of the frac{Γ_{Θ^{+}}}{Γ_{Ξ^{--}_{3/2}}}. The results obtained are found to be in good agreement with the present experi…
The diquark-diquark-antiquark model describes pentaquark states both in terms of quarks and hadrons. The latest LHCb data for pentaquarks with open charm emphasize the importance of hadron components in the structure of pentaquarks. We discuss pentaquark states with hidden charm $P(\bar c cuud)$ and those with open charm $P(\bar uussc)$ which were discovered recently in LHCb data ($J/Ψp$ and $Ξ_c^+ K^-$ spectra correspondingly). Considering the observed states as members of the lowest (s-wave) multiplet we discuss the mass splitting of states and the dumping of their widths.
We investigate the meson, baryon and anti-baryon productions in πp and Kp collisions in terms of a constituent cascade model which includes charm flavour. The constituent diquark in an incident baryon has a tendency to get a large momentum fraction, resulting in considerable difference of subenergies for particle productions from quark-diquark and quark-antiquark chains in a meson-baryon collision. As a consequence, the leading particle effects on D meson productions are expected to be quite different in π+ and π- beams at present accelerator energies.
Charm spectroscopy has studied under a string model. Charmed baryons are composed of diquark and charm quark which are connected by a constant tension. In a diquark picture, the quantum numbers $J^P$ of confirmed baryons are well assigned. We give energy predictions for the first and second orbital excitations. We see some correspondences with the experimental data. Meanwhile, we have obtained diquark masses in the background of charm quark which satisfy a splitting relation based on spin-spin interaction.
Heavy-light diquarks can be the building blocks of a rich spectrum of states which can accommodate some of the newly observed charmonium-like resonances not fitting a pure c-cbar assignment. We examine this possibility for hidden and open charm diquark-antidiquark states deducing spectra from constituent quark masses and spin-spin interactions. Taking the X(3872) as input we predict the existence of a 2++ state that can be associated to the X(3940) observed by Belle and re-examine the state claimed by SELEX, X(2632). The possible assignment of the previously discovered states D_s(2317) and D_s…
This paper calculates the magnetic moments of the hidden-charm strange pentaquark states with a quantum number of $J^P={\frac{1}{2}}^{\pm}$, ${\frac{3}{2}}^{\pm}$, ${\frac{5}{2}}^{\pm}$, and ${\frac{7}{2}}^{+}$ in the molecular, diquark-diquark-antiquark, and diquark-triquark models, respectively. Numerical results demonstrate that the magnetic moments change for a different spin-orbit coupling with the same model and when involving different models with the same angular momentum.
Using the dynamical diquark model, we calculate the electric-dipole radiative decay widths to $X(3872)$ of the lightest negative-parity exotic candidates, including the four $I=0$, $J^{PC} \! = \! 1^{--}$ ("$Y$") states. The $O$(100--1000 keV) values obtained test the hypothesis of a common substructure shared by all of these states. We also calculate the magnetic-dipole radiative decay width for $Z_c(4020)^0 \! \to \! γX(3872)$, and find it to be rather smaller ($<$~10 keV) than its predicted value in molecular models.
The antiquark-diquark-diquark model describes pentaquark states both in terms of quarks and hadrons. We discuss pentaquark states with hidden charm $P(\bar c cuud)$ discovered in the $J/Ψp$ spectrum by the LHCb collaboration. We consider three pentaquark states as members of the lowest ($S$-wave) multiplet and discuss the mass splitting scheme. The latest LHCb data for pentaquarks with hidden charm provide an opportunity to make an assumption about the diquark content of the pentaquark states. We give a classification for the LHCb pentaquarks and define recombination channels for these states.
Exotic mesons with hidden strange ($s\bar s$) and heavy quark pairs ($Q\bar Q$), where $Q=c,b$, are considered as diquark-antidiquark systems, $(Qs)(\bar Q\bar s)$. Taking into account that these states can recombinate into two-meson ones, we study the interplay of these states in terms of the dispersion relation D-function technique. The classification of exotic mesons is discussed, coefficients for decay modes are given, predictions for new states are presented. The nonet structure for $((Qq)(\bar Q \bar q)$, ($(Qs)(\bar Q\bar s$)), ($(Qq)(\bar Q\bar s))$- states ($q=u,d$) is suggested.
We apply the diabatic formalism, an extension of the adiabatic approximation inherent to the Born-Oppenheimer (BO) approach of atomic physics, to the problem of mixing between exotic multiquark hadrons and their nearby di-hadron thresholds. The unperturbed BO eigenstates are obtained using the dynamical diquark model, while the diabatic calculation introduces a mixing potential between these states and the threshold states. We solve the resulting coupled Schrödinger equations numerically for hidden-charm tetraquarks of both open and closed strangeness to obtain physical mass eigenvalues, and e…
The LHCb has discovered two new states with preferred $J^P$ quantum numbers $3/2^-$ and $5/2^+$ from $Λ_b$ decays. These new states can be interpreted as hidden charm pentaquarks. It has been argued that the main features of these pentaquarks can be described by diquark model. The diquark model predicts that the $3/2^-$ and $5/2^+$ are in two separate octet multiplets of flavor $SU(3)$ and there is also an additional decuplet pentaquark multiplet. Finding the states in these multiplets can provide crucial evidence for this model. The weak decays of b-baryon to a light meson and a pentaquark ca…
Motivated by diquark exchange, we construct a class of extensions of the standard model. These models can generate large CP conserving and CP violating contributions to the doubly Cabbibo suppressed decays D^0\to K^+π^- without affecting D^0-\overline{D^0} mixing, contrary to what is usually believed in the literature. We find an interesting specific realization of these models, which has the LR chiral structure and can induce novel density \times density operators. It is new for non-leptonic kaon decays, and particularly, may provide a possible solution to the ΔI=1/2 rule and direct CP violat…
Non-strange and strange pentaquaks with hidden charm are considered as diquark-diquark-antiquark composite systems. Spin and isospin content of such exotic states is discussed and masses are evaluated.
The observation by BESIII and LHCb of states with hidden charm and open strangeness ($c\bar c q\bar s$) presents new opportunities for the development of a global model of heavy-quark exotics. Here we extend the dynamical diquark model to encompass such states, using the same values of Hamiltonian parameters previously obtained from the nonstrange and hidden-strange sectors. The large mass splitting between $Z_{cs}(4000)$ and $Z_{cs}(4220)$ suggests substantial SU(3)$_{\rm flavor}$ mixing between all $J^P \! = \! 1^+$ states, while their average mass compared to that of other sectors offers a …
In this article, we study the scalar-diquark-scalar-diquark-antiquark type $udsc\bar{c}$ pentaquark state with the QCD sum rules, the predicted mass $M_P=4.47\pm0.11\,\rm{GeV}$ is in excellent agreement with the experimental data $ 4458.8 \pm 2.9 {}^{+4.7}_{-1.1} \mbox{ MeV}$ from the LHCb collaboration, and supports assigning the $P_{cs}(4459)$ to be the hidden-charm pentaquark state with the spin-parity $J^P={\frac{1}{2}}^-$. We take into account the flavor $SU(3)$ mass-breaking effect, and estimate the mass spectrum of the diquark-diquark-antiquark type $udsc\bar{c}$ pentaquark states with …
The masses of the ground state and excited heavy tetraquarks with hidden charm and bottom are calculated within the relativistic diquark-antidiquark picture. The dynamics of the light quark in a heavy-light diquark is treated completely relativistically. The diquark structure is taken into account by calculating the diquark-gluon form factor. New experimental data on charmonium-like states above the open charm threshold are discussed. The obtained results indicate that X(3872), Y(4260), Y(4360), Z(4433) and Y(4660) can be tetraquark states with hidden charm.
Bottom-Charm $[bc]$ Diquark Masses from QCD Laplace Sum-Rules
National Yang Ming Chiao Tung University（国立阳明交通大学）；University of Saskatchewan（萨斯喀彻温大学）；Dordt University（多尔特大学）；Thompson Rivers University（汤普森河大学）；Johannes Gutenberg-Universität Mainz（美因茨约翰内斯·古腾堡大学）；University of the Fraser Valley（弗雷泽河谷大学）
The masses of heavy tetraquarks with hidden charm and bottom are calculated in the framework of the relativistic quark model. The tetraquark is considered as the bound state of a heavy-light diquark and antidiquark. The light quark in a heavy-light diquark is treated completely relativistically. The internal structure of the diquark is taken into account by calculating the diquark-gluon form factor in terms of the diquark wave functions. New experimental data on charmonium-like states above open charm threshold are discussed. The obtained results indicate that the X(3872) can be the tetraquark…
Using the QCD sum rule approach we investigate the possible four-quark structure of the recently observed charmed scalar mesons $D_0^{0}(2308)$ (BELLE) and $D_0^{0,+}(2405)$ (FOCUS) and also of the very narrow $D_{sJ}^{+}(2317)$, firstly observed by BABAR. We use diquak-antidiquark currents and work to the order of $m_s$ in full QCD, without relying on $1/m_c$ expansion. Our results indicate that a four-quark structure is acceptable for the resonances observed by BELLE and BABAR: $D_0^{0}(2308)$ and $D_{sJ}^{+}(2317)$ respectively, but not for the resonances observed by FOCUS: $D_0^{0,+}(2405)…
We use a non-relativistic model to study the mass spectroscopy of a tetraquark composed by $c \, \bar{c} \, c \, \bar{c}$ quarks in the diquark-antidiquark picture. By numerically solving the Schrödinger equation with a Cornell-inspired potential, we separate the four-body problem into three two-body problems. Spin-dependent terms (spin-spin, spin-orbit and tensor) are used to describe the splitting structure of the $c\bar{c}$ spectrum and are also extended to the interaction between diquarks. Recent experimental data on charmonium states are used to fix the parameters of the model and a satis…
In this article, we introduce a relative P-wave to construct the doubly-charm axialvector diquark operator, then take the doubly-charm axialvector (anti)diquark operator as the basic constituent to construct the scalar and tensor tetraquark currents to study the scalar, axialvector and tensor fully-charm tetraquark states with the QCD sum rules. We observe that the ground state $\tilde{A}\tilde{A}$ type tetraquark states and the first radial excited states of the $AA$ type tetraquark states have almost degenerated masses, where the $\tilde{A}$ and $A$ stand for the diquark operators with and w…
The hadronization effects induced by different colour connections of $c\bar{c}q\bar{q}$ system in $e^+e^-$ annihilation are investigated by a toy model where diquark fragmentation is employed based on Pythia. It is found that the correlations between the charm baryons and charm antibaryons produced via diquark pair fragmentation are much stronger, and their momentum spectra are harder than those from the standard colour connection in Pythia.
In this article, we construct both the axialvector-diquark-axialvector-diquark-antiquark type and axialvector-diquark-scalar-diquark-antiquark type interpolating currents, then calculate the contributions of the vacuum condensates up to dimension-10 in the operator product expansion, and study the masses and pole residues of the $J^P={\frac{1}{2}}^\pm$ hidden-charm pentaquark states with the QCD sum rules in a systematic way. In calculations, we use the formula $μ=\sqrt{M^2_{P}-(2{\mathbb{M}}_c)^2}$ to determine the energy scales of the QCD spectral densities. We take into account the $SU(3)$ …
In this article, we study the mass spectrum of the scalar hidden charm and bottom tetraquark states with the QCD sum rules. The numerical results are compared with the corresponding ones from a relativistic quark model based on a quasipotential approach in QCD. The relevant values from the constituent diquark model based on the constituent diquark masses and the spin-spin interactions are also discussed.
The masses of the heavy tetraquarks with open charm and bottom are calculated within the diquark-antidiquark picture in the framework of the relativistic quark model. The dynamics of the light quarks and diquarks is treated completely relativistically. The diquark structure is taken into account by calculating the diquark-gluon form factor. New experimental data on charmed and charmed-strange mesons are discussed. Our results indicate that the anomalous scalar D_{s0}^*(2317) and axial vector D_{s1}(2460) mesons could not be considered as diquark-antidiquark bound states. On the other hand, D_s…
In this article, we construct the scalar-diquark-axialvector-diquark-antiquark type interpolating currents, and study the masses and pole residues of the $J^{P}=\frac{3}{2}^{\pm}$ hidden-charmed pentaquark states with the QCD sum rules. In calculations, we use the formula $μ=\sqrt{M^2_{P}-(2{\mathbb{M}}_c)^2}$ to determine the energy scales of the QCD spectral densities. We obtain the masses of the hidden-charm pentaquark states with the strangeness $S=-1$ and $S=-2$, which can be confronted to the experimental data in the future.
A menage a trois is very different from an ordinary family. Similarly, exotic hadrons with both qq and qbar q pairs have important color-space correlations that are completely absent in ordinary mesons and baryons. The presence of both types of pairs requires attention to the basic QCD physics that the q qbar interaction is much stronger than the qq interaction. This new physics in multiquark systems produces color structures totally different from those of normal hadrons, for example the ud system is utterly unlike the ud diquark in the uds Lambda baryon. The color-space correlations produce …
The mass spectrum of hidden charm pentaquark states composed of two diquarks and an antiquark are calculated by use of an effective Hamiltonian which includes explicitly the spin, color, and flavor dependent interactions. The results show that the $P_c(4312)^+$ and $P_c(4440)^+$ states could be explained as hidden charm pentaquark states with isospin and spin-parity $IJ^P=1/2\left(3/2^-\right)$, the $P_c(4457)^+$ state could be explained as a hidden charm pentaquark state with $IJ^P=1/2\left(5/2^-\right)$, and the $P_{cs}(4459)^+$ state could be explained as a hidden charm pentaquark state wit…
The perturbative QCD calculation of heavy quark fragmentation into a heavy meson is extended to predict fragmentation into heavy flavor baryons. This is accomplished by implementing the quark-diquark model of the baryons. Several diquark form factors are used to enable the integration over the virtual heavy quark momentum. The resulting spin independent functions for charmed quarks to fragment into charmed baryons with spin 1/2 and 3/2 are compared with recent data. Predictions are made for the spin dependent fragmentation functions as well, particularly for the functions $\hat{g}_1$ in the ca…
We apply the dynamical diquark model to predict the spectrum of hidden-charm pentaquark states in both unflavored and open-strange sectors. Using only Hamiltonian parameters introduced in the tetraquark $S$- and $P$-wave multiplets, the model naturally produces the level spacing supported by the most recent LHCb results for $P_c$ structures. Furthermore, using model inputs obtained from data of hidden-charm, open-strange tetraquarks ($Z_{cs}$), we predict the spectrum of $P_{cs}$ states, including the recently observed $P_{cs}(4459)$. We find all pentaquark candidates observed to date to belon…
We calculate open charm production in $Pb+Pb$ reactions at SPS energies within the HSD transport approach - which is based on string, quark, diquark ($q, \bar{q}, qq, \bar{q}\bar{q}$) and hadronic degrees of freedom - including the production of open charm pairs from secondary 'meson'-'baryon' (or quark-diquark and antiquark-diquark) collisions. It is argued that at collision energies close to the $c\bar{c}$ pair threshold the dominant production mechanism is related to the two body (or quasi two body) reactions $πN \to \bar{D} (\bar{D^*}) Λ_c, (Σ_c)$. Estimates within the framework of the Qua…
Diquarks with $J^{P}=0^{\pm}$, $1^{\pm}$ containing a heavy (charm or bottom) quark and a light quark are investigated using QCD Laplace sum rules. Masses are determined using appropriately constructed gauge invariant correlation functions, including for the first time next-to-leading order perturbative contributions. The $J^P=0^+$ and $1^+$ charm-light diquark masses are respectively found to be 1.86$\pm$0.05 GeV and 1.87$\pm$0.10 GeV, while those of the $0^+$ and $1^+$ bottom-light diquarks are both determined to be 5.08$\pm$0.04 GeV. The sum rules derived for heavy-light diquarks with negat…
In this article, we study the masses and pole residues of the pseudoscalar-diquark-pseudoscalar-antidiquark type and vector-diquark-vector-antidiquark type scalar hidden-charm $cu\bar{c}\bar{d}$ ($cu\bar{c}\bar{s}$) tetraquark states with QCD sum rules by taking into account the contributions of the vacuum condensates up to dimension-10 in the operator product expansion. The predicted masses can be confronted with the experimental data in the future. Possible decays of those tetraquark states are also discussed.
In this paper, we study four-body systems consisting of diquark antidiquark, and we analyze diquark-antidiquark in the framework of a two body (pseudo point) problem. We solve Lippman Schwinger equation numerically for charm diquark antidiquark systems and find the eigenvalues to calculate the binding energies and masses of heavy tetraquarks with hidden charms. Our results are in good agreement with theoretical and experimental data.
A chiral effective theory of quarks and diquarks is formulated and applied to exotic tetraquarks and pentaquarks. The effective theory is similar to the chiral quark effective theory with the addition of diquark degrees of freedom and couplings to quarks. Chiral symmetry through generalized Goldberger-Treiman relations, fixes the mass splitting between the even and odd parity diquarks to be about 600 MeV. We provide an estimate of the parameters of the effective theory from both the random instanton model and known data on the low lying scalar nonet. We assess the static properties of the exot…
We use a non-relativistic model to study the spectroscopy of a tetraquark composed of $[cc][\bar{c}\bar{c}]$ in a diquark-antidiquark configuration. By numerically solving the Schrödinger equation with a Cornell-inspired potential, we separate the four-body problem into three two-body problems. Spin-dependent terms (spin-spin, spin-orbit and tensor) are used to describe the splitting structure of the $c\bar{c}$ spectrum and are also extended to the interaction between diquarks. Recent experimental data on charmonium states are used to fix the parameters of the model and a satisfactory descript…
We incorporate fine-structure corrections into the dynamical diquark model of multiquark exotic hadrons. These improvements include effects due to finite diquark size, spin-spin couplings within the diquarks, and most significantly, isospin-dependent couplings in the form of pionlike exchanges assumed to occur between the light quarks within the diquarks. Using a simplified two-parameter interaction Hamiltonian, we obtain fits in which the isoscalar $J^{PC} = 1^{++}$ state---identified as the $X(3872)$---appears naturally as the lightest exotic (including all states that are predicted by the m…
A perturbative QCD calculation of heavy flavor quark fragmentation into heavy flavor baryons is developed along the lines of corresponding heavy meson models. The non-perturbative formation of the baryon is accomplished by implementing the quark-diquark model of the baryons. Diquark color form factors are used to enable the integration over the virtual heavy quark momentum. The resulting spin independent functions for charmed and bottom quarks to fragment into charmed and bottom baryons with spin 1/2 and 3/2 are compared with recent data. Predictions are made for the spin dependent fragmentati…
We study the spectroscopy of the states which defy conventional $c\bar{c}$ charmonium and $b\bar{b}$ bottomonium interpretation respectively, and are termed as exotic states. In August 2003 a state X(3872), was discovered [K. Abe\textit{\ et al.} (Belle Collaboration), Phys. Rev. Lett. \textbf{91}, 262001 (2003) [arXiv:hep-ex/0309032]] and in December 2007 a state Y(10890) was reported [K. F. Chen \textit{et. al.} [Belle Collaboration], Phys. Rev. Lett. \textbf{100}, 112001 (2008) [arXiv:0710.2577]. One possible interpretation of such exotic state is that they are tetraquark (diquark-antiquark…
The production of baryons containing two charmed quarks Xi_cc in hadronic interactions at high energies and large transverse momenta is considered. It is supposed, that Xi_cc-baryon is formed during a non-perturbative fragmentation of the (cc)-diquark, which was produced in the hard process of $c$-quark scattering from the colliding protons: c+c -> (cc) +g. It is shown that such mechanism enhances the expected doubly charmed baryon production cross section on Tevatron and LHC colliders approximately 2 times in contrast to predictions, obtained in the model of gluon - gluon production of (cc)-d…
In this article, we study the mass spectrum of the scalar and axial-vector heavy diquark states with the QCD sum rules in a systematic way. Once the reasonable values are obtained, we can take them as basic parameters and study the new charmonium-like states as the tetraquark states.
