Four-quark Structure Research Articles

Four-quark structure of the Zc(3900) , Z(4430) , and Xb(5568) states

We examine the four-quark structure of the recently discovered charged $Z_c(3900)$, $Z(4430)$, and $X_b(5568)$ states. We calculate the widths of the strong decays $Z_c^+ \to J/\psi \pi^+$ ($\eta_c\rho^+$, $\bar D^0D^{\ast\,+}$, $\bar D^{\ast\,0}D^+$), $Z(4430)^+ \to J/\psi \pi^+$ ($\psi(2s) \pi^+$), and $X^+_b\to B_s\pi^+$ within a covariant quark model previously developed by us. We find that the tetraquark-type current widely used in the literature for the $Z_c(3900)$ leads to a significant suppression of the $\bar D D^\ast$ and $\bar D^\ast D$ modes. Contrary to this a molecular-type current provides an enhancement by a factor of 6-7 for the $\bar D D^\ast$ modes compared with the $Z_c^+\to J/\psi\pi^+$, $\eta_c\rho^+$ modes in agreement with recent experimental data from the BESIII Collaboration. In case of the $Z(4430)$ state we test a sensitivity of the ratio $R_Z$ of the $Z(4430)^+ \to \psi(2s) \pi^+$ and $Z(4430)^+ \to J/\psi \pi^+$ decay rates to a choice of the size parameter $\Lambda_{Z(4430)}$ of the $Z(4430)$. Using upper constraint for the sum of these two modes deduced from the LHCb Collaboration data we find that $R_Z$ varies from 4.64 to 4.08 when $\Lambda_{Z(4430)}$ changes from 2.2 to 3.2 GeV. Also we make the prediction for the $Z(4430)^+ \to D^{\ast\,+} \bar D^{\ast\,0}$ decay rate.

Testing the tetraquark structure for the X resonances in the low-lying region

Assuming four-quark structure for the $X$ resonances in low-lying region, we calculate their masses using the color-spin interaction. In specific, the hyperfine masses of the color-spin interaction are calculated for the possible states in spin-0, spin-1, spin-2 channels. The two states in spin-0 channel as well as the two states in spin-1 channel are diagonalized in order to generate the physical hyperfine masses. By matching the difference in hyperfine masses with the splitting in corresponding hadron masses and using the $X(3872)$ mass as an input, we estimate the masses corresponding to the states $J^{PC}=0^{++}, 1^{+-},2^{++}$. We find the masses of two states in $1^{+-}$ are close to those of $X(3823)$, $X(3900)$, and the mass of the $2^{++}$ state is close to that of $X(3940)$. For them, the discrepancies are about $\sim 10$ MeV. This may suggest that the quantum numbers of the controversial states are $X(3823)=1^{+-}, X(3900)=1^{+-}, X(3940)=2^{++}$. In this work, we use the same inputs parameters, the constituent quark masses and the strength of the color-spin interaction, that have been adopted in the previous work on the $D$ or $B$-meson excited states. There, it was shown that the four-quark structure can be manifested in their excited states. Thus, our results in this work provide a consistent treatment on open- and hidden-charm mesons as far as the four-quark model is concerned.

QCD sum rule study of a charged bottom-strange scalar meson

Using the QCD sum rule approach we investigate the possible four-quark structure for the new observed $B_{s}^0\pi^\pm$ narrow structure (D0). We use a diquak-antidiquark scalar current and work to the order of $m_s$ in full QCD, without relying on $1/m_Q$ expansion. Our study indicates that although it is possible to obtain a stable mass in agreement with the state found by the D0 collaboration, a more constraint analysis (simultaneous requirement of the OPE convergence and the dominance of the pole on the phenomenological side) leads to a higher mass. We also predict the masses of the bottom scalar tetraquark resonances with zero and two strange quarks.

Four-quark structure of the excited states of heavy mesons

We propose a four-quark structure for some of the excited states of heavy mesons containing a single charm or bottom quark. The four-quark wave functions are constructed based on a diquark-antidiquark form under the constraint that they form an antitriplet $\bar{\bf{3}}_f$ in $\mbox{SU(3)}_f$, which seems to be realized in some of the excited states listed in Particle Data Group. Depending on the structure of antidiquark, we construct two possible models for its wave functions: Model I) the antidiquark is symmetric in flavor ($\bar{\bf{6}}_f$) and antisymmetric in color ($\bf{3}_c$) and Model II) the antidiquark is antisymmetric in flavor ($\bf{3}_f$) and symmetric in color ($\bar{\bf{6}}_c$). To test phenomenological relevance of these wave functions, we calculate the mass differences among the excited states of spin $J=0,1,2$ using color-spin interactions. The four-quark wave functions based on Model~I is found to reproduce the observed mass of the excited states of heavy mesons. Also, our four-quark model provides an interesting phenomenology relating to the decay widths of the excited states. To further pursue the possibility of the four-quark structure, we make a few predictions for open charm and open bottom states that may be discovered in future experiments. Most of them are expected to have broad widths, which would make them difficult to be identified experimentally. However, one resonance with $J=1$ containing bottom and strange quarks is expected to appear as a sharp peak with its mass around $B^{\bar s}_{1N} \sim 5753$~MeV. Confirmation of the existence of such states in future experiments will shed light on our understanding of the structure of heavy meson excited states.

F 0(980) and a 0(980) resonances near the thresholds of the γγ → K + K − and γγ → K 0 K̇ 0 reactions

High-statistical data on the γγ → K + K − and γγ → K 0 K 0 reactions constitute the last missing link in investigations of light scalar mesons f 0(980) and a 0(980) in photon-photon collisions. It is expected that the manifestation of the four-quark structure of the f 0(980) and a 0(980) resonances in these reactions will be very peculiar. The possibilities of the observation of scalar contributions in the γγ → K + K − and γγ → K 0 K 0 reactions near their thresholds at modern colliders have been estimated.

Docc¯nn¯bound states exist?

The four-quark system $c\overline{c}n\overline{n}$ is studied in the framework of the constituent quark model. Using different types of quark-quark potentials, we solve the four-body Schr\odinger equation by means of the hyperspherical harmonic formalism. Exploring the low laying ${J}^{\mathrm{PC}}$ states for different isospin configurations no four-quark bound states have been found. Of particular interest is the possible four-quark structure of the $X(3872)$. We rule out the possibility that this particle is a compact tetraquark system, unless additional correlations, either in the form of diquarks or at the level of the interacting potential, not considered in simple quark models do contribute.

Testing the nature of the [formula omitted] and [formula omitted] states using QCD sum rules

We use the QCD sum rules to analize the masses and partial hadronic decays widths of the mesons D s J + ( 2317 ) and X ( 3872 ) , in the hypotesis that these mesons can be identified as four-quark states. We use a diquak-antidiquark current and work to the order of m s in full QCD. Our results indicate that a four-quark structure is acceptable for D s J + ( 2317 ) , but it is dificult to explain the very narrow width of the meson X ( 3872 ) .

Investigating the tetraquark structure of the new mesons

Using the QCD sum rule approach we investigate the possible four-quark structure of the recently observed mesons $D_{sJ}^{+}(2317)$, firstly observed by BaBaR, X(3872), firstly observed by BELLE and $D_0^{*0}(2308)$ observed by BELLE. We use diquark-antidiquark currents and work in full QCD, without relying on $1/m_c$ expansion. Our results indicate that a four-quark structure is acceptable for these mesons.

Diquark-Antidiquark with open charm in QCD sum rules

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: $D_0^{0,+}(2405)$.

Disentangling two- and four-quark state pictures of the charmed scalar mesons

We suggest that the recently observed charmed scalar mesons D00(2308) (Belle) and D00,+(2405) (FOCUS) are considered as different resonances. Using the QCD sum rule approach we investigate the possible four-quark structure of these mesons and also of the very narrow DsJ+(2317), firstly observed by BaBar. We use diquark–antidiquark currents and work to the order of ms in full QCD, without relying on 1/mc expansion. Our results indicate that a four-quark structure is acceptable for the resonances observed by Belle and BaBar: D00(2308) and DsJ+(2317) respectively, but not for the resonances observed by FOCUS: D00,+(2405).

QCD sum rule approach for the light scalar mesons as four-quark states

We study the two point-function for the scalar mesons σ, κ, f0(980) and a0(980) as diquak–antidiquark states. We also study the decays of these mesons into ππ, Kπ and KK¯. We find that the couplings are consistent with existing experimental data, supporting the four-quark structure for the light scalar mesons.