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Register a new userTetraquark state $X(6900)$ and the interaction between diquark and antidiquark
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Recently LHCb declared a new structure $X(6900)$ in the final state di-$J/psi$ which is popularly regarded as a $cc$-$bar cbar c$ tetraquark state. %popularly. Within the Bethe-Salpeter (B-S) frame we study the possible $cc$-$bar cbar c$ bound states and the interaction between diquark ($cc$) and antidiquark ($bar cbar c$). In this work $cc$ ($bar cbar c$) is treated as a color anti-triplet (triplet) axial-vector so the quantum numbers of $cc$-$bar cbar c$ bound state are $0^+$, $1^+$ and $2^+$. Learning from the interaction in meson case and using the effective coupling we suggest the interaction kernel for diquark and antidiquark system. Then we deduce the B-S equations for different quantum numbers. Solving these equations numerically we find the spectra of some excited states can be close to the mass of $X(6900)$ when we assign appropriate values for parameter $kappa$ introduced in the interaction (kernel).We also briefly calculate the spectra of $bb$-$bar bbar b$ bound states. Future measurement of $bb$-$bar bbar b$ state will help us to determine the exact form of effective interaction.
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The recently discovered fully charmed tetraquark candidate $X(6900)$ is analyzed within the frameworks of effective-range expansion, compositeness relation and width saturation, and a coupled multichannel dynamical study. By taking into account constraints from heavy-quark spin symmetry, the coupled-channel amplitude including the $J/psi J/psi,~ chi_{c0}chi_{c0}$ and $chi_{c1}chi_{c1}$ is constructed to fit the experimental di-$J/psi$ event distributions around the energy region near $6.9$ GeV. Another dynamical two-coupled-channel amplitude with the $J/psi J/psi$ and $psi(3770) J/psi$ is also considered to describe the same datasets. The three different theoretical approaches lead to similar conclusions that the two-meson components do not play dominant roles in the $X(6900)$. Our determinations of the resonance poles in the complex energy plane from the refined coupled-channel study are found to be consistent with the experimental analyses. The coupled-channel amplitudes also have another pole corresponding to a narrow resonance $X(6825)$ that we predict sitting below the $chi_{c0}chi_{c0}$ threshold and of molecular origin. We give predictions to the line shapes of the $chi_{c0}chi_{c0}$ and $chi_{c1}chi_{c1}$ channels, which could provide a useful guide for future experimental measurements.
We compare two frequently discussed competing structures for a stable $bar b bar b u d$ tetraquark with quantum numbers $I(J^P) = 0(1^+)$ by considering a meson-meson as well as a diquark-antidiquark creation operator. We treat the heavy antiquarks as static with fixed positions and find diquark-antidiquark dominance for $bar b bar b$ separations $r < 0.2 , text{fm}$, while for $r > 0.5 , text{fm}$ the system essentially corresponds to a pair of $B$ mesons. For the meson-meson to diquark-antidiquark ratio of the tetraquark we obtain around $58%/42%$.
We discuss a recent lattice study of charmonium-like mesons with $J^{PC}=1^{++}$ and three quark contents $bar ccbar du$, $bar cc(bar uu + bar dd)$ and $bar ccbar ss$, where the latter two can mix with $bar cc$. In this quantum channel, the long known exotic candidate, X(3872), resides. This simulation employs $N_f=2$, $m_pi=266~$MeV and a large basis of $bar cc$, two-meson and diquark-antidiquark interpolating fields, with diquarks in both anti-triplet and sextet color representations. It aims at the possible signatures of four-quark exotic states. Along the way, we discuss the relations between the diquark-antidiquark operators and the two-meson operators via the Fierz transformations.
We perform a lattice study of charmonium-like mesons with $J^{PC}=1^{++}$ and three quark contents $bar cc bar du$, $bar cc(bar uu+bar dd)$ and $bar cc bar ss$, where the later two can mix with $bar cc$. This simulation with $N_f=2$ and $m_pi=266$ MeV aims at the possible signatures of four-quark exotic states. We utilize a large basis of $bar cc$, two-meson and diquark-antidiquark interpolating fields, with diquarks in both anti-triplet and sextet color representations. A lattice candidate for X(3872) with I=0 is observed very close to the experimental state only if both $bar cc$ and $Dbar D^*$ interpolators are included; the candidate is not found if diquark-antidiquark and $Dbar D^*$ are used in the absence of $bar cc$. No candidate for neutral or charged X(3872), or any other exotic candidates are found in the I=1 channel. We also do not find signatures of exotic $bar ccbar ss$ candidates below 4.3 GeV, such as Y(4140). Possible physics and methodology related reasons for that are discussed. Along the way, we present the diquark-antidiquark operators as linear combinations of the two-meson operators via the Fierz transformations.
In recent years, the existence of a hadronically stable $bar{b} bar{b} u d$ tetraquark with quantum numbers $I(J^P) = 0(1^+)$ was confirmed by first principles lattice QCD computations. In this work we use lattice QCD to compare two frequently discussed competing structures for this tetraquark by considering meson-meson as well as diquark-antidiquark creation operators. We use the static-light approximation, where the two $bar{b}$ quarks are assumed to be infinitely heavy with frozen positions, while the light $u$ and $d$ quarks are fully relativistic. By minimizing effective energies and by solving generalized eigenvalue problems we determine the importance of the meson-meson and the diquark-antidiquark creation operators with respect to the ground state. It turns out, that the diquark-antidiquark structure dominates for $bar{b} bar{b}$ separations $r < 0.25 , text{fm}$, whereas it becomes increasingly more irrelevant for larger separations, where the $I(J^P) = 0(1^+)$ tetraquark is mostly a meson-meson state. We also estimate the meson-meson to diquark-antidiquark ratio of this tetraquark and find around $60% / 40%$.
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