Abstract
Fully-heavy tetraquark states, i.e. $cc\bar{c}\bar{c}$, $bb\bar{b}\bar{b}$, $bb\bar{c}\bar{c}$ ($cc\bar{b}\bar{b}$), $cb\bar{c}\bar{c}$, $cb\bar{b}\bar{b}$, and $cb\bar{c}\bar{b}$, are systematically investigated by means of a non-relativistic quark model based on lattice-QCD studies of the two-body $Q\bar{Q}$ interaction, which exhibits a spin-independent Cornell potential along with a spin-spin term. The four-body problem is solved using the Gaussian expansion method; additionally, the so-called complex scaling technique is employed so that bound, resonance, and scattering states can be treated on the same footing. Moreover, a complete set of four-body configurations, including meson-meson, diquark-antidiquark, and K-type configurations, as well as their couplings, are considered for spin-parity quantum numbers $J^{P(C)}=0^{+(+)}$, $1^{+(\pm)}$, and $2^{+(+)}$ in the $S$-wave channel. Several narrow resonances, with two-meson strong decay widths less than 30 MeV, are found in all of the tetraquark systems studied. Particularly, the fully-charm resonances recently reported by the LHCb Collaboration, at the energy range between 6.2 and 7.2 GeV in the di-$J/\psi$ invariant spectrum, can be well identified in our calculation. Focusing on the fully-bottom tetraquark spectrum, resonances with masses between 18.9 and 19.6 GeV are found. For the remaining charm-bottom cases, the masses are obtained within a energy region from 9.8 GeV to 16.4 GeV. All these predicted resonances can be further examined in future experiments.
Highlights
Many efforts have been made in the past twenty years in order to understand exotic tetra, penta, and even hexaquark systems, constituted mostly by heavy quarks
The four-body problem is solved using the Gaussian expansion method; the so-called complex scaling technique is employed so that bound, resonance, and scattering states can be treated on the same footing
We present our results for the low-lying S-wave states (L 1⁄4 0 and J 1⁄4 S) of the fully-heavy tetraquark systems QQQ Q (Q 1⁄4 c, b)
Summary
Many efforts have been made in the past twenty years in order to understand exotic tetra-, penta-, and even hexaquark systems, constituted mostly by heavy quarks. In a nonrelativistic model with a compact diquark-antidiquark configuration, masses of the S-wave fully-charm tetraquark states are predicted to be between 5.96 and 6.32 GeV [36]. The narrow and broad structures observed in the di-J=ψ invariant mass spectrum are explained as radial excitations of the fully-charm state within the QCD sum rules approach [39], the string-junction picture [40], and the extended relativized quark model [41]. A coupled-channels calculation which treats the bound, resonance, and scattering states on the same footing is performed by employing the complex scaling method [57,58,59,60,61] according to the so-called ABC theorem [57,58] This tool has been already used in previous studies of nuclear [62,63,64,65] and hadron [66,67,68,69] physics.
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