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Spectrum and rearrangement decays of tetraquark states with four different flavors

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 Added by Yanrui Liu
 Publication date 2020
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and research's language is English




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We have systematically investigated the mass spectrum and rearrangement decay properties of the exotic tetraquark states with four different flavors using a color-magnetic interaction model. Their masses are estimated by assuming that the $X(4140)$ is a $csbar{c}bar{s}$ tetraquark state and their decay widths are obtained by assuming that the Hamiltonian for decay is a constant. According to the adopted method, we find that the most stable states are probably the isoscalar $bsbar{u}bar{d}$ and $csbar{u}bar{d}$ with $J^P=0^+$ and $1^+$. The width for most unstable tetraquarks is about tens of MeVs, but that for unstable $cubar{s}bar{d}$ and $csbar{u}bar{d}$ can be around 100 MeV. For the $X(5568)$, our method cannot give consistent mass and width if it is a $bubar{s}bar{d}$ tetraquark state. For the $I(J^P)=0(0^+),0(1^+)$ double-heavy $T_{bc}=bcbar{u}bar{d}$ states, their widths can be several MeVs.

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We systematically study the mass spectrum and strong decays of the S-wave $bar cbar s q q$ states in the compact tetraquark scenario with the quark model. The key ingredients of the model are the Coulomb, the linear confinement, and the hyperfine interactions. The hyperfine potential leads to the mixing between different color configurations, as well as the large mass splitting between the two ground states with $I(J^P)=0(0^+)$ and $I(J^P)=1(0^+)$. We calculate their strong decay amplitudes into the $bar D^{(*)}K^{(*)}$ channels with the wave functions from the mass spectrum calculation and the quark interchange method. We examine the interpretation of the recently observed $X_0(2900)$ as a tetraquark state. The mass and decay width of the $I(J^P)=1(0^+)$ state are $M=2941$ MeV and $Gamma_X=26.6$ MeV, respectively, which indicates that it might be a good candidate for the $X_0(2900)$. Meanwhile, we also obtain an isospin partner state $I(J^P)=0(0^+)$ with $M=2649$ MeV and $Gamma_{Xrightarrow bar D K}=48.1$ MeV, respectively. Future experimental search for $X(2649)$ will be very helpful.
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We use the Laplace/Borel sum rules (LSR) and the finite energy/local duality sum rules (FESR) to investigate the non-strange $udbar ubar d$ and hidden-strange $usbar ubar s$ tetraquark states with exotic quantum numbers $J^{PC}=0^{+-}$ . We systematically construct all eight possible tetraquark currents in this channel without covariant derivative operator. Our analyses show that the $udbar ubar d$ systems have good behaviour of sum rule stability and expansion series convergence in both the LSR and FESR analyses, while the LSR for the $usbar ubar s$ states do not associate with convergent OPE series in the stability regions and only the FESR can provide valid results. We give the mass predictions $1.43pm0.09$ GeV and $1.54pm0.12$ GeV for the $udbar ubar d$ and $usbar ubar s$ tetraquark states, respectively. Our results indicate that the $0^{+-}$ isovector $usbar ubar s$ tetraquark may only decay via weak interaction mechanism, e.g. $X_{usbar{u}bar{s}}to Kpipi$, since its strong decays are forbidden by kinematics and the symmetry constraints on the exotic quantum numbers. It is predicted to be very narrow, if it does exist. The $0^{+-}$ isoscalar $usbar ubar s$ tetraquark is also predicted to be not very wide because its dominate decay mode $X_{usbar{u}bar{s}}tophipipi$ is in $P$-wave.
We calculate the masses of the $QQbar{q}bar{q}$ ($Q=c,b$; $q=u,d,s$) tetraquark states with the aid of heavy diquark-antiquark symmetry (HDAS) and the chromomagnetic interaction (CMI) model. The masses of the highest-spin ($J=2$) tetraquarks that have only the $(QQ)_{bar{3}_c}(bar{q}bar{q})_{3_c}$ color structure are related with those of conventional hadrons using HDAS. Thereafter, the masses of their partner states are determined with the mass splittings in the CMI model. Our numerical results reveal that: (i) the lightest $ccbar{n}bar{n}$ ($n=u,d$) is an $I(J^P)=0(1^+)$ state around 3929 MeV (53 MeV above the $DD^*$ threshold) and none of the double-charm tetraquarks are stable; (ii) the stable double-bottom tetraquarks are the lowest $0(1^+)$ $bbbar{n}bar{n}$ around 10488 MeV ($approx116$ MeV below the $BB^*$ threshold) and the lowest $1/2(1^+)$ $bbbar{n}bar{s}$ around 10671 MeV ($approx20$ MeV below the $BB_s^*/B_sB^*$ threshold); and (iii) the two lowest $bcbar{n}bar{n}$ tetraquarks, namely the lowest $0(0^+)$ around 7167 MeV and the lowest $0(1^+)$ around 7223 MeV, are near-threshold states. Moreover, we discuss the constraints on the masses of double-heavy hadrons. Specifically, for the lowest nonstrange tetraquarks, we obtain $T_{cc}<3965$ MeV, $T_{bb}<10627$ MeV, and $T_{bc}<7199$ MeV.
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