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Register a new userHeavy exotic scalar meson $T_{bb;bar{u}bar{s}}^{-}$
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The spectroscopic parameters and decay channels of the scalar tetraquark $ T_{bb;overline{u}overline{s}}^{-}$ (in what follows $T_{b:overline{s} }^{-} $) are investigated. The mass and coupling of the $T_{b:s}^{-}$ are calculated using the two-point sum rules by taking into account quark, gluon and mixed vacuum condensates up to dimension 10. Our result for its mass $m=(10250 pm 270)~mathrm{MeV}$ demonstrates that $T_{b:overline{s}}^{-} $ is stable against the strong and electromagnetic decays. Therefore to find the width and mean lifetime of the $T_{b:overline{s}}^{-}$, we explore its dominant weak decays generated by the transition $b to W^{-}c$. These channels embrace the semileptonic decay $T_{b:overline{s}}^{-} to Z_{bc;overline{u}overline{s}}^{0}loverline{ u }_{l}$ and nonleptonic modes $T_{b:overline{s}}^{-} to Z_{bc;overline{ u}overline{s}}^{0}pi^{-}(K^{-}, D^{-}, D_s^{-})$, which at the final state contain the scalar tetraquark $Z_{bc;overline{u}overline{s}}^{0}$. Key quantities to compute partial widths of the weak decays are the form factors $G_1(q^2)$ and $G_2(q^2)$: they determine differential rate $dGamma/dq^2$ of the semileptonic and partial widths of the nonleptonic processes, respectively. These form factors are extracted from relevant three-point sum rules at momentum transfers $q^2$ accessible for such analysis. By means of the fit functions $F_{1(2)}(q^2)$ they are extrapolated to cover the whole integration region $m_l^{2}leq q2leq(m-widetilde m)^2$, where $widetilde m$ is the mass of $Z_{bc;overline{u}overline{s}}^{0}$. Predictions for the full width $Gamma _{mathrm{full}}=(15.21pm 2.59)times 10^{-10}~mathrm{ MeV}$ and mean lifetime $4.33_{-0.63}^{+0.89}times 10^{-13}~mathrm{s}$ of the $T_{b:s}^{-} $ are useful for experimental and theoretical investigations of this exotic meson.
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The mass and coupling of the scalar tetraquark $T_{bb;overline{u}overline{d }}^{-}$ (hereafter $T_{b:overline{d}}^{-} $) are calculated in the context of the QCD two-point sum rule method. In computations we take into account effects of various quark, gluon and mixed condensates up to dimension ten. The result obtained for the mass of this state $m=(10135pm 240)~mathrm{MeV} $ demonstrates that it is stable against the strong and electromagnetic decays. We also explore the dominant semileptonic $T_{b:overline{d}}^{-} to widetilde{Z}_{bc;bar{u}bar{d}}^{0}loverline{ u }_{l}$ and nonleptonic decays $T_{b:overline{d}}^{-} to widetilde{Z}_{bc;bar{u}bar{ d}}^{0}M$, where $widetilde{Z}_{bc;bar{u}bar{d}}^{0}$ is the scalar tetraquark composed of color-sextet diquark and antidiquark, and $M$ is one of the final-state pseudoscalar mesons $pi^{-}, K^{-}, D^{-}$ and $D_s^{-}$ , respectively. The partial widths of these processes are calculated in terms of the weak form factors $G_{1(2)}(q^2)$, which are determined from the QCD three-point sum rules. Predictions for the mass, full width $Gamma _{mathrm{full}} =(10.88pm 1.88)times 10^{-10}~mathrm{MeV}$, and mean lifetime $tau=0.61_{-0.09}^{+0.13}~mathrm{ps}$ of the $T_{b:overline{d} }^{-}$ obtained in the present work can be used in theoretical and experimental studies of this exotic state.
The spectroscopic parameters and decay channels of the axial-vector tetraquark $T_{bb;overline{u}overline{s}}^{-}$ (in what follows, $T_{b: overline{s}}^{mathrm{AV}}$) are explored using the quantum chromodynamics (QCD) sum rule method. The mass and coupling of this state are calculated using two-point sum rules by taking into account various vacuum condensates, up to 10 dimensions. Our prediction for the mass of this state $m=(10215pm 250)~ mathrm{MeV}$ confirms that it is stable with respect to strong and electromagnetic decays and can dissociate to conventional mesons only via weak transformations. We investigate the dominant semileptonic $T_{b:overline{s} }^{mathrm{AV}} to mathcal{Z}_{b:overline{s}}^{0}loverline{ u}_l$ and nonleptonic $T_{b:overline{s}}^{mathrm{AV}} to mathcal{Z}_{b:overline{s} }^{0}M$ decays of $T_{b:overline{s}}^{mathrm{AV}}$. In these processes, $ mathcal{Z}_{b:overline{s}}^{0}$ is a scalar tetraquark $[bc][overline{u} overline{s}]$ built of a color-triplet diquark and an antidiquark, whereas $M$ is one of the vector mesons $rho ^{-}$, $K^{ast}(892)$, $D^{ast }(2010)^{-}$, and $D_{s}^{ast -}$. To calculate the partial widths of these decays, we use the QCD three-point sum rule approach and evaluate the weak transition form factors $G_{i}$ $(i=0,1,2,3)$, which govern these processes. The full width $Gamma _{mathrm{full}} =(12.9pm 2.1)times 10^{-8}~mathrm{MeV}$ and the mean lifetime $ tau=5.1_{-0.71}^{+0.99}~mathrm{fs}$ of the tetraquark $T_{b:overline{s}}^{ mathrm{AV}}$ are computed using the aforementioned weak decays. The obtained information about the parameters of $T_{b:overline{s}}^{mathrm{AV}}$ and $ mathcal{Z}_{b:overline{s}}^{0}$ is useful for experimental investigations of these double-heavy exotic mesons.
The weak decays of the axial-vector tetraquark $T_{bb;bar{u} bar{d}}^{-}$ to the scalar state $Z_{bc;bar{u} bar{d}}^{0}$ are investigated using the QCD three-point sum rule approach. In order to explore the process $T_{bb; bar{u} bar{d}}^{-} to Z_{bc;bar{u} bar{d}}^{0}l bar{ u_l}$, we recalculate the spectroscopic parameters of the tetraquark $T_{bb;bar{u} bar{d}}^{-}$ and find the mass and coupling of the scalar four-quark system $Z_{bc;bar{u} bar{d}}^{0}$, which are important ingredients of calculations. The spectroscopic parameters of these tetraquarks are computed in the framework of the QCD two-point sum rule method by taking into account various condensates up to dimension ten. The mass of the $T_{bb;bar{u} bar{ d}}^{-}$ state is found to be $m=(10035~pm 260)~mathrm{MeV}$, which demonstrates that it is stable against the strong and electromagnetic decays. The full width $Gamma$ and mean lifetime $tau$ of $T_{bb;bar{u} bar{d} }^{-}$ are evaluated using its semileptonic decay channels $T_{bb; bar{u} bar{d}}^{-} to Z_{bc;bar{u} bar{d}}^{0}l bar{ u_l}$, $l=e,mu$ and $tau$. The obtained results, $Gamma=(7.17pm 1.23)times 10^{-8 } mathrm{MeV}$ and $tau =9.18_{-1.34}^{+1.90}~mathrm{fs}$, can be useful for experimental investigations of the doubly-heavy tetraquarks.
The mass and coupling of the doubly charmed $J^P=0^{-}$ diquark-antidiquark states $T_{cc;bar{s} bar{s}}^{++}$ and $T_{cc;bar{d} bar{s}}^{++}$ that bear two units of the electric charge are calculated by means of QCD two-point sum rule method. Computations are carried out by taking into account vacuum condensates up to and including terms of tenth dimension. The dominant $S$-wave decays of these tetraquarks to a pair of conventional $ D_{s}^{+}D_{s0}^{ast +}(2317)$ and $D^{+}D_{s0}^{ast +}(2317)$ mesons are explored using QCD three-point sum rule approach, and their widths are found. The obtained results $m_{T}=(4390~pm 150)~mathrm{MeV}$ and $Gamma =(302 pm 113~mathrm{MeV}$) for the mass and width of the state $T_{cc;bar{ s} bar{s}}^{++}$, as well as spectroscopic parameters $widetilde{m} _{T}=(4265pm 140)~mathrm{MeV}$ and $widetilde{Gamma }=(171~pm 52)~ mathrm{MeV}$ of the tetraquark $T_{cc;bar{d} bar{s}}^{++}$ may be useful in experimental studies of exotic resonances.
In this work, we study systematically the mass splittings of the $qqbar{Q}bar{Q}$ ($q=u$, $d$, $s$ and $Q=c$, $b$) tetraquark states with the color-magnetic interaction by considering color mixing effects and estimate roughly their masses. We find that the color mixing effect is relatively important for the $J^P=0^+$ states and possible stable tetraquarks exist in the $nnbar{Q}bar{Q}$ ($n=u$, $d$) and $nsbar{Q}bar{Q}$ systems either with $J=0$ or with $J=1$. Possible decay patterns of the tetraquarks are briefly discussed.
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