The mass and coupling of the doubly charmed J P = 0 − diquark-antidiquark states T ++ cc;ss and T ++ cc;ds 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 (2317) and D + D * + s0 (2317) mesons are explored using QCD three-point sum rule approach, and their widths are found. The obtained results mT = (4390 ± 150) MeV and Γ = (302 ± 113 MeV) for the mass and width of the state T ++ cc;ss , as well as spectroscopic parameters mT = (4265 ± 140) MeV and Γ = (171 ± 52) MeV of the tetraquark T ++ cc;ds may be useful in experimental studies of exotic resonances.

The spectroscopic parameters and decay channels of the scalar tetraquark T − bb;us (in what follows T − b:s ) are investigated in the framework of the QCD sum rule method. 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 ± 270) MeV demonstrates that T − b:s is stable against the strong and electromagnetic decays. Therefore to find the width and mean lifetime of the T − b:s , we explore its dominant weak decays generated by the transition b → W − c. These channels embrace the semileptonic decays T − b:s → Z 0 bc;us lν l and nonleptonic modes, which at the final state contain the scalar tetraquark Z 0 bc;us . Key quantities to compute partial widths of the weak decays are the form factors G1(q 2 ) and G2(q 2 ): they determine differential rates dΓ/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 2 l ≤ q2 ≤ (m − m) 2 , where m is the mass of Z 0 bc;us . Predictions for the full width Γ full = (15.21 ± 2.59) × 10 −10 MeV and mean lifetime 4.33 +0.89 −0.63 × 10 −13 s of the T − b:s are useful for experimental and theoretical investigation of this exotic meson.

The weak decays of the axial-vector tetraquark T − bb;ūd to the scalar state Z 0 bc;ūd are investigated using the QCD three-point sum rule approach. In order to explore the process T − bb;ūd → Z 0 bc;ūd lν l , we recalculate the spectroscopic parameters of the tetraquark T − bb;ūd and find the mass and coupling of the scalar four-quark system Z 0 bc;ūd , 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;ūd state is found to be m = (10035 ± 260) MeV, which demonstrates that it is stable against the strong and electromagnetic decays. The full width Γ and mean lifetime τ of T − bb;ūd are evaluated using its semileptonic decay channels T − bb;ūd → Z 0 bc;ūd lν l , l = e, µ and τ . The obtained results, Γ = (7.17 ± 1.23) × 10 −8 MeV and τ = 9.18 +1.90 −1.34 fs, can be useful for experimental investigations of the doubly-heavy tetraquarks.