Strong decays of double-charmed pseudoscalar and scalar $cc\overline{u}\overline{d}$ tetraquarks

The strong decays of the pseudoscalar and scalar double-charmed tetraquarks ${T}_{cc;\overline{u}\overline{d}}^{+}$ and ${\stackrel{˜}{T}}_{cc;\overline{u}\overline{d}}^{+}$ are investigated in the framework of the QCD sum rule method. The mass and coupling of these exotic four-quark mesons are calculated in the framework of the QCD two-point sum rule approach by taking into account vacuum condensates of the quark, gluon, and mixed local operators up to dimension 10. Our results for masses ${m}_{T}=\left(4130±170\right)\text{}\text{}\mathrm{MeV}$ and ${m}_{\stackrel{˜}{T}}=\left(3845±175\right)\text{}\text{}\mathrm{MeV}$ demonstrate that these tetraquarks are strong-interaction unstable resonances and decay to conventional mesons through the channels ${T}_{cc;\overline{u}\overline{d}}^{+}\to {D}^{+}{D}^{*}\left(2007{\right)}^{0}$, ${D}^{0}{D}^{*}\left(2010{\right)}^{+}$ and ${\stackrel{˜}{T}}_{cc;\overline{u}\overline{d}}^{+}\to {D}^{+}{D}^{0}$. Key quantities necessary to compute the partial width of these decay modes, i.e., the strong couplings of two $D$ mesons and a corresponding tetraquark ${g}_{i}$, $i=1$, 2, and $G$, are extracted from the QCD three-point sum rules. The full width ${\Gamma }_{T}=\left(129.9±23.5\right)\text{}\text{}\mathrm{MeV}$ demonstrates that the tetraquark ${T}_{cc;\overline{u}\overline{d}}^{+}$ is a broad resonance, whereas the scalar exotic meson with ${\Gamma }_{\stackrel{˜}{T}}=\left(12.4±3.1\right)\text{}\text{}\mathrm{MeV}$ can be classified as a relatively narrow state.