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 ${\tilde{T}}_{cc;\overline{u}\overline{d}}^{+}$ 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 $m_T=(4130\pm 170)\mathrm{MeV}$ and $m_{\tilde{T}}=(3845\pm 175)\mathrm{MeV}$ demonstrate that these tetraquarks are strong-interaction unstable resonances and decay to conventional mesons through the channels $T_{cc;\overline{u}\overline{d}}^{+}\to D^{+}{D}^{*}(2007{)}^0$, $D^0{D}^{*}(2010{)}^{+}$ and ${\tilde{T}}_{cc;\overline{u}\overline{d}}^{+}\to D^{+}{D}^0$. 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 ${\mathrm{\Gamma }}_T=(129.9\pm 23.5)\mathrm{MeV}$ demonstrates that the tetraquark $T_{cc;\overline{u}\overline{d}}^{+}$ is a broad resonance, whereas the scalar exotic meson with ${\mathrm{\Gamma }}_{\tilde{T}}=(12.4\pm 3.1)\mathrm{MeV}$ can be classified as a relatively narrow state.

Figure 1

The mass of the tetraquark $T$ as a function of the Borel parameter $M^2$ (left panel) and as a function of the continuum threshold $s_0$ (right panel).

Figure 2

The same as in Fig. 1, but for the coupling $f_T$ of the state $T$.

Figure 3

The strong coupling $g_1(Q^2)$ as a function of the Borel parameters ${\mathbf{M}}^2=(M_1^2,M_2^2)$ at the fixed $(s_0,s_0^{\prime })=(21,7){\mathrm{GeV}}^2$ and $Q^2=5{\mathrm{GeV}}^2$.

Figure 4

The sum rule predictions and fit function for the strong coupling $g_1(Q^2)$. The star shows the point $Q^2=-m_D^2$.