First Observation of a Doubly Charged Tetraquark and Its Neutral Partner

A combined amplitude analysis is performed for the decays $B^0\to \overline{D}{{}^{0}D}_s^{+}{\pi }^{-}$ and $B^{+}\to D^{-}{D}_s^{+}{\pi }^{+}$, which are related by isospin symmetry. The analysis is based on data collected by the LHCb detector in proton-proton collisions at center-of-mass energies of 7, 8, and 13 TeV. The full data sample corresponds to an integrated luminosity of $9{\mathrm{fb}}^{-1}$. Two new resonant states with masses of $2.908\pm 0.011\pm 0.020\mathrm{GeV}$ and widths of $0.136\pm 0.023\pm 0.013\mathrm{GeV}$ are observed, which decay to $D_s^{+}{\pi }^{+}$ and $D_s^{+}{\pi }^{-}$ respectively. The former state indicates the first observation of a doubly charged open-charm tetraquark state with minimal quark content $[c\overline{s}u\overline{d}]$, and the latter state is a neutral tetraquark composed of $[c\overline{s}\overline{u}d]$ quarks. Both states are found to have spin-parity of $0^{+}$, and their resonant parameters are consistent with each other, which suggests that they belong to an isospin triplet.

Figure 1

Dalitz plots of (a) $B^0\to {\overline{D}}^0{D}_s^{+}{\pi }^{-}$ and (b) $B^{+}\to D^{-}{D}_s^{+}{\pi }^{+}$ decays after the full selection is applied.

Figure 2

Distributions of (a) $M({\overline{D}}^0{\pi }^{-})$, (b) $\mathrm{M}(D_s^{+}{\pi }^{-})$, and (c) $M({\overline{D}}^0{D}_s^{+})$ for the $\overline{D}\pi$ components of the $B^0\to {\overline{D}}^0{D}_s^{+}{\pi }^{-}$ candidates and (d) $M(D^{-}{\pi }^{+})$, (e) $M(D_s^{+}{\pi }^{+})$, and (f) $M(D^{-}{D}_s^{+})$ of the $B^{+}\to D^{-}{D}_s^{+}{\pi }^{+}$ candidates. The data are overlaid with the results of the fits.

Figure 3

Distributions of (a) $M(D_s^{+}{\pi }^{-})$ of $B^0\to {\overline{D}}^0{D}_s^{+}{\pi }^{-}$ decays and (b) $M(D_s^{+}{\pi }^{+})$ for the $B^{+}\to D^{-}{D}_s^{+}{\pi }^{+}$ sample. The data are overlaid with the fit results with the inclusion of the new $0^{+}$ $D_s^{+}\pi$ resonant states.

Figure 4

Spin analysis for the $J^P=0^{+}$ hypothesis over $J^P=1^{-}$. The solid blue and black dashed histograms are the distributions of the $2\mathrm{\Delta }\mathrm{LL}$ of the pseudoexperiments based on the fit results with the $0^{+}$ and $1^{+}$ hypotheses, respectively. The purple vertical line shows the $2\mathrm{\Delta }\mathrm{LL}$ of the data fitted with the new $D_s^{+}\pi$ exotic state under the $J^P=0^{+}$ and $J^P=1^{-}$ hypotheses. The red curve shows the result of a fit with the Gaussian function to the black dashed histogram.

Figure 5

Argand diagram for the $T_{c\overline{s}0}^a(2900)$ exotic state. The green star and black dots show the start point and phase variation for a $T_{c\overline{s}0}^a(2900)$ Breit-Wigner function. The red solid line shows the fitted spline function used to model the $J^P=0^{+}$ $D_s^{+}\pi$ component in the $T_{c\overline{s}0}^a(2900)$ mass region, and the blue error bars show the uncertainties on the values of the spline at the knots.