Model-Independent Study of Structure in $B^{+}\to D^{+}{D}^{-}{K}^{+}$ Decays

The only anticipated resonant contributions to $B^{+}\to D^{+}{D}^{-}{K}^{+}$ decays are charmonium states in the $D^{+}{D}^{-}$ channel. A model-independent analysis, using LHCb proton-proton collision data taken at center-of-mass energies of $\sqrt{s}=7$, 8, and 13 TeV, corresponding to a total integrated luminosity of $9{\mathrm{fb}}^{-1}$, is carried out to test this hypothesis. The description of the data assuming that resonances only manifest in decays to the $D^{+}{D}^{-}$ pair is shown to be incomplete. This constitutes evidence for a new contribution to the decay, potentially one or more new charm-strange resonances in the $D^{-}{K}^{+}$ channel with masses around $2.9\mathrm{GeV}/c^2$.

Figure 1

Invariant-mass distribution for $B$ candidates with the results of the fit superimposed, where the signal component is indicated in red and background (barely visible) in blue (a). Dalitz plot for candidates with $m(D^{+}{D}^{-}{K}^{+})$ values in the signal window (b).

Figure 2

Distributions of the first nine unnormalized moments, $⟨Y_k^j⟩$, defined in Eq. (2), as a function of $m(D^{+}{D}^{-})$ for the selected $B^{+}\to D^{+}{D}^{-}{K}^{+}$ candidates after efficiency correction and background subtraction have been applied.

Figure 3

Comparison between data (points with error bars) and a weighted generated sample (filled histogram) as a function of (a) $m(D^{-}{K}^{+})$ and (b) $m(D^{+}{K}^{+})$, where the weights account for the Legendre polynomial moments of orders up to and including 29.

Figure 4

Comparison between data (points with error bars) and a weighted generated sample (filled histogram) as a function of (a) $m(D^{-}{K}^{+})$ and (b) $m(D^{+}{K}^{+})$, where the weights account for the Legendre polynomial moments of orders up to and including 4. The uncertainty on the weighted shape (dark band) is also shown.

Figure 5

Comparison of the test statistic evaluated for the data (black dashed line) and for the ensemble of pseudoexperiments (blue histogram) generated according to the PDF constructed using the first four moments of the $h(D^{+}{D}^{-})$ distribution in data.