Dalitz plot analysis of $D_s^{+}\to K^{+}{K}^{-}{\pi }^{+}$

We perform a Dalitz plot analysis of about 100 000 $D_s^{+}$ decays to $K^{+}{K}^{-}{\pi }^{+}$ and measure the complex amplitudes of the intermediate resonances which contribute to this decay mode. We also measure the relative branching fractions of $D_s^{+}\to K^{+}{K}^{+}{\pi }^{-}$ and $D_s^{+}\to K^{+}{K}^{+}{K}^{-}$. For this analysis we use a 384 ${\mathrm{fb}}^{-1}$ data sample, recorded by the BABAR detector at the PEP-II asymmetric-energy $e^{+}{e}^{-}$ collider running at center-of-mass energies near 10.58 $\mathrm{GeV}$.

Figure 1

Normalized probability distribution functions for signal (solid) and background events (hatched) used in a likelihood-ratio test for the event selection of $D_s^{+}\to K^{+}{K}^{-}{\pi }^{+}$: (a) the center-of-mass momentum $p^{*}$, (b) the signed decay distance $d_{xy}$, and (c) the difference in probability $P_1-P_2$.

Figure 2

(a) $K^{+}{K}^{-}{\pi }^{+}$ mass distribution for the $D_s^{+}$ analysis sample; the signal region is as indicated; (b) $D_s^{+}\to K^{+}{K}^{-}{\pi }^{+}$ Dalitz plot.

Figure 3

(a) Dalitz plot efficiency map; the projection onto (b) the $K^{+}{K}^{-}$, and (c) the $K^{-}{\pi }^{+}$ axis.

Figure 4

$K^{+}{K}^{-}$ mass spectrum in the threshold region weighted by (a) $Y_0^0$, (b) $Y_1^0$, and (c) $Y_2^0$, corrected for efficiency and phase space, and background subtracted.

Figure 5

Squared (a) $\mathcal{S}$- and (b) $\mathcal{P}$-wave amplitudes; (c) the phase difference ${\varphi }_{\mathcal{S}\mathcal{P}}$; (d) ${\varphi }_{\mathcal{S}}$ obtained as explained in the text. The curves result from the fit described in the text.

Figure 6

(a) Comparison between $K\overline{K}$ $\mathcal{S}$-wave intensities from different charmed meson Dalitz plot analyses. (b) Comparison of the $K\overline{K}$ $\mathcal{S}$-wave intensity from $D_s^{+}\to K^{+}{K}^{-}{\pi }^{+}$ with the ${\pi }^{+}{\pi }^{-}$ $\mathcal{S}$-wave intensity from $D_s^{+}\to {\pi }^{+}{\pi }^{-}{\pi }^{+}$.

Figure 7

$K^{-}{\pi }^{+}$ mass spectrum in the threshold region weighted by (a) $Y_0^0$, (b) $Y_1^0$, and (c) $Y_2^0$, corrected for efficiency, phase space, and background subtracted. (d) The $K^{-}{\pi }^{+}$ mass dependence of $|\mathcal{S}{|}^2$.

Figure 8

(a) Dalitz plot of sideband regions projected onto (b) the $K^{+}{K}^{-}$ and (c) the $K^{-}{\pi }^{+}$ axis.

Figure 9

$D_s^{+}\to K^{+}{K}^{-}{\pi }^{+}$: Dalitz plot projections from the best fit. The data are represented by points with error bars, the fit results by the histograms.

Figure 10

$K^{+}{K}^{-}$ mass dependence of the spherical harmonic moments, $⟨Y_k^0⟩$, obtained from the fit to the $D_s^{+}\to K^{+}{K}^{-}{\pi }^{+}$ Dalitz plot compared to the data moments. The data are represented by points with error bars, the fit results by the histograms. The insets show an expanded view of the $\varphi (1020)$ region.

Figure 11

$K^{-}{\pi }^{+}$ mass dependence of the spherical harmonic moments, $⟨Y_k^0⟩$, obtained from the fit to the $D_s^{+}\to K^{+}{K}^{-}{\pi }^{+}$ Dalitz plot compared to the data moments. The data are represented by points with error bars, the fit results by the histograms.

Figure 12

(a) $K^{+}{K}^{-}{K}^{+}$ mass spectrum showing a $D_s^{+}$ signal. The curve is the result of the fit described in the text. (b) Symmetrized Dalitz plot, (c) $K^{+}{K}^{-}$ mass spectrum (two combinations per event), and (d) the $⟨Y_1^0⟩$ moment. The insert in (c) shows an expanded view of the $\varphi (1020)$ region. The Dalitz plot and its projection are background subtracted and efficiency corrected. The curve results from the fit described in the text.

Figure 13

(a) $K^{+}{K}^{+}{\pi }^{-}$ mass spectrum showing a $D_s^{+}$ signal. (b) Symmetrized Dalitz plot for $D_s^{+}\to K^{+}{K}^{+}{\pi }^{-}$ decay. (c) $K^{+}{\pi }^{-}$ mass distribution (two combinations per event). The Dalitz plot and its projection are background subtracted and efficiency corrected. The curves result from the fits described in the text.