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

A Dalitz plot analysis of approximately 13 000 $D_s^{+}$ decays to ${\pi }^{+}{\pi }^{-}{\pi }^{+}$ has been performed. The analysis uses a $384{\mathrm{fb}}^{-1}$ data sample recorded by the BABAR detector at the PEP-II asymmetric-energy $e^{+}{e}^{-}$ storage ring running at center of mass energies near 10.6 GeV. Amplitudes and phases of the intermediate resonances which contribute to this final state are measured. A high precision measurement of the ratio of branching fractions is performed: $\mathcal{B}(D_s^{+}\to {\pi }^{+}{\pi }^{-}{\pi }^{+})/\mathcal{B}(D_s^{+}\to K^{+}{K}^{-}{\pi }^{+})=0.199\pm 0.004\pm 0.009$. Using a model-independent partial wave analysis, the amplitude and phase of the $\mathcal{S}$ wave have been measured.

Figure 1

(a) ${\pi }^{+}{\pi }^{-}{\pi }^{+}$ invariant mass distribution for the $D_s^{+}$ analysis sample. The line is the result of the fit described in the text. (b) Symmetrized $D_s^{+}\to {\pi }^{+}{\pi }^{-}{\pi }^{+}$ Dalitz plot (two entries per event).

Figure 2

(a) $\mathcal{S}$ wave amplitude extracted from the best fit, (b) corresponding $\mathcal{S}$ wave phase, (c) $\mathcal{S}$ wave amplitude compared to the FOCUS and E791 amplitudes, and (d) $\mathcal{S}$ wave phase compared to the FOCUS and E791 phases. Errors are statistical only.

Figure 3

Dalitz plot projections (points with error bars) and fit results (solid histogram). (a) $m^2({\pi }^{+}{\pi }^{-}{)}_{\mathrm{low}}$, (b) $m^2({\pi }^{+}{\pi }^{-}{)}_{\mathrm{high}}$, (c) total $m^2({\pi }^{+}{\pi }^{-})$, and (d) $m^2({\pi }^{+}{\pi }^{+})$. The hatched histograms show the background distribution.

Figure 4

Unnormalized spherical harmonic moments $⟨Y_L^0⟩$ as a function of ${\pi }^{+}{\pi }^{-}$ effective mass. The data are presented with error bars, and the histograms represent the fit projections.