Amplitude analysis of the decay $B^{\pm }\to {\pi }^{\pm }{\pi }^{\pm }{\pi }^{\mp }$

We present a Dalitz-plot analysis of charmless $B^{\pm }$ decays to the final state ${\pi }^{\pm }{\pi }^{\pm }{\pi }^{\mp }$ using $210{\mathrm{fb}}^{-1}$ of data recorded by the BABAR experiment at $\sqrt{s}=10.58\mathrm{GeV}$. We measure the branching fractions $\mathcal{B}({\mathrm{B}}^{\pm }\to {\pi }^{\pm }{\pi }^{\pm }{\pi }^{\mp })=(16.2\pm 1.2\pm 0.9)\times {10}^{-6}$ and $\mathcal{B}(B^{\pm }\to {\rho }^0(770){\pi }^{\pm })=(8.8\pm 1.0\pm {0.6}_{-0.7}^{+0.1})\times {10}^{-6}$. Measurements of branching fractions for the quasi-two-body decays $B^{\pm }\to {\rho }^0(1450){\pi }^{\pm }$, $B^{\pm }\to {\mathrm{f}}_0(980){\pi }^{\pm }$ and $B^{\pm }\to {\mathrm{f}}_2(1270){\pi }^{\pm }$ are also presented. We observe no charge asymmetries for the above modes, and there is no evidence for the decays $B^{\pm }\to {\chi }_{c0}{\pi }^{\pm }$, $B^{\pm }\to {\mathrm{f}}_0(1370){\pi }^{\pm }$ and $B^{\pm }\to \sigma {\pi }^{\pm }$.

Figure 1

The $m_{\mathrm{ES}}$ distribution along the $\Delta E$ strip ($-65<\Delta E<55\mathrm{MeV}$): the data are the black points with statistical error bars, the lower solid red (dark) area is the $q\overline{q}$ component, the middle solid green (light) area is the $B\overline{B}$ background contribution, while the upper (blue) line shows the total fit result.

Figure 2

Dalitz plot of the $q\overline{q}$ background obtained from on-resonance sideband and off-resonance data. The left plot shows the distribution in normal Dalitz-plot coordinates, while the right plot shows the equivalent distribution in the new square Dalitz-plot coordinates, defined in Eq. (15). The empty regions correspond to events removed by the charm vetoes. The area of each small square is proportional to the number of events in that bin.

Figure 3

Dalitz plot of the $B\overline{B}$ background obtained from Monte Carlo simulated events. The left plot shows the distribution in normal Dalitz-plot coordinates, while the right plot shows the equivalent distribution in the new square Dalitz-plot coordinates, defined in Eq. (15). The empty regions correspond to events removed by the charm vetoes. The area of each small square is proportional to the number of events in that bin.

Figure 4

Projection plots of the fit results for $B^{-}\to {\pi }^{-}{\pi }^{-}{\pi }^{+}$ and $B^{+}\to {\pi }^{+}{\pi }^{+}{\pi }^{-}$ onto the mass variables $m_{{\pi }^{+}{\pi }^{-}}$ and $m_{{\pi }^{-}{\pi }^{-}}$ ($m_{{\pi }^{+}{\pi }^{+}}$). The upper (lower) plots are for the $B^{-}$ ($B^{+}$) data sample. The data are the black points with statistical error bars, the lower solid red (dark) histogram is the $q\overline{q}$ component, the middle solid green (light) histogram is the $B\overline{B}$ background contribution, while the upper (blue) histogram shows the total fit result. The large dips in the spectra correspond to the charm vetoes.

Figure 5

Background-subtracted Dalitz plot of the combined $B^{\pm }\to {\pi }^{\pm }{\pi }^{\pm }{\pi }^{\mp }$ data sample in the signal region. The Dalitz plot is symmetrized about the $y=x$ axis. The empty regions correspond to events removed by the charm vetoes.