Invariant mass spectra of (a) $ { B ^\pm \rightarrow K ^\pm \pi ^+ \pi ^- }$ , (b) $ { B ^\pm \rightarrow K ^\pm K ^+ K ^- }$ , (c) $ { B ^\pm \rightarrow \pi ^\pm \pi ^+ \pi ^- }$ and (d) $ { B ^\pm \rightarrow \pi ^\pm K ^+ K ^- }$ decays. The left panel on each figure shows the $ B ^- $ candidates and the right panel shows the $ B ^+ $ candidates. The results of the unbinned maximum likelihood fits are overlaid. The main components of the fits are also shown.

Dalitz plot distributions of (a) $ { B ^\pm \rightarrow K ^\pm K ^+ K ^- }$ , (b) $ { B ^\pm \rightarrow K ^\pm \pi ^+ \pi ^- }$ , (c) $ { B ^\pm \rightarrow \pi ^\pm \pi ^+ \pi ^- }$ and (d) $ { B ^\pm \rightarrow \pi ^\pm K ^+ K ^- }$ candidates. The visible gaps correspond to the exclusion of the $J/\psi$ (in the $ { B ^\pm \rightarrow K ^\pm \pi ^+ \pi ^- }$ decay) and $ D ^0$ (all plots, except for the $ { B ^\pm \rightarrow \pi ^\pm K ^+ K ^- }$ decay) mesons from the samples.

(colour online) Measured $ A_{\rm raw}^{N}$ in Dalitz plot bins of background-subtracted and acceptance-corrected events for (a) $ { B ^\pm \rightarrow K ^\pm K ^+ K ^- }$ , (b) $ { B ^\pm \rightarrow K ^\pm \pi ^+ \pi ^- }$ , (c) $ { B ^\pm \rightarrow \pi ^\pm \pi ^+ \pi ^- }$ and (d) $ { B ^\pm \rightarrow \pi ^\pm K ^+ K ^- }$ decays.

Projections in bins of the $ m(\pi ^+ \pi ^- )_{\rm low}$ variable of (a, b) the number of $ B ^- $ and $ B ^+ $ signal events and (c, d) their difference for $ { B ^\pm \rightarrow \pi ^\pm \pi ^+ \pi ^- }$ decays. The plots are restricted to events with (a, c) $\cos\theta<0$ and (b, d) $\cos\theta>0$, with $\cos\theta$ defined in the text. The yields are acceptance-corrected and background-subtracted. A guide line for zero (horizontal red line) was included on plots (c, d).

Projections in bins of the $ m(\pi ^+ \pi ^- )$ variable of (a, b) the number of $ B ^- $ and $ B ^+ $ signal events and (c, d) their difference for $ { B ^\pm \rightarrow K ^\pm \pi ^+ \pi ^- }$ decays. The plots are restricted to events with (a, c) $\cos\theta<0$ and (b, d) $\cos\theta>0$. The yields are acceptance-corrected and background-subtracted. A guide line for zero (horizontal red line) was included on plots (c, d).

Projections in bins of the $ m( K ^+ K ^- )_{\rm low}$ variable of (a, b) the number of $ B ^- $ and $ B ^+ $ signal events and (c, d) their difference for $ { B ^\pm \rightarrow K ^\pm K ^+ K ^- }$ decays. The inset plots show the $\phi$ resonance region of $ m( K ^+ K ^- )_{\rm low}$ between 1.00 and $1.05 {\mathrm{ Ge V /}c^2} $, which is excluded from the main plots. The plots are restricted to events with (a, c) $\cos\theta<0$ and (b, d) $\cos\theta>0$. The yields are acceptance-corrected and background-subtracted. A guide line for zero (horizontal red line) was included on plots (c, d).

Projections in bins of the $ m( K ^+ K ^- )$ variable of (a) the number of $ B ^- $ and $ B ^+ $ signal events and (b) their difference for $ { B ^\pm \rightarrow \pi ^\pm K ^+ K ^- }$ decays. The yields are acceptance-corrected and background-subtracted. A guide line for zero (horizontal red line) was included on plot (b).

Invariant mass distributions in the rescattering regions ($ m(\pi ^+ \pi ^- ) $ or $ m( K ^+ K ^- ) $ between $1.0$ and $1.5 {\mathrm{ Ge V /}c^2} $) for (a) $ { B ^\pm \rightarrow K ^\pm \pi ^+ \pi ^- }$ , (b) $ { B ^\pm \rightarrow K ^\pm K ^+ K ^- }$ , (c) $ { B ^\pm \rightarrow \pi ^\pm \pi ^+ \pi ^- }$ and (d) $ { B ^\pm \rightarrow \pi ^\pm K ^+ K ^- }$ decays. The left panel in each figure shows the $B^{-}$ candidates and the right panel shows the $B^{+}$ candidates.

Invariant mass distribution of $ { B ^\pm \rightarrow \pi ^\pm \pi ^+ \pi ^- }$ candidates restricted to (a) sector I, (b) sector II, (c) sector III and (d) sector IV. The left panel in each figure shows the $B^{-}$ candidates and the right panel shows the $B^{+}$ candidates.

Animated gif made out of all figures.

Signal yields of charmless three-body $ B ^\pm$ decays for the full data set.

Systematic uncertainties on the measured asymmetries, where the total is the sum in quadrature of the individual contributions. The $ A_{\rm D}^{\pi}$ uncertainty is taken from Ref. [37].

Signal yields and charge asymmetries in the rescattering regions of $ m(\pi ^+ \pi ^- )$ or $ m( K ^+ K ^- )$ between $1.0$ and $1.5 {\mathrm{ Ge V /}c^2} $. For the charge asymmetries, the first uncertainty is statistical, the second systematic, and the third is due to the $ C P$ asymmetry of the $ { B ^\pm \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K ^\pm }$ reference mode.

Signal yields and charge asymmetries in the regions dominated by the vector resonances. For the charge asymmetries, the first uncertainty is statistical, the second systematic, and the third is due to the $ C P$ asymmetry of the $ { B ^\pm \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K ^\pm }$ reference mode.

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