cern.ch

Measurements of $C\!P$ violation in the three-body phase space of charmless $B^{\pm}$ decays

[to restricted-access page]

Abstract

The charmless three-body decay modes $B^{\pm} \rightarrow K^{\pm} \pi^{+} \pi^{-}$, $B^{\pm} \rightarrow K^{\pm} K^{+} K^{-}$, $B^{\pm} \rightarrow \pi^{\pm} K^{+} K^{-}$ and $B^{\pm} \rightarrow \pi^{\pm} \pi^{+} \pi^{-}$ are reconstructed using data, corresponding to an integrated luminosity of 3.0\;$\,fb^{-1}$, collected by the LHCb detector. The inclusive $C\!P$ asymmetries of these modes are measured to be $$ A_{C\!P}(B^{\pm} \rightarrow K^{\pm} \pi^{+} \pi^{-})= +0.025 \pm 0.004 \pm 0.004 \pm 0.007 \\ A_{C\!P}(B^{\pm} \rightarrow K^{\pm} K^{+} K^{-}) = -0.036 \pm 0.004 \pm 0.002 \pm 0.007 \\ A_{C\!P}(B^{\pm} \rightarrow \pi^{\pm} \pi^{+} \pi^{-})= +0.058 \pm 0.008 \pm 0.009 \pm 0.007 \\ A_{C\!P}(B^{\pm} \rightarrow \pi^{\pm} K^{+} K^{-})= -0.123 \pm 0.017 \pm 0.012 \pm 0.007 $$ %% where the first uncertainty is statistical, the second systematic, and the third is due to the $C\!P$ asymmetry of the $B^{\pm} \rightarrow J/\psi K^{\pm}$ reference mode. The distributions of these asymmetries are also studied as functions of position in the Dalitz plot and suggest contributions from rescattering and resonance interference processes.

Figures and captions

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.

Fig1a.pdf [38 KiB]
HiDef png [386 KiB]
Thumbnail [100 KiB]
*.C file
Fig1a.pdf
Fig1b.pdf [36 KiB]
HiDef png [315 KiB]
Thumbnail [90 KiB]
*.C file
Fig1b.pdf
Fig1c.pdf [35 KiB]
HiDef png [372 KiB]
Thumbnail [96 KiB]
*.C file
Fig1c.pdf
Fig1d.pdf [38 KiB]
HiDef png [545 KiB]
Thumbnail [112 KiB]
*.C file
Fig1d.pdf

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.

Fig2a.pdf [89 KiB]
HiDef png [537 KiB]
Thumbnail [99 KiB]
*.C file
Fig2a.pdf
Fig2b.pdf [137 KiB]
HiDef png [626 KiB]
Thumbnail [105 KiB]
*.C file
Fig2b.pdf
Fig2c.pdf [59 KiB]
HiDef png [456 KiB]
Thumbnail [116 KiB]
*.C file
Fig2c.pdf
Fig2d.pdf [31 KiB]
HiDef png [292 KiB]
Thumbnail [100 KiB]
*.C file
Fig2d.pdf

(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.

Fig3a.pdf [31 KiB]
HiDef png [244 KiB]
Thumbnail [92 KiB]
*.C file
Fig3a.pdf
Fig3b.pdf [31 KiB]
HiDef png [215 KiB]
Thumbnail [85 KiB]
*.C file
Fig3b.pdf
Fig3c.pdf [18 KiB]
HiDef png [157 KiB]
Thumbnail [67 KiB]
*.C file
Fig3c.pdf
Fig3d.pdf [15 KiB]
HiDef png [125 KiB]
Thumbnail [55 KiB]
*.C file
Fig3d.pdf

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).

Fig4a.pdf [15 KiB]
HiDef png [201 KiB]
Thumbnail [65 KiB]
*.C file
Fig4a.pdf
Fig4b.pdf [15 KiB]
HiDef png [185 KiB]
Thumbnail [60 KiB]
*.C file
Fig4b.pdf
Fig4c.pdf [15 KiB]
HiDef png [133 KiB]
Thumbnail [48 KiB]
*.C file
Fig4c.pdf
Fig4d.pdf [15 KiB]
HiDef png [128 KiB]
Thumbnail [47 KiB]
*.C file
Fig4d.pdf

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).

Fig5a.pdf [15 KiB]
HiDef png [157 KiB]
Thumbnail [63 KiB]
*.C file
Fig5a.pdf
Fig5b.pdf [15 KiB]
HiDef png [135 KiB]
Thumbnail [54 KiB]
*.C file
Fig5b.pdf
Fig5c.pdf [15 KiB]
HiDef png [129 KiB]
Thumbnail [48 KiB]
*.C file
Fig5c.pdf
Fig5d.pdf [15 KiB]
HiDef png [129 KiB]
Thumbnail [47 KiB]
*.C file
Fig5d.pdf

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).

Fig6a.pdf [17 KiB]
HiDef png [251 KiB]
Thumbnail [87 KiB]
*.C file
Fig6a.pdf
Fig6b.pdf [17 KiB]
HiDef png [253 KiB]
Thumbnail [87 KiB]
*.C file
Fig6b.pdf
Fig6c.pdf [16 KiB]
HiDef png [158 KiB]
Thumbnail [61 KiB]
*.C file
Fig6c.pdf
Fig6d.pdf [16 KiB]
HiDef png [152 KiB]
Thumbnail [58 KiB]
*.C file
Fig6d.pdf

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).

Fig7a.pdf [14 KiB]
HiDef png [138 KiB]
Thumbnail [60 KiB]
*.C file
Fig7a.pdf
Fig7b.pdf [14 KiB]
HiDef png [108 KiB]
Thumbnail [46 KiB]
*.C file
Fig7b.pdf

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.

Fig8a.pdf [37 KiB]
HiDef png [378 KiB]
Thumbnail [100 KiB]
*.C file
Fig8a.pdf
Fig8b.pdf [37 KiB]
HiDef png [329 KiB]
Thumbnail [96 KiB]
*.C file
Fig8b.pdf
Fig8c.pdf [34 KiB]
HiDef png [343 KiB]
Thumbnail [92 KiB]
*.C file
Fig8c.pdf
Fig8d.pdf [34 KiB]
HiDef png [386 KiB]
Thumbnail [103 KiB]
*.C file
Fig8d.pdf

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.

Fig9a.pdf [35 KiB]
HiDef png [354 KiB]
Thumbnail [95 KiB]
*.C file
Fig9a.pdf
Fig9b.pdf [34 KiB]
HiDef png [337 KiB]
Thumbnail [92 KiB]
*.C file
Fig9b.pdf
Fig9c.pdf [35 KiB]
HiDef png [356 KiB]
Thumbnail [93 KiB]
*.C file
Fig9c.pdf
Fig9d.pdf [34 KiB]
HiDef png [333 KiB]
Thumbnail [90 KiB]
*.C file
Fig9d.pdf

Animated gif made out of all figures.

PAPER-2014-044.gif
Thumbnail
thumbnail_PAPER-2014-044.gif

Tables and captions

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

Table_1.pdf [43 KiB]
HiDef png [91 KiB]
Thumbnail [15 KiB]
tex code
Table_1.pdf

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].

Table_2.pdf [47 KiB]
HiDef png [127 KiB]
Thumbnail [19 KiB]
tex code
Table_2.pdf

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.

Table_3.pdf [49 KiB]
HiDef png [58 KiB]
Thumbnail [10 KiB]
tex code
Table_3.pdf

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.

Table_4.pdf [54 KiB]
HiDef png [144 KiB]
Thumbnail [24 KiB]
tex code
Table_4.pdf

Supplementary Material [file]

Supplementary material full pdf

Supple[..].pdf [382 KiB]
Supplementary.pdf
Fig1a.pdf [16 KiB]
HiDef png [149 KiB]
Thumbnail [59 KiB]
*C file
Fig1a.pdf
Fig1b.pdf [16 KiB]
HiDef png [139 KiB]
Thumbnail [58 KiB]
*C file
Fig1b.pdf
Fig1c.pdf [17 KiB]
HiDef png [159 KiB]
Thumbnail [58 KiB]
*C file
Fig1c.pdf
Fig1d.pdf [17 KiB]
HiDef png [140 KiB]
Thumbnail [50 KiB]
*C file
Fig1d.pdf
Fig2a.pdf [15 KiB]
HiDef png [156 KiB]
Thumbnail [61 KiB]
*C file
Fig2a.pdf
Fig2b.pdf [16 KiB]
HiDef png [137 KiB]
Thumbnail [54 KiB]
*C file
Fig2b.pdf
Fig2c.pdf [16 KiB]
HiDef png [144 KiB]
Thumbnail [54 KiB]
*C file
Fig2c.pdf
Fig2d.pdf [17 KiB]
HiDef png [155 KiB]
Thumbnail [51 KiB]
*C file
Fig2d.pdf
Fig3a.pdf [16 KiB]
HiDef png [172 KiB]
Thumbnail [67 KiB]
*C file
Fig3a.pdf
Fig3b.pdf [17 KiB]
HiDef png [149 KiB]
Thumbnail [60 KiB]
*C file
Fig3b.pdf
Fig3c.pdf [17 KiB]
HiDef png [156 KiB]
Thumbnail [57 KiB]
*C file
Fig3c.pdf
Fig3d.pdf [17 KiB]
HiDef png [164 KiB]
Thumbnail [55 KiB]
*C file
Fig3d.pdf
Fig4a.pdf [17 KiB]
HiDef png [210 KiB]
Thumbnail [83 KiB]
*C file
Fig4a.pdf
Fig4b.pdf [16 KiB]
HiDef png [156 KiB]
Thumbnail [64 KiB]
*C file
Fig4b.pdf
Fig4c.pdf [17 KiB]
HiDef png [169 KiB]
Thumbnail [63 KiB]
*C file
Fig4c.pdf
Fig4d.pdf [17 KiB]
HiDef png [155 KiB]
Thumbnail [56 KiB]
*C file
Fig4d.pdf

Created on 20 April 2019.Citation count from INSPIRE on 25 April 2019.