# Measurement of $C\!P$ violation in the phase space of $B^{\pm} \to K^{\pm} \pi^{+} \pi^{-}$ and $B^{\pm} \to K^{\pm} K^{+} K^{-}$ decays

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## Abstract

The charmless decays $B^{\pm}\to K^{\pm}\pi^+\pi^-$ and $B^{\pm}\to K^{\pm}K^+K^-$ are reconstructed using data, corresponding to an integrated luminosity of 1.0 fb$^{-1}$, collected by LHCb in 2011. The inclusive charge asymmetries of these modes are measured as $A_{C\!P}(B^{\pm}\to K^{\pm}\pi^+\pi^-) = 0.032 \pm 0.008 \stat \pm 0.004 \syst \pm 0.007 (J\psi K^{\pm})$ and $A_{C\!P}(B^{\pm}\to K^{\pm}K^+K^-) = -0.043 \pm 0.009 \stat \pm 0.003 \syst \pm 0.007 (J\psi K^{\pm})$, where the third uncertainty is due to the $C\!P$ asymmetry of the $B^{\pm}\to J\psi K^{\pm}$ reference mode. The significance of $A_{C\!P}(B^{\pm}\to K^{\pm}K^+K^-)$ exceeds three standard deviations and is the first evidence of an inclusive $C\!P$ asymmetry in charmless three-body $B$ decays. In addition to the inclusive $C\!P$ asymmetries, larger asymmetries are observed in localised regions of phase space.

## Figures and captions

 Invariant mass spectra of (a) ${ B ^\pm \rightarrow K ^\pm \pi ^+ \pi ^- }$ decays and (b) ${ B ^\pm \rightarrow K ^\pm K ^+ K ^- }$ decays. The left panel in each figure shows the $B ^-$ modes and the right panel shows the $B ^+$ modes. The results of the unbinned maximum likelihood fits are overlaid. The main components of the fit are also shown. kpipi_[..].pdf [21 KiB] HiDef png [359 KiB] Thumbnail [93 KiB] *.C file kkk_fi[..].pdf [17 KiB] HiDef png [272 KiB] Thumbnail [77 KiB] *.C file Asymmetries of the number of signal events in bins of the Dalitz plot, $A_{ C\!P }^{N}$ , for (a) ${ B ^\pm \rightarrow K ^\pm \pi ^+ \pi ^- }$ and (b) ${ B ^\pm \rightarrow K ^\pm K ^+ K ^- }$ decays. The inset figures show the projections of the number of background-subtracted events in bins of (left) the $m^2_{\pi ^+ \pi ^- }$ variable for $m^2_{ K ^\pm \pi ^\mp } <15 {\mathrm{\,GeV^2\!/}c^4}$ and (right) the $m^2_{ K ^+ K ^- \,{\rm low}}$ variable for $m^2_{ K ^+ K ^- \,{\rm high}} <15 {\mathrm{\,GeV^2\!/}c^4}$. The distributions are not corrected for acceptance. kpipi_[..].pdf [21 KiB] HiDef png [249 KiB] Thumbnail [95 KiB] *.C file kkk_dalitz.pdf [22 KiB] HiDef png [256 KiB] Thumbnail [100 KiB] *.C file Invariant mass spectra of (a) ${ B ^\pm \rightarrow K ^\pm \pi ^+ \pi ^- }$ decays in the region $0.08 < m^2_{\pi ^+ \pi ^- } < 0.66 {\mathrm{\,GeV^2\!/}c^4}$ and $m^2_{ K ^\pm \pi ^\mp } < 15 {\mathrm{\,GeV^2\!/}c^4}$, and (b) ${ B ^\pm \rightarrow K ^\pm K ^+ K ^- }$ decays in the region $1.2 < m^2_{ K ^+ K ^- \,{\rm low}} < 2.0 {\mathrm{\,GeV^2\!/}c^4}$ and $m^2_{ K ^+ K ^- \,{\rm high}} < 15 {\mathrm{\,GeV^2\!/}c^4}$. The left panel in each figure shows the $B ^-$ modes and the right panel shows the $B ^+$ modes. The results of the unbinned maximum likelihood fits are overlaid. kpipi_[..].pdf [18 KiB] HiDef png [329 KiB] Thumbnail [102 KiB] *.C file kkk_fi[..].pdf [18 KiB] HiDef png [284 KiB] Thumbnail [80 KiB] *.C file Animated gif made out of all figures. PAPER-2013-027.gif Thumbnail

## Tables and captions

 Systematic uncertainties on $A_{\mathcal{C}_{P} } ( { K ^\pm \pi ^+ \pi ^- } )$ and $A_{\mathcal{C}_{P} } ( { K ^\pm K ^+ K ^- } )$. The total systematic uncertainties are the sum in quadrature of the individual contributions. Table_I.pdf [37 KiB] HiDef png [100 KiB] Thumbnail [15 KiB] tex code

Created on 16 February 2019.Citation count from INSPIRE on 16 February 2019.