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Study of $B^{-}\to DK^-\pi^+\pi^-$ and $B^-\to D\pi^-\pi^+\pi^-$ decays and determination of the CKM angle $\gamma$

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Abstract

We report a study of the suppressed $B^-\to DK^-\pi^+\pi^-$ and favored $B^-\to D\pi^-\pi^+\pi^-$ decays, where the neutral $D$ meson is detected through its decays to the $K^{\mp}\pi^{\pm}$ and CP-even $K^+K^-$ and $\pi^+\pi^-$ final states. The measurement is carried out using a proton-proton collision data sample collected by the LHCb experiment, corresponding to an integrated luminosity of 3.0 fb$^{-1}$. We observe the first significant signals in the CP-even final states of the $D$ meson for both the suppressed $B^-\to DK^-\pi^+\pi^-$ and favored $B^-\to D\pi^-\pi^+\pi^-$ modes, as well as in the doubly Cabibbo-suppressed $D\to K^+\pi^-$ final state of the $B^-\to D\pi^-\pi^+\pi^-$ decay. Evidence for the ADS suppressed decay $B^{-}\to DK^-\pi^+\pi^-$, with $D\to K^+\pi^-$, is also presented. From the observed yields in the $B^-\to DK^-\pi^+\pi^-$, $B^-\to D\pi^-\pi^+\pi^-$ and their charge conjugate decay modes, we measure the value of the weak phase to be $\gamma=(74^{+20}_{-19})^{\rm o}$. This is one of the most precise single-measurement determinations of $\gamma$ to date.

Figures and captions

Signal efficiencies for the $ B ^- \rightarrow [ K ^- \pi ^+ ]_DX_d^-$ decay when applying the GLW and ADS selections. The efficiencies are shown as a function of five different two- and three-body masses.

 EffOve[..].pdf [24 KiB]
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EffOverlayDalitz_B2D0A1_Paper.pdf

Signal efficiencies for the $ B ^- \rightarrow [ K ^- \pi ^+ ]_DX_s^-$ decay when applying the GLW and ADS selections. The efficiencies are shown as a function of five different two- and three-body masses.

 EffOve[..].pdf [23 KiB]
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EffOverlayDalitz_B2D0K1_Paper.pdf

Signal distributions of the (left) $X_d^-$ invariant mass in $ B ^- \rightarrow DX_d^-$ decays and (right) $X_s^-$ invariant mass, in $ B ^- \rightarrow DX_s^-$ decays, for $D\rightarrow K ^- \pi ^+ $. The distributions are obtained using the sPlot method. In both cases, all selections, except the $M(X^-)<2$ $ {\mathrm{ Ge V /}c^2}$ and the $ K ^{*0} $ mass selection, are applied. The dip at 1.97 $ {\mathrm{ Ge V /}c^2}$ is due to the $ D ^+_ s $ meson veto.

 Xdm_mass.pdf [15 KiB]
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Xdm_mass.pdf
Xsm_mass.pdf [16 KiB]
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Xsm_mass.pdf

Mass distributions of $ B ^- \rightarrow DX_s^-$ candidates using the ADS selections, for (top left) $ B ^- \rightarrow [ K ^- \pi ^+ ]_DX_s^-$, (top right) $ B ^+ \rightarrow [ K ^+ \pi ^- ]_DX_s^+$, (bottom left) $ B ^- \rightarrow [ K ^+ \pi ^- ]_DX_s^-$, and (bottom right) $ B ^+ \rightarrow [ K ^- \pi ^+ ]_DX_s^+$.

 ADS_Km[..].pdf [25 KiB]
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ADS_KminusPiplus_kpp_minus.pdf
ADS_Kp[..].pdf [22 KiB]
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ADS_KplusPiminus_kpp_plus.pdf
ADS_Kp[..].pdf [25 KiB]
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ADS_KplusPiminus_kpp_minus.pdf
ADS_Km[..].pdf [25 KiB]
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ADS_KminusPiplus_kpp_plus.pdf

Mass distributions of $ B ^- \rightarrow DX_s^-$ candidates using the GLW selections, for (top left) $ B ^- \rightarrow [ K ^- \pi ^+ ]_DX_s^-$, (top right) $ B ^+ \rightarrow [ K ^+ \pi ^- ]_DX_s^+$, (middle left) $ B ^- \rightarrow [ K ^+ K ^- ]_DX_s^-$, (middle right) $ B ^+ \rightarrow [ K ^+ K ^- ]_DX_s^+$, (bottom left) $ B ^- \rightarrow [\pi ^+ \pi ^- ]_DX_s^-$, and (bottom right) $ B ^+ \rightarrow [\pi ^+ \pi ^- ]_DX_s^+$.

 GLW_kp[..].pdf [26 KiB]
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GLW_kpi_kpp_minus.pdf
GLW_kp[..].pdf [26 KiB]
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GLW_kpi_kpp_plus.pdf
GLW_kk[..].pdf [25 KiB]
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GLW_kk_kpp_minus.pdf
GLW_kk[..].pdf [25 KiB]
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GLW_kk_kpp_plus.pdf
GLW_pi[..].pdf [25 KiB]
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GLW_pipi_kpp_minus.pdf
GLW_pi[..].pdf [25 KiB]
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GLW_pipi_kpp_plus.pdf

Mass distributions of $ B ^- \rightarrow DX_d^-$ candidates using the ADS selections, for (top left) $ B ^- \rightarrow [ K ^- \pi ^+ ]_DX_d^-$, (top right) $ B ^+ \rightarrow [ K ^+ \pi ^- ]_DX_d^+$, (bottom left) $ B ^- \rightarrow [ K ^+ \pi ^- ]_DX_d^-$, and (bottom right) $ B ^+ \rightarrow [ K ^- \pi ^+ ]_DX_d^+$.

 ADS_Km[..].pdf [20 KiB]
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ADS_KminusPiplus_ppp_minus.pdf
ADS_Kp[..].pdf [20 KiB]
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ADS_KplusPiminus_ppp_plus.pdf
ADS_Kp[..].pdf [25 KiB]
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ADS_KplusPiminus_ppp_minus.pdf
ADS_Km[..].pdf [24 KiB]
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ADS_KminusPiplus_ppp_plus.pdf

Mass distributions of $ B ^- \rightarrow DX_d^-$ candidates using the GLW selections, for (top left) $ B ^- \rightarrow [ K ^- \pi ^+ ]_DX_d^-$, (top right) $ B ^+ \rightarrow [ K ^+ \pi ^- ]_DX_d^+$, (middle left) $ B ^- \rightarrow [ K ^+ K ^- ]_DX_d^-$, and (middle right) $ B ^+ \rightarrow [ K ^+ K ^- ]_DX_d^+$, (bottom left) $ B ^- \rightarrow [\pi ^+ \pi ^- ]_DX_d^-$, and (bottom right) $ B ^+ \rightarrow [\pi ^+ \pi ^- ]_DX_d^+$

 GLW_kp[..].pdf [20 KiB]
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GLW_kpi_ppp_minus.pdf
GLW_kp[..].pdf [20 KiB]
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GLW_kpi_ppp_plus.pdf
GLW_kk[..].pdf [20 KiB]
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GLW_kk_ppp_minus.pdf
GLW_kk[..].pdf [20 KiB]
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GLW_kk_ppp_plus.pdf
GLW_pi[..].pdf [21 KiB]
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GLW_pipi_ppp_minus.pdf
GLW_pi[..].pdf [21 KiB]
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GLW_pipi_ppp_plus.pdf

Mass distributions for the suppressed ADS mode, $B^{\pm}\rightarrow [K^{\mp}\pi^{\pm}]_DK^{\pm}\pi^{\mp}\pi^{\pm}$ (sum of $ B ^+ $ and $ B ^- $).

 chgcom[..].pdf [25 KiB]
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chgcombined.pdf

Projections of 1$-$CL versus (left) $\gamma$, (right) $r_B^{ B ^- \rightarrow D K ^- \pi ^+ \pi ^- }$, and (bottom) $r_B^{ B ^- \rightarrow D K ^- \pi ^+ \pi ^- }$ versus $\gamma$, using only $ B ^- \rightarrow \ D K ^- \pi ^+ \pi ^- $ decays, and the combination of $ B ^- \rightarrow \ D K ^- \pi ^+ \pi ^- $ and $ B ^- \rightarrow \ D\pi ^- \pi ^+ \pi ^- $ decays. The 68.3% and 95.5% confidence level (CL) limits are indicated for the $\gamma$ and $r_B$ projections. The 39% level contours in $r_B^{ B ^- \rightarrow D K ^- \pi ^+ \pi ^- }$ versus $\gamma$ correspond to the 68.3% level contours in the one-dimensional projections.

 gammac[..].pdf [15 KiB]
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gammacombo_BDKpipi_BDhpipi_g_pluginonly.pdf
gammac[..].pdf [15 KiB]
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gammacombo_BDKpipi_BDhpipi_r_dkpipi_pluginonly.pdf
rb_vs_g.pdf [15 KiB]
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rb_vs_g.pdf

Animated gif made out of all figures.

 PAPER-2015-020.gif
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thumbnail_PAPER-2015-020.gif

Tables and captions

Fitted yields in the ADS modes with $f=K\pi$, for the signal and corresponding normalization modes.

 Table_1.pdf [74 KiB]
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tex code 		Table_1.pdf

Fitted yields used in the GLW analysis with $f=K^{\pm}\pi^{\pm}, K ^+ K ^- $ and $\pi ^+ \pi ^- $, for the signal and corresponding normalization modes.

 Table_2.pdf [74 KiB]
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tex code 		Table_2.pdf

Systematic uncertainties, in percent, on the fitted parameters.

 Table_3.pdf [64 KiB]
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tex code 		Table_3.pdf

Created on 02 May 2024.