Constraints on the unitarity triangle angle $\gamma$ from Dalitz plot analysis of $B^0 \to D K^+ \pi^-$ decays
- Aaij, Roel et al
- arXiv:1602.03455LHCB-PAPER-2015-059CERN-EP-2016-024
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 | Feynman diagrams for the contributions to $\Bd\to D\Kp\pim$ from (a) $\Bz \to D_2^*(2460)^-\Kp$, (b) $\Bz \to \Dzb\Kstar(892)^0$ and (c) $\Bz \to \Dz\Kstar(892)^0$ decays. |
 | Feynman diagrams for the contributions to $\Bd\to D\Kp\pim$ from (a) $\Bz \to D_2^*(2460)^-\Kp$, (b) $\Bz \to \Dzb\Kstar(892)^0$ and (c) $\Bz \to \Dz\Kstar(892)^0$ decays. |
 | \small Results of fits to $D\Kp\pim$ candidates in the (a) $D\to \Kp\pim$, (b) $D\to \Kp\Km$ and (c) $D\to \pip\pim$ samples. The data and the fit results in each NN output bin have been weighted according to ${\cal S}/({\cal S}+{\cal B})$ as described in the text. The components are as described in the legend. |
 | Feynman diagrams for the contributions to $\Bd\to D\Kp\pim$ from (a) $\Bz \to D_2^*(2460)^-\Kp$, (b) $\Bz \to \Dzb\Kstar(892)^0$ and (c) $\Bz \to \Dz\Kstar(892)^0$ decays. |
 | Illustration of the method to determine $\gamma$ from Dalitz plot analysis of $\Bd \to \D\Kp\pim$ decays~\cite{Gershon:2008pe,Gershon:2009qc}: (left) the $V_{cb}$ amplitude for $\Bz \to \Dzb\Kstarz$ compared to that for $\Bz \to D_2^{*-}\Kp$ decay; (right) the effect of the $V_{ub}$ amplitude that contributes to $\Bz\to D_{\CP}\Kstarz$ and $\Bzb\to D_{\CP}\Kstarzb$ decays provides sensitivity to $\gamma$. The notation $D_{\CP}$ represents a neutral \D meson reconstructed in a \CP eigenstate, while $D^{*-}_{2\,\CP}$ denotes the decay chain $D_2^{*-}\to \D_{\CP}\pim$, where the charge of the pion tags the flavour of the neutral \D meson, independently of the mode in which it is reconstructed, so there is no contribution from the $V_{ub}$ amplitude. |
 | Illustration of the method to determine $\gamma$ from Dalitz plot analysis of $\Bd \to \D\Kp\pim$ decays~\cite{Gershon:2008pe,Gershon:2009qc}: (left) the $V_{cb}$ amplitude for $\Bz \to \Dzb\Kstarz$ compared to that for $\Bz \to D_2^{*-}\Kp$ decay; (right) the effect of the $V_{ub}$ amplitude that contributes to $\Bz\to D_{\CP}\Kstarz$ and $\Bzb\to D_{\CP}\Kstarzb$ decays provides sensitivity to $\gamma$. The notation $D_{\CP}$ represents a neutral \D meson reconstructed in a \CP eigenstate, while $D^{*-}_{2\,\CP}$ denotes the decay chain $D_2^{*-}\to \D_{\CP}\pim$, where the charge of the pion tags the flavour of the neutral \D meson, independently of the mode in which it is reconstructed, so there is no contribution from the $V_{ub}$ amplitude. |
 | \small Results of fits to $D\Kp\pim$ candidates in the (a,b) $D\to \Kp\pim$, (c,d) $D\to \Kp\Km$ and (e,f) $D\to \pip\pim$ samples. The data and the fit results in each NN output bin have been weighted according to ${\cal S}/({\cal S}+{\cal B})$ as described in the text. The left and right plots are identical but with (left) linear and (right) logarithmic $y$-axis scales. The components are as described in the legend. |
 | \small Results of fits to $D\Kp\pim$ candidates in the (a,b) $D\to \Kp\pim$, (c,d) $D\to \Kp\Km$ and (e,f) $D\to \pip\pim$ samples. The data and the fit results in each NN output bin have been weighted according to ${\cal S}/({\cal S}+{\cal B})$ as described in the text. The left and right plots are identical but with (left) linear and (right) logarithmic $y$-axis scales. The components are as described in the legend. |
 | \small Results of fits to $D\Kp\pim$ candidates in the (a,b) $D\to \Kp\pim$, (c,d) $D\to \Kp\Km$ and (e,f) $D\to \pip\pim$ samples. The data and the fit results in each NN output bin have been weighted according to ${\cal S}/({\cal S}+{\cal B})$ as described in the text. The left and right plots are identical but with (left) linear and (right) logarithmic $y$-axis scales. The components are as described in the legend. |
 | \small Projections of the $D\to\Kp\Km$ and $\pip\pim$ samples and the fit result onto $m(\Kpm\pimp)$ for (a) $\Bzb$ and (b) $\Bz$ candidates. The data and the fit results in each NN output bin have been weighted according to ${\cal S}/({\cal S}+{\cal B})$ and combined. The components are described in the legend. |
 | \small Results of fits to $D\Kp\pim$ candidates in the (a,b) $D\to \Kp\pim$, (c,d) $D\to \Kp\Km$ and (e,f) $D\to \pip\pim$ samples. The data and the fit results in each NN output bin have been weighted according to ${\cal S}/({\cal S}+{\cal B})$ as described in the text. The left and right plots are identical but with (left) linear and (right) logarithmic $y$-axis scales. The components are as described in the legend. |
 | \small Results of fits to $D\Kp\pim$ candidates in the (a,b) $D\to \Kp\pim$, (c,d) $D\to \Kp\Km$ and (e,f) $D\to \pip\pim$ samples. The data and the fit results in each NN output bin have been weighted according to ${\cal S}/({\cal S}+{\cal B})$ as described in the text. The left and right plots are identical but with (left) linear and (right) logarithmic $y$-axis scales. The components are as described in the legend. |
 | \small Results of fits to $D\Kp\pim$ candidates in the (a,b) $D\to \Kp\pim$, (c,d) $D\to \Kp\Km$ and (e,f) $D\to \pip\pim$ samples. The data and the fit results in each NN output bin have been weighted according to ${\cal S}/({\cal S}+{\cal B})$ as described in the text. The left and right plots are identical but with (left) linear and (right) logarithmic $y$-axis scales. The components are as described in the legend. |
 | \small Results of fits to $D\Kp\pim$ candidates in the (a,b) $D\to \Kp\pim$, (c,d) $D\to \Kp\Km$ and (e,f) $D\to \pip\pim$ samples. The data and the fit results in each NN output bin have been weighted according to ${\cal S}/({\cal S}+{\cal B})$ as described in the text. The left and right plots are identical but with (left) linear and (right) logarithmic $y$-axis scales. The components are as described in the legend. |
 | \small Results of the fit to $\D\Kp\pim$, $\D\to\Kp\pim$ candidates shown separately in the five bins of the neural network output variable. The bins are shown, from (a)--(e), in order of increasing ${\cal S}/{\cal B}$. The components are as indicated in the legend. The vertical dotted lines in (a) show the signal window used for the fit to the Dalitz plot. |
 | \small Results of the fit to $\D\Kp\pim$, $\D\to\Kp\pim$ candidates shown separately in the five bins of the neural network output variable. The bins are shown, from (a)--(e), in order of increasing ${\cal S}/{\cal B}$. The components are as indicated in the legend. The vertical dotted lines in (a) show the signal window used for the fit to the Dalitz plot. |
 | \small Results of fits to $D\Kp\pim$ candidates in the (a) $D\to \Kp\pim$, (b) $D\to \Kp\Km$ and (c) $D\to \pip\pim$ samples. The data and the fit results in each NN output bin have been weighted according to ${\cal S}/({\cal S}+{\cal B})$ and combined. |
 | \small Results of the fit to $\D\Kp\pim$, $\D\to\Kp\pim$ candidates shown separately in the five bins of the neural network output variable. The bins are shown, from (a)--(e), in order of increasing ${\cal S}/{\cal B}$. The components are as indicated in the legend. The vertical dotted lines in (a) show the signal window used for the fit to the Dalitz plot. |
 | \small Results of the fit to $\D\Kp\pim$, $\D\to\Kp\pim$ candidates shown separately in the five bins of the neural network output variable. The bins are shown, from (a)--(e), in order of increasing ${\cal S}/{\cal B}$. The components are as indicated in the legend. The vertical dotted lines in (a) show the signal window used for the fit to the Dalitz plot. |
 | \small Results of the fit to $\D\Kp\pim$, $\D\to\Kp\pim$ candidates shown separately in the five bins of the neural network output variable. The bins are shown, from (a)--(e), in order of increasing ${\cal S}/{\cal B}$. The components are as indicated in the legend. The vertical dotted lines in (a) show the signal window used for the fit to the Dalitz plot. |
 | \small Results of the fit to $\D\Kp\pim$, $\D\to\Kp\pim$ candidates shown separately in the five bins of the neural network output variable. The bins are shown, from (a)--(e), in order of increasing ${\cal S}/{\cal B}$. The components are as indicated in the legend. The vertical dotted lines in (a) show the signal window used for the fit to the Dalitz plot. |
 | \small Results of the fit to $\D\Kp\pim$, $\D\to\Kp\Km$ candidates shown separately in the five bins of the neural network output variable. The bins are shown, from (a)--(e), in order of increasing ${\cal S}/{\cal B}$. The components are as indicated in the legend. The vertical dotted lines in (a) show the signal window used for the fit to the Dalitz plot. |
 | \small Results of the fit to $\D\Kp\pim$, $\D\to\Kp\Km$ candidates shown separately in the five bins of the neural network output variable. The bins are shown, from (a)--(e), in order of increasing ${\cal S}/{\cal B}$. The components are as indicated in the legend. The vertical dotted lines in (a) show the signal window used for the fit to the Dalitz plot. |
 | \small Results of the fit to $\D\Kp\pim$, $\D\to\Kp\Km$ candidates shown separately in the five bins of the neural network output variable. The bins are shown, from (a)--(e), in order of increasing ${\cal S}/{\cal B}$. The components are as indicated in the legend. The vertical dotted lines in (a) show the signal window used for the fit to the Dalitz plot. |
 | \small Results of the fit to $\D\Kp\pim$, $\D\to\Kp\pim$ candidates shown separately in the five bins of the neural network output variable. The bins are shown, from (a)-(e), in order of increasing ${\cal S}/{\cal B}$. The components are as indicated in the legend. The vertical dotted lines in (a) show the signal window used for the fit to the Dalitz plot. |
 | \small Results of the fit to $\D\Kp\pim$, $\D\to\Kp\Km$ candidates shown separately in the five bins of the neural network output variable. The bins are shown, from (a)--(e), in order of increasing ${\cal S}/{\cal B}$. The components are as indicated in the legend. The vertical dotted lines in (a) show the signal window used for the fit to the Dalitz plot. |
 | \small Results of the fit to $\D\Kp\pim$, $\D\to\Kp\Km$ candidates shown separately in the five bins of the neural network output variable. The bins are shown, from (a)--(e), in order of increasing ${\cal S}/{\cal B}$. The components are as indicated in the legend. The vertical dotted lines in (a) show the signal window used for the fit to the Dalitz plot. |
 | \small Results of the fit to $\D\Kp\pim$, $\D\to\Kp\Km$ candidates shown separately in the five bins of the neural network output variable. The bins are shown, from (a)--(e), in order of increasing ${\cal S}/{\cal B}$. The components are as indicated in the legend. The vertical dotted lines in (a) show the signal window used for the fit to the Dalitz plot. |
 | \small Results of the fit to $\D\Kp\pim$, $\D\to\Kp\Km$ candidates shown separately in the five bins of the neural network output variable. The bins are shown, from (a)-(e), in order of increasing ${\cal S}/{\cal B}$. The components are as indicated in the legend. The vertical dotted lines in (a) show the signal window used for the fit to the Dalitz plot. |
 | \small Results of the fit to $\D\Kp\pim$, $\D\to\pip\pim$ candidates shown separately in the five bins of the neural network output variable. The bins are shown, from (a)--(e), in order of increasing ${\cal S}/{\cal B}$. The components are as indicated in the legend. The vertical dotted lines in (a) show the signal window used for the fit to the Dalitz plot. |
 | \small Results of the fit to $\D\Kp\pim$, $\D\to\Kp\Km$ candidates shown separately in the five bins of the neural network output variable. The bins are shown, from (a)-(e), in order of increasing ${\cal S}/{\cal B}$. The components are as indicated in the legend. The vertical dotted lines in (a) show the signal window used for the fit to the Dalitz plot. |
 | \small Results of the fit to $\D\Kp\pim$, $\D\to\pip\pim$ candidates shown separately in the five bins of the neural network output variable. The bins are shown, from (a)--(e), in order of increasing ${\cal S}/{\cal B}$. The components are as indicated in the legend. The vertical dotted lines in (a) show the signal window used for the fit to the Dalitz plot. |
 | \small Results of the fit to $\D\Kp\pim$, $\D\to\Kp\Km$ candidates shown separately in the five bins of the neural network output variable. The bins are shown, from (a)-(e), in order of increasing ${\cal S}/{\cal B}$. The components are as indicated in the legend. The vertical dotted lines in (a) show the signal window used for the fit to the Dalitz plot. |
 | \small Results of the fit to $\D\Kp\pim$, $\D\to\pip\pim$ candidates shown separately in the five bins of the neural network output variable. The bins are shown, from (a)--(e), in order of increasing ${\cal S}/{\cal B}$. The components are as indicated in the legend. The vertical dotted lines in (a) show the signal window used for the fit to the Dalitz plot. |
 | \small Results of the fit to $\D\Kp\pim$, $\D\to\Kp\Km$ candidates shown separately in the five bins of the neural network output variable. The bins are shown, from (a)-(e), in order of increasing ${\cal S}/{\cal B}$. The components are as indicated in the legend. The vertical dotted lines in (a) show the signal window used for the fit to the Dalitz plot. |
 | \small Results of the fit to $\D\Kp\pim$, $\D\to\pip\pim$ candidates shown separately in the five bins of the neural network output variable. The bins are shown, from (a)--(e), in order of increasing ${\cal S}/{\cal B}$. The components are as indicated in the legend. The vertical dotted lines in (a) show the signal window used for the fit to the Dalitz plot. |
 | \small Results of the fit to $\D\Kp\pim$, $\D\to\pip\pim$ candidates shown separately in the five bins of the neural network output variable. The bins are shown, from (a)--(e), in order of increasing ${\cal S}/{\cal B}$. The components are as indicated in the legend. The vertical dotted lines in (a) show the signal window used for the fit to the Dalitz plot. |
 | \small Results of the fit to $\D\Kp\pim$, $\D\to\pip\pim$ candidates shown separately in the five bins of the neural network output variable. The bins are shown, from (a)--(e), in order of increasing ${\cal S}/{\cal B}$. The components are as indicated in the legend. The vertical dotted lines in (a) show the signal window used for the fit to the Dalitz plot. |
 | \small Dalitz plots for candidates in the \B candidate mass signal region in the $\D\to\Kp\Km$ and $\pip\pim$ samples for (a) \Bzb and (b) \Bz candidates. Only candidates in the three purest NN bins are included. Background has not been subtracted, and therefore some contribution from $\Bsb \to \Dstarz\Kp\pim$ decays is expected at low $m(D\Kp)$ (\ie\ along the top right diagonal). |
 | \small Dalitz plots for candidates in the \B candidate mass signal region in the $\D\to\Kp\Km$ and $\pip\pim$ samples for (a) \Bzb and (b) \Bz candidates. Only candidates in the three purest NN bins are included. Background has not been subtracted, and therefore some contribution from $\Bsb \to \Dstarz\Kp\pim$ decays is expected at low $m(D\Kp)$ (\ie\ along the top right diagonal). |
 | \small Projections of the $D\to\Kp\Km$ and $\pip\pim$ samples and the fit result onto (a,b)~$m(\D\pimp)$, (c,d)~$m(\Kpm\pimp)$ and (e,f)~$m(\D\Kpm)$ for (a,c,e)~\Bzb and (b,d,f)~\Bz candidates. The data and the fit results in each NN output bin have been weighted according to ${\cal S}/({\cal S}+{\cal B})$ and combined. The components are described in the legend. |
 | \small Projections of the $D\to\Kp\Km$ and $\pip\pim$ samples and the fit result onto (a,b)~$m(\D\pimp)$, (c,d)~$m(\Kpm\pimp)$ and (e,f)~$m(\D\Kpm)$ for (a,c,e)~\Bzb and (b,d,f)~\Bz candidates. The data and the fit results in each NN output bin have been weighted according to ${\cal S}/({\cal S}+{\cal B})$ and combined. The components are described in the legend. |
 | \small Results of the fit to $\D\Kp\pim$, $\D\to\pip\pim$ candidates shown separately in the five bins of the neural network output variable. The bins are shown, from (a)-(e), in order of increasing ${\cal S}/{\cal B}$. The components are as indicated in the legend. The vertical dotted lines in (a) show the signal window used for the fit to the Dalitz plot. |
 | \small Projections of the $D\to\Kp\Km$ and $\pip\pim$ samples and the fit result onto (a,b)~$m(\D\pimp)$, (c,d)~$m(\Kpm\pimp)$ and (e,f)~$m(\D\Kpm)$ for (a,c,e)~\Bzb and (b,d,f)~\Bz candidates. The data and the fit results in each NN output bin have been weighted according to ${\cal S}/({\cal S}+{\cal B})$ and combined. The components are described in the legend. |
 | \small Projections of the $D\to\Kp\Km$ and $\pip\pim$ samples and the fit result onto (a,b)~$m(\D\pimp)$, (c,d)~$m(\Kpm\pimp)$ and (e,f)~$m(\D\Kpm)$ for (a,c,e)~\Bzb and (b,d,f)~\Bz candidates. The data and the fit results in each NN output bin have been weighted according to ${\cal S}/({\cal S}+{\cal B})$ and combined. The components are described in the legend. |
 | \small Projections of the $D\to\Kp\Km$ and $\pip\pim$ samples and the fit result onto (a,b)~$m(\D\pimp)$, (c,d)~$m(\Kpm\pimp)$ and (e,f)~$m(\D\Kpm)$ for (a,c,e)~\Bzb and (b,d,f)~\Bz candidates. The data and the fit results in each NN output bin have been weighted according to ${\cal S}/({\cal S}+{\cal B})$ and combined. The components are described in the legend. |
 | \small Projections of the $D\to\Kp\Km$ and $\pip\pim$ samples and the fit result onto (a,b)~$m(\D\pimp)$, (c,d)~$m(\Kpm\pimp)$ and (e,f)~$m(\D\Kpm)$ for (a,c,e)~\Bzb and (b,d,f)~\Bz candidates. The data and the fit results in each NN output bin have been weighted according to ${\cal S}/({\cal S}+{\cal B})$ and combined. The components are described in the legend. |
 | \small Projections of the $D\to\Kp\Km$ and $\pip\pim$ samples and the fit result onto (a,b) $m(\D\pimp)$ and (c,d) $m(\D\Kpm)$ for (a,c) \Bzb and (b,d) \Bz candidates. The data and the fit results in each NN output bin have been weighted according to ${\cal S}/({\cal S}+{\cal B})$ and combined. The components are described in the legend. The projections onto $m(\Kpm\pimp)$ are given in Fig.~\ref{fig:CPDP-proj}. |
 | \small Projections of the $D\to\Kp\Km$ and $\pip\pim$ samples and the fit result onto (a,b)~$m(\D\pimp)$, (c,d)~$m(\Kpm\pimp)$ and (e,f)~$m(\D\Kpm)$ for (a,c,e)~\Bzb and (b,d,f)~\Bz candidates. The data and the fit results in each NN output bin have been weighted according to ${\cal S}/({\cal S}+{\cal B})$ and combined. The components are described in the legend. |
 | \small Projections of the $D\to\Kp\Km$ and $\pip\pim$ samples and the fit result onto (a,b) $m(\D\pimp)$ and (c,d) $m(\D\Kpm)$ for (a,c) \Bzb and (b,d) \Bz candidates. The data and the fit results in each NN output bin have been weighted according to ${\cal S}/({\cal S}+{\cal B})$ and combined. The components are described in the legend. The projections onto $m(\Kpm\pimp)$ are given in Fig.~\ref{fig:CPDP-proj}. |
 | \small Contours at $68\,\%$ CL for the (blue) $(x_+,y_+)$ and (red) $(x_-,y_-)$ parameters associated with the $\Bz \to D\Kstar(892)^0$ decay, with statistical uncertainties only. The central values are marked by a circle and a cross, respectively. |
 | \small Contours at $68\,\%$ CL for the (blue) $(x_+,y_+)$ and (red) $(x_-,y_-)$ parameters associated with the $\Bz \to D\Kstar(892)^0$ decay, with statistical uncertainties only. The central values are marked by a circle and a cross, respectively. |
 | \small Results of likelihood scans for (a) $\gamma$, (b) $r_B$ and (c) $\delta_B$. |
 | \small Results of likelihood scans for (a) $\gamma$, (b) $r_B$ and (c) $\delta_B$. |
 | \small Results of likelihood scans for (a) $\gamma$, (b) $r_B$ and (c) $\delta_B$. |
 | \small Confidence level contours for (a) $\gamma$ and $r_B$, (b) $\gamma$ and $\delta_B$ and (c) $r_B$ and $\delta_B$. The shaded regions are allowed at $68\,\%$ CL. |
 | \small Confidence level contours for (a) $\gamma$ and $r_B$, (b) $\gamma$ and $\delta_B$ and (c) $r_B$ and $\delta_B$. The shaded regions are allowed at $68\,\%$ CL. |
 | \small Confidence level contours for (a) $\gamma$ and $r_B$, (b) $\gamma$ and $\delta_B$ and (c) $r_B$ and $\delta_B$. The shaded regions are allowed at $68\,\%$ CL. |
 | \small Distributions of (a) $\kappa$, (b) $\bar{R}_B$ and (c) $\Delta \bar{\delta}_B$, obtained as described in the text. |
 | \small Distributions of (a) $\kappa$, (b) $\bar{R}_B$ and (c) $\Delta \bar{\delta}_B$, obtained as described in the text. |
 | \small Distributions of (a) $\kappa$, (b) $\bar{R}_B$ and (c) $\Delta \bar{\delta}_B$, obtained as described in the text. |