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First observation and amplitude analysis of the $B^{-}\to D^{+}K^{-}\pi^{-}$ decay

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Abstract

The $B^{-}\to D^{+}K^{-}\pi^{-}$ decay is observed in a data sample corresponding to $3.0 \rm{fb}^{-1}$ of $pp$ collision data recorded by the LHCb experiment during 2011 and 2012. Its branching fraction is measured to be ${\cal B}(B^{-}\to D^{+}K^{-}\pi^{-}) = (7.31 \pm 0.19 \pm 0.22 \pm 0.39) \times 10^{-5}$ where the uncertainties are statistical, systematic and from the branching fraction of the normalisation channel $B^{-}\to D^{+}\pi^{-}\pi^{-}$, respectively. An amplitude analysis of the resonant structure of the $B^{-}\to D^{+}K^{-}\pi^{-}$ decay is used to measure the contributions from quasi-two-body $B^{-}\to D_{0}^{*}(2400)^{0}K^{-}$, $B^{-}\to D_{2}^{*}(2460)^{0}K^{-}$, and $B^{-}\to D_{J}^{*}(2760)^{0}K^{-}$ decays, as well as from nonresonant sources. The $D_{J}^{*}(2760)^{0}$ resonance is determined to have spin 1.

Figures and captions

Results of the fit to the $ B ^- \rightarrow D ^+ \pi ^- \pi ^- $ candidate invariant mass distribution for the (left) TOS and (right) TIS-only subsamples. Data points are shown in black, the full fitted model as solid blue lines and the components as shown in the legend.

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Results of the fit to the $ B ^- \rightarrow D ^+ K ^- \pi ^- $ candidate invariant mass distribution for the (left) TOS and (right) TIS-only subsamples. Data points are shown in black, the full fitted model as solid blue lines and the components as shown in the legend.

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Signal efficiency across the SDP for (left) TOS and (right) TIS-only $ B ^- \rightarrow D ^+ K ^- \pi ^- $ decays. The relative uncertainty at each point is typically $5\,\%$.

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The first seven Legendre-polynomial weighted moments for background-subtracted and efficiency-corrected $ B ^- \rightarrow D ^+ K ^- \pi ^- $ data (black points) as a function of $m( D ^+ \pi ^- )$ in the range $2.0$--$3.0\mathrm{\,GeV} $. Candidates from both TOS and TIS-only subsamples are included. The blue line shows the result of the DP fit described in Sec. 7.

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Distribution of $ B ^- \rightarrow D ^+ K ^- \pi ^- $ candidates in the signal region over (left) the DP and (right) the SDP. Candidates from both TOS and TIS-only subsamples are included.

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Square Dalitz plot distributions used in the Dalitz plot fit for (top) combinatorial background, (middle) $ B ^- \rightarrow D^{(*)+}\pi ^- \pi ^- $ decays and (bottom) $ B ^- \rightarrow D ^+_ s K ^- \pi ^- $ decays. Candidates the TOS (TIS-only) subsamples are shown in the left (right) column.

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Differences between the data SDP distribution and the fit model across the SDP, in terms of the per-bin pull.

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Projections of the data and amplitude fit onto (a) $m(D\pi)$, (c) $m(DK)$ and (e) $m(K\pi)$, with the same projections shown in (b), (d) and (f) with a logarithmic $y$-axis scale. Components are described in the legend.

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Projections of the data and amplitude fit onto $m(D\pi)$ in (a) the threshold region, (b) the $D^*_2(2460)^0$ region and (c) the $D^*_1(2760)^0$ region. Components are as shown in Fig. 8.

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Projections of the data and amplitude fit onto the cosine of the helicity angle for the $D\pi$ system in (a) the threshold region, (b) the $D^*_2(2460)^0$ region and (c) the $D^*_1(2760)^0$ region. Components are as shown in Fig. 8.

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Tables and captions

Measured properties of neutral $D^{**}$ states. Where more than one uncertainty is given, the first is statistical and the others systematic.

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Yields of the various components in the fit to $ B ^- \rightarrow D ^+ \pi ^- \pi ^- $ candidate invariant mass distribution.

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Yields of the various components in the fit to $ B ^- \rightarrow D ^+ K ^- \pi ^- $ candidate invariant mass distribution.

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Relative systematic uncertainties on the measurement of the ratio of branching fractions for $ B ^- \rightarrow D ^+ K ^- \pi ^- $ and $ B ^- \rightarrow D ^+ \pi ^- \pi ^- $ decays.

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Signal contributions to the fit model, where parameters and uncertainties are taken from Ref. [9]. States labelled with subscript $v$ are virtual contributions.

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Masses and widths determined in the fit to data, with statistical uncertainties only.

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Complex coefficients and fit fractions determined from the Dalitz plot fit. Uncertainties are statistical only.

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Experimental systematic uncertainties on the fit fractions and complex amplitudes.

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Model uncertainties on the fit fractions and complex amplitudes.

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Breakdown of experimental systematic uncertainties on the fit fractions (%) and masses $(\mathrm{MeV} )$ and widths $(\mathrm{MeV} )$.

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Breakdown of model uncertainties on the fit fractions (%) and masses $(\mathrm{MeV} )$ and widths $(\mathrm{MeV} )$.

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Results for the complex amplitudes and their uncertainties. The three quoted errors are statistical, experimental systematic and model uncertainties, respectively.

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Results for the complex amplitudes and their uncertainties. The three quoted errors are statistical, experimental systematic and model uncertainties, respectively.

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Results for the fit fractions and their uncertainties (%). The three quoted errors are statistical, experimental systematic and model uncertainties, respectively.

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Results for the product branching fractions ${\cal B}( B ^- \rightarrow R K ^- ) \times {\cal B}(R \rightarrow D ^+ \pi ^- )$ ($10^{-6}$). The four quoted errors are statistical, experimental systematic, model and inclusive branching fraction uncertainties, respectively.

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Results for the fit fractions and complex coefficients for the secondary minima with $2{\rm NLL}$ values 2.8 and 3.3 units greater than that of the global minimum of the NLL function.

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Interference fit fractions (%) and statistical uncertainties. The amplitudes are: ($A_0$) $D^*_v(2007)^0$, ($A_1$) $D^*_0(2400)^0$, ($A_2$) $D^*_2(2460)^0$, ($A_3$) $D^*_1(2760)^0$, ($A_4$) $B^*_v$, ($A_5$) nonresonant S-wave, ($A_6$) nonresonant P-wave. The diagonal elements are the same as the conventional fit fractions.

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Experimental systematic uncertainies on the interference fit fractions (%). The amplitudes are: ($A_0$) $D^*_v(2007)^0$, ($A_1$) $D^*_0(2400)^0$, ($A_2$) $D^*_2(2460)^0$, ($A_3$) $D^*_1(2760)^0$, ($A_4$) $B^*_v$, ($A_5$) nonresonant S-wave, ($A_6$) nonresonant P-wave. The diagonal elements are the same as the conventional fit fractions.

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Model systematic uncertainies on the interference fit fractions (%). The amplitudes are: ($A_0$) $D^*_v(2007)^0$, ($A_1$) $D^*_0(2400)^0$, ($A_2$) $D^*_2(2460)^0$, ($A_3$) $D^*_1(2760)^0$, ($A_4$) $B^*_v$, ($A_5$) nonresonant S-wave, ($A_6$) nonresonant P-wave. The diagonal elements are the same as the conventional fit fractions.

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Supplementary Material [file]

Supplementary material full pdf

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Created on 09 December 2018.Citation count from INSPIRE on 18 December 2018.