cern.ch

Amplitude analysis of $B^0 \rightarrow \bar{D}^0 K^+ \pi^-$ decays

[to restricted-access page]

Abstract

The Dalitz plot distribution of $B^0 \rightarrow \bar{D}^0 K^+ \pi^-$ decays is studied using a data sample corresponding to $3.0\rm{fb}^{-1}$ of $pp$ collision data recorded by the LHCb experiment during 2011 and 2012. The data are described by an amplitude model that contains contributions from intermediate $K^*(892)^0$, $K^*(1410)^0$, $K^*_2(1430)^0$ and $D^*_2(2460)^-$ resonances. The model also contains components to describe broad structures, including the $K^*_0(1430)^0$ and $D^*_0(2400)^-$ resonances, in the $K\pi$ S-wave and the $D\pi$ S- and P-waves. The masses and widths of the $D^*_0(2400)^-$ and $D^*_2(2460)^-$ resonances are measured, as are the complex amplitudes and fit fractions for all components included in the amplitude model. The model obtained will be an integral part of a future determination of the angle $\gamma$ of the CKM quark mixing matrix using $B^0 \rightarrow D K^+ \pi^-$ decays.

Figures and captions

Decay diagrams for the quasi-two-body contributions to $ B ^0 \rightarrow D K ^+ \pi ^- $ from (a) $ B ^0 \rightarrow D K ^* (892)^0$ and (b) $ B ^0 \rightarrow D^{*}_{2}(2460)^{-} K ^+ $ decays.

Fig1a.pdf [14 KiB]
HiDef png [41 KiB]
Thumbnail [9 KiB]
*.C file
Fig1a.pdf
Fig1b.pdf [14 KiB]
HiDef png [41 KiB]
Thumbnail [9 KiB] *.C file
Fig1b.pdf

Results of the fit to the $ B $ candidate invariant mass distribution with (a) linear and (b) logarithmic $y$-axis scales. The components are as described in the legend.

Fig2a.pdf [32 KiB]
HiDef png [327 KiB]
Thumbnail [99 KiB]
*.C file
Fig2a.pdf
Fig2b.pdf [30 KiB]
HiDef png [299 KiB]
Thumbnail [88 KiB] *.C file
Fig2b.pdf

Distribution of $ B ^0 \rightarrow \overline{ D }{} {}^0 K ^+ \pi ^- $ candidates in the signal region over (a) the Dalitz plot and (b) the square Dalitz plot. The definition of the square Dalitz plot is given in Sec. ???.

Fig3a.pdf [49 KiB]
HiDef png [153 KiB]
Thumbnail [36 KiB]
*.C file
Fig3a.pdf
Fig3b.pdf [49 KiB]
HiDef png [174 KiB]
Thumbnail [46 KiB] *.C file
Fig3b.pdf

Efficiency variation as a function of SDP position for candidates triggered by (a) signal decay products and (b) by the rest of the event. The vertical white stripe is due to the $ D ^*$ veto and the curved white band is due to the $\overline{ D }{} {}^0$ veto.

Fig4a.pdf [210 KiB]
HiDef png [1 MiB]
Thumbnail [183 KiB]
*.C file
Fig4a.pdf
Fig4b.pdf [209 KiB]
HiDef png [1 MiB]
Thumbnail [171 KiB] *.C file
Fig4b.pdf

SDP distributions of the background contributions from (a) combinatorial background and (b) $ B ^0 \rightarrow \overline{ D }{} {}^{(*)0} \pi ^+ \pi ^- $ decays.

Fig5a.pdf [19 KiB]
HiDef png [196 KiB]
Thumbnail [82 KiB]
*.C file
Fig5a.pdf
Fig5b.pdf [30 KiB]
HiDef png [261 KiB]
Thumbnail [98 KiB] *.C file
Fig5b.pdf

Projections of the data and amplitude fit results onto (a) $m(\overline{ D }{} {}^0 \pi ^- )$, (c) $m( K ^+ \pi ^- )$ and (e) $m(\overline{ D }{} {}^0 K ^+ )$, with the same projections shown in (b), (d) and (f) with a logarithmic $y$-axis scale. Components are described in the legend.

Fig6a.pdf [32 KiB]
HiDef png [272 KiB]
Thumbnail [72 KiB]
*.C file
Fig6a.pdf
Fig6b.pdf [24 KiB]
HiDef png [516 KiB]
Thumbnail [120 KiB] *.C file
Fig6b.pdf
Fig6c.pdf [31 KiB]
HiDef png [247 KiB]
Thumbnail [69 KiB] *.C file
Fig6c.pdf
Fig6d.pdf [23 KiB]
HiDef png [532 KiB]
Thumbnail [117 KiB] *.C file
Fig6d.pdf
Fig6e.pdf [32 KiB]
HiDef png [314 KiB]
Thumbnail [87 KiB] *.C file
Fig6e.pdf
Fig6f.pdf [24 KiB]
HiDef png [543 KiB]
Thumbnail [124 KiB] *.C file
Fig6f.pdf
Fig6leg.pdf [12 KiB]
HiDef png [60 KiB]
Thumbnail [18 KiB] *.C file
Fig6leg.pdf

Projections of the data and amplitude fit results onto (a) $m(\overline{ D }{} {}^0 \pi ^- )$ in the $D^*_2(2460)^-$ region and (b) the low $m( K ^+ \pi ^- )$ region. Components are as shown in Fig. ???.

Fig7a.pdf [26 KiB]
HiDef png [317 KiB]
Thumbnail [94 KiB]
*.C file
Fig7a.pdf
Fig7b.pdf [32 KiB]
HiDef png [262 KiB]
Thumbnail [75 KiB] *.C file
Fig7b.pdf

Projections of the data and amplitude fit results onto $\cos \theta(\overline{ D }{} {}^0 \pi ^- )$ in the mass ranges (a) $2.04 < m(\overline{ D }{} {}^0 \pi ^- ) < 2.35 \mathrm{\,GeV} $ and (b) $2.35 < m(\overline{ D }{} {}^0 \pi ^- ) < 2.55 \mathrm{\,GeV} $. Components are as shown in Fig. ???.

Fig8a.pdf [35 KiB]
HiDef png [322 KiB]
Thumbnail [91 KiB]
*.C file
Fig8a.pdf
Fig8b.pdf [33 KiB]
HiDef png [313 KiB]
Thumbnail [95 KiB] *.C file
Fig8b.pdf

Projections of the data and amplitude fit results onto $\cos \theta( K ^+ \pi ^- )$ in the mass ranges (a) $m( K ^+ \pi ^- ) < 0.8 \mathrm{\,GeV} $, (b) $0.8 < m( K ^+ \pi ^- ) < 1.0 \mathrm{\,GeV} $, (c) $1.0 < m( K ^+ \pi ^- ) < 1.3 \mathrm{\,GeV} $ and (d) $1.4 < m( K ^+ \pi ^- ) < 1.5 \mathrm{\,GeV} $. Components are as shown in Fig. ???.

Fig9a.pdf [31 KiB]
HiDef png [273 KiB]
Thumbnail [81 KiB]
*.C file
Fig9a.pdf
Fig9b.pdf [31 KiB]
HiDef png [259 KiB]
Thumbnail [81 KiB] *.C file
Fig9b.pdf
Fig9c.pdf [32 KiB]
HiDef png [256 KiB]
Thumbnail [72 KiB] *.C file
Fig9c.pdf
Fig9d.pdf [34 KiB]
HiDef png [278 KiB]
Thumbnail [82 KiB] *.C file
Fig9d.pdf

Background-subtracted and efficiency-corrected Legendre moments up to order 7 calculated as a function of $m(\overline{ D }{} {}^0 \pi ^- )$ for data (black data points) and the fit result (solid blue curve).

Fig10a.pdf [16 KiB]
HiDef png [170 KiB]
Thumbnail [67 KiB]
*.C file
Fig10a.pdf
Fig10b.pdf [16 KiB]
HiDef png [166 KiB]
Thumbnail [66 KiB] *.C file
Fig10b.pdf
Fig10c.pdf [16 KiB]
HiDef png [150 KiB]
Thumbnail [60 KiB] *.C file
Fig10c.pdf
Fig10d.pdf [16 KiB]
HiDef png [149 KiB]
Thumbnail [60 KiB] *.C file
Fig10d.pdf
Fig10e.pdf [16 KiB]
HiDef png [151 KiB]
Thumbnail [59 KiB] *.C file
Fig10e.pdf
Fig10f.pdf [16 KiB]
HiDef png [152 KiB]
Thumbnail [61 KiB] *.C file
Fig10f.pdf
Fig10g.pdf [16 KiB]
HiDef png [151 KiB]
Thumbnail [61 KiB] *.C file
Fig10g.pdf
Fig10h.pdf [16 KiB]
HiDef png [150 KiB]
Thumbnail [60 KiB] *.C file
Fig10h.pdf

Background-subtracted and efficiency-corrected Legendre moments up to order 7 calculated as a function of $m( K ^+ \pi ^- )$ for data (black data points) and the fit result (solid blue curve).

Fig11a.pdf [16 KiB]
HiDef png [158 KiB]
Thumbnail [59 KiB]
*.C file
Fig11a.pdf
Fig11b.pdf [16 KiB]
HiDef png [151 KiB]
Thumbnail [58 KiB] *.C file
Fig11b.pdf
Fig11c.pdf [16 KiB]
HiDef png [159 KiB]
Thumbnail [60 KiB] *.C file
Fig11c.pdf
Fig11d.pdf [16 KiB]
HiDef png [153 KiB]
Thumbnail [62 KiB] *.C file
Fig11d.pdf
Fig11e.pdf [16 KiB]
HiDef png [158 KiB]
Thumbnail [64 KiB] *.C file
Fig11e.pdf
Fig11f.pdf [16 KiB]
HiDef png [147 KiB]
Thumbnail [59 KiB] *.C file
Fig11f.pdf
Fig11g.pdf [16 KiB]
HiDef png [156 KiB]
Thumbnail [63 KiB] *.C file
Fig11g.pdf
Fig11h.pdf [17 KiB]
HiDef png [152 KiB]
Thumbnail [62 KiB] *.C file
Fig11h.pdf

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

Fig12.pdf [19 KiB]
HiDef png [137 KiB]
Thumbnail [50 KiB]
*.C file
Fig12.pdf

Animated gif made out of all figures.

PAPER-2015-017.gif
Thumbnail
thumbnail_PAPER-2015-017.gif

Tables and captions

Yields from the fit to the $\overline{ D }{} {}^0 K ^+ \pi ^- $ data sample. The full mass range is $5100$--$5900\mathrm{\,MeV} $ and the signal region is $5248.55$--$5309.05\mathrm{\,MeV} $.

Table_0.pdf [54 KiB]
HiDef png [88 KiB]
Thumbnail [15 KiB]
tex code
Table_0.pdf

Signal contributions to the fit model, where parameters and uncertainties are taken from Ref. \cite{PDG2014}. The models are described in Sec. ???.

Table_1.pdf [58 KiB]
HiDef png [79 KiB]
Thumbnail [11 KiB]
tex code
Table_1.pdf

Masses and widths $(\mathrm{MeV} )$ determined in the fit to data, with statistical uncertainties only.

Table_2.pdf [43 KiB]
HiDef png [49 KiB]
Thumbnail [7 KiB]
tex code
Table_2.pdf

Complex coefficients and fit fractions determined from the Dalitz plot fit. Uncertainties are statistical only. Note that the fit fractions, magnitudes and phases are derived quantities.

Table_3.pdf [50 KiB]
HiDef png [99 KiB]
Thumbnail [14 KiB]
tex code
Table_3.pdf

Experimental systematic uncertainties on the fit fractions (%) and masses and widths $(\mathrm{MeV} )$. Uncertainties given on the central values are statistical only.

Table_4.pdf [49 KiB]
HiDef png [101 KiB]
Thumbnail [14 KiB]
tex code
Table_4.pdf

Model uncertainties on the fit fractions (%) and masses and widths $(\mathrm{MeV} )$. Uncertainties given on the central values are statistical only.

Table_5.pdf [49 KiB]
HiDef png [93 KiB]
Thumbnail [13 KiB]
tex code
Table_5.pdf

Results for the complex amplitudes and their uncertainties presented (top) in terms of real and imaginary parts and (bottom) in terms and magnitudes and phases. The three quoted errors are statistical, experimental systematic and model uncertainties, respectively.

Table_6.pdf [48 KiB]
HiDef png [80 KiB]
Thumbnail [10 KiB]
tex code
Table_6.pdf

Results for the fit fractions and their uncertainties (%). The three quoted errors are statistical, experimental systematic and model uncertainties, respectively. Upper limits are given at 90 % (95 %) confidence level.

Table_7.pdf [47 KiB]
HiDef png [103 KiB]
Thumbnail [17 KiB]
tex code
Table_7.pdf

Results for the product branching fractions. The four quoted errors are statistical, experimental systematic, model and PDG uncertainties, respectively. Upper limits are given at 90 % (95 %) confidence level.

Table_8.pdf [48 KiB]
HiDef png [97 KiB]
Thumbnail [15 KiB]
tex code
Table_8.pdf

Results for the branching fractions. The four quoted errors are statistical, experimental systematic, model and PDG uncertainties, respectively. Upper limits are given at 90 % (95 %) confidence level.

Table_9.pdf [46 KiB]
HiDef png [63 KiB]
Thumbnail [9 KiB]
tex code
Table_9.pdf

Interference fit fractions (%) from the nominal DP fit. The amplitudes are all pairwise products involving: ($A_{0}$) $ K ^* (892)^{0}$, ($A_{1}$) $ K ^* (1410)^{0}$, ($A_{2}$) $ K ^*_{0}(1430)^{0}$, ($A_{3}$) LASS nonresonant, ($A_{4}$) $ K ^*_{2}(1430)^{0}$, ($A_{5}$) $D^{*}_{0}(2400)^{-}$, ($A_{6}$) $D^{*}_{2}(2460)^{-}$, ($A_{7}$) $D\pi$ S-wave (dabba), ($A_{8}$) $D\pi$ P-wave (EFF). The diagonal elements are the same as the conventional fit fractions.

Table_10.pdf [33 KiB]
HiDef png [45 KiB]
Thumbnail [7 KiB]
tex code
Table_10.pdf

Statistical uncertainties on the interference fit fractions (%). The amplitudes are all pairwise products involving: ($A_{0}$) $ K ^* (892)^{0}$, ($A_{1}$) $ K ^* (1410)^{0}$, ($A_{2}$) $ K ^*_{0}(1430)^{0}$, ($A_{3}$) LASS nonresonant, ($A_{4}$) $ K ^*_{2}(1430)^{0}$, ($A_{5}$) $D^{*}_{0}(2400)^{-}$, ($A_{6}$) $D^{*}_{2}(2460)^{-}$, ($A_{7}$) $D\pi$ S-wave (dabba), ($A_{8}$) $D\pi$ P-wave (EFF). The diagonal elements are the same as the conventional fit fractions.

Table_11.pdf [27 KiB]
HiDef png [67 KiB]
Thumbnail [10 KiB]
tex code
Table_11.pdf

Experimental systematic uncertainties on the interference fit fractions (%). The amplitudes are all pairwise products involving: ($A_{0}$) $ K ^* (892)^{0}$, ($A_{1}$) $ K ^* (1410)^{0}$, ($A_{2}$) $ K ^*_{0}(1430)^{0}$, ($A_{3}$) LASS nonresonant, ($A_{4}$) $ K ^*_{2}(1430)^{0}$, ($A_{5}$) $D^{*}_{0}(2400)^{-}$, ($A_{6}$) $D^{*}_{2}(2460)^{-}$, ($A_{7}$) $D\pi$ S-wave (dabba), ($A_{8}$) $D\pi$ P-wave (EFF). The diagonal elements are the same as the conventional fit fractions.

Table_12.pdf [27 KiB]
HiDef png [67 KiB]
Thumbnail [10 KiB]
tex code
Table_12.pdf

Model uncertainties on the interference fit fractions (%). The amplitudes are all pairwise products involving: ($A_{0}$) $ K ^* (892)^{0}$, ($A_{1}$) $ K ^* (1410)^{0}$, ($A_{2}$) $ K ^*_{0}(1430)^{0}$, ($A_{3}$) LASS nonresonant, ($A_{4}$) $ K ^*_{2}(1430)^{0}$, ($A_{5}$) $D^{*}_{0}(2400)^{-}$, ($A_{6}$) $D^{*}_{2}(2460)^{-}$, ($A_{7}$) $D\pi$ S-wave (dabba), ($A_{8}$) $D\pi$ P-wave (EFF). The diagonal elements are the same as the conventional fit fractions.

Table_13.pdf [27 KiB]
HiDef png [67 KiB]
Thumbnail [10 KiB]
tex code
Table_13.pdf

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