Measurement of the relative $B^{-} \rightarrow D^{0} / D^{*0} / D^{**0} \mu^{-} \overline{\nu}_\mu$ branching fractions using $B^{-}$ mesons from $\overline{B}{}_{s2}^{*0}$ decays

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Abstract

The decay of the narrow resonance $\overline{B}{}_{s2}^{*0}\!\rightarrow B^- K^+$ can be used to determine the $B^-$ momentum in partially reconstructed decays without any assumptions on the decay products of the $B^-$ meson. This technique is employed for the first time to distinguish contributions from $D^0$, $D^{*0}$, and higher-mass charmed states ($D^{**0}$) in semileptonic $B^-$ decays by using the missing-mass distribution. The measurement is performed using a data sample corresponding to an integrated luminosity of 3.0 fb${}^{-1}$ collected with the LHCb detector in $pp$ collisions at center-of-mass energies of 7 and 8 TeV. The resulting branching fractions relative to the inclusive $B^- \!\rightarrow D^0 X \mu^- \overline{\nu}_\mu$ are $f_{D^0} = \mathcal{B}( B^- \rightarrow D^0\mu^-\overline{\nu}_\mu )/\mathcal{B}( B^- \rightarrow D^0 X \mu^- \overline{\nu}_\mu ) = 0.25 \pm 0.06$, $f_{D^{**0}} = \mathcal{B}( B^- \rightarrow ( D^{**0} \rightarrow D^0 X)\mu^-\overline{\nu}_\mu )/\mathcal{B}( B^- \rightarrow D^0 X \mu^- \overline{\nu}_\mu ) = 0.21 \pm 0.07$, with $f_{D^{*0}} = 1 - f_{D^0} - f_{D^{**0}}$ making up the remainder.

Figures and captions

 Decay topology for the ${ B ^- \!\rightarrow D ^0 X \mu ^- \overline{\nu } _\mu }$ signal decays. A $\overline{ B }{} {}_{s2}^{*0}$ meson decays at the primary vertex position, producing a $B ^-$ meson and a $K ^+$ meson. The angle in the laboratory frame between the $K ^+$ and $B ^-$ directions is defined as $\theta$. The $B ^-$ meson then decays semileptonically to a $D ^0$ meson and a muon, accompanied by an undetected neutrino and potentially other particles, referred to collectively as $X$. Fig1.pdf [47 KiB] HiDef png [41 KiB] Thumbnail [7 KiB] *.C file Distribution of the minimum mass difference for $B ^- K ^+$ (\text{OS} $K$ ) candidates and $B ^- K ^-$ (\text{SS} $K$ ) candidates. For \text{OS} $K$ combinations, peaks for the $\overline{ B }{} {}_{s2}^{*0}$ and $\overline{ B }{} {}_{s1}^0$ states are visible. The contribution of decays in which a kaon from a $b$-hadron decay is chosen as prompt produces the sharp increase near zero. The \text{SS} $K$ sample is used for background estimation. Fig2.pdf [24 KiB] HiDef png [199 KiB] Thumbnail [81 KiB] *.C file The difference $\Delta m_{\mathrm{miss}}^2$ between the reconstructed missing mass squared and the corresponding true values for the ${ B ^- \!\rightarrow D ^0 \mu ^- \overline{\nu } _\mu }$ channel. The contributions from events in which there is only one physical solution, in which there are two and the chosen lower energy solution is correct, or in which the incorrect solution is chosen are shown. Fig3.pdf [17 KiB] HiDef png [257 KiB] Thumbnail [84 KiB] *.C file The missing mass shapes from simulation for the signal samples are shown. The bands around the points represent the systematic uncertainties on the form factors in the simulation and the branching fractions for different contributions to the $D^{**0}$ channel. Fig4.pdf [27 KiB] HiDef png [357 KiB] Thumbnail [105 KiB] *.C file Missing-mass distribution for data and estimated background contributions in the (left) same-sign kaon sample and (right) opposite-sign sample. The other background decays include contributions from misreconstructed backgrounds, and semileptonic decays of $\overline{ B }{} {}^0_ s$ and $\Lambda ^0_ b$ mesons. The remainder of the \text{SS} $K$ sample not from $\overline{ B }{} {}^0$ or other background decays is used to define the background contribution from $B ^-$ semileptonic decays. This is then extrapolated to the \text{OS} $K$ sample, where the remainder is composed of signal. The background distributions are stacked. Fig5a.pdf [27 KiB] HiDef png [259 KiB] Thumbnail [75 KiB] *.C file Fig5b.pdf [32 KiB] HiDef png [487 KiB] Thumbnail [106 KiB] *.C file Distribution of the minimum mass difference for (left) $B ^- K ^+$ opposite-sign candidates and (right) $B ^- K ^-$ same-sign candidates. All candidates are compared to the estimated background from other sources besides decays of a $B ^-$ or $\overline{ B }{} {}^0$ meson to $D ^0 X\mu ^- \overline{\nu } _\mu$. The remaining non-peaking part of the distributions is made up of $B ^-$ and $\overline{ B }{} {}^0$ semileptonic decays that do not come from an excited $\overline{ B }{} {}^0_ s$ state. Fig6a.pdf [30 KiB] HiDef png [268 KiB] Thumbnail [80 KiB] *.C file Fig6b.pdf [27 KiB] HiDef png [232 KiB] Thumbnail [75 KiB] *.C file Fits to the opposite-sign and same-sign kaon $m_{\mathrm{min}} - m_B - m_K$ distributions with non- $B ^-$ and $\overline{ B }{} {}^0$ backgrounds subtracted, and the resulting estimations of the non- $\overline{ B }{} {}_{s2}^{*0}$ and $\overline{ B }{} {}_{s1}^0$ contributions. The fits are done separately in three bins of the prompt kaon $p_{\mathrm{ T}}$ : (top left) $0.5 < p_{\mathrm{ T}} < 1.25\mathrm{\,GeV}$, (top right) $1.25 < p_{\mathrm{ T}} < 2\mathrm{\,GeV}$, and (bottom) $p_{\mathrm{ T}} > 2\mathrm{\,GeV}$. The dashed line shows the background estimation using a fit to the full \text{OS} $K$ distribution with signal templates from simulation and a fifth-order polynomial for the background. The points estimate the background using a linear extrapolation of the \text{OS} $K$ to \text{SS} $K$ ratio in the region $m_{\mathrm{min}} - m_B - m_K > 100\mathrm{\,MeV}$. Fig7a.pdf [20 KiB] HiDef png [256 KiB] Thumbnail [77 KiB] *.C file Fig7b.pdf [20 KiB] HiDef png [254 KiB] Thumbnail [75 KiB] *.C file Fig7c.pdf [20 KiB] HiDef png [281 KiB] Thumbnail [81 KiB] *.C file Template fit to the missing-mass distribution. The nuisance parameters used to quantify the template statistical uncertainties are set to their nominal values. The full distribution (left) is shown, comparing the background to the sum of the signal templates. The background-subtracted distribution (right) is compared to the breakdown of the signal components. The statistical uncertainty in the background templates is represented as the shaded band around the fit. In the pull distribution, the statistical uncertainty of the background templates is added to the statistical uncertainty of the data points. Fig8a.pdf [38 KiB] HiDef png [476 KiB] Thumbnail [141 KiB] *.C file Fig8b.pdf [32 KiB] HiDef png [472 KiB] Thumbnail [144 KiB] *.C file Contours for 68.3% and 95.5% confidence intervals for the fractions of ${ B ^- \!\rightarrow D ^0 X \mu ^- \overline{\nu } _\mu }$ into the exclusive ${ B ^- \!\rightarrow D ^0 \mu ^- \overline{\nu } _\mu }$ channel and the higher excited ${ B ^- \!\rightarrow \left( { D^{**0} \!\rightarrow D ^0 X} \right)\mu ^- \overline{\nu } _\mu }$ channels. The alternate fit using different branching fractions for different $D^{**0}$ states is not included. Fig9.pdf [14 KiB] HiDef png [168 KiB] Thumbnail [56 KiB] *.C file Animated gif made out of all figures. PAPER-2018-024.gif Thumbnail

Tables and captions

 Estimates of the breakdown of the total uncertainty. All estimates are done by repeating the fit with systematic nuisance parameters fixed to their best fit values. The statistical uncertainty of the \text{OS} $K$ sample is estimated from the uncertainty on the signal fractions with the template statistical nuisance parameters fixed to their best fit values. The template statistical uncertainty is added in by allowing only the statistical nuisance parameters to vary. The effect of each floating systematic uncertainty is estimated by refitting with its systematic nuisance parameter shifted by the uncertainty found by the best fit and taking the difference in the signal fractions as the uncertainty. The total uncertainty is taken from the best fit, with the fixed systematic uncertainties added in quadrature. Table_1.pdf [56 KiB] HiDef png [108 KiB] Thumbnail [16 KiB] tex code

Supplementary Material [file]

 Supplementary material full pdf Supple[..].pdf [575 KiB] his ZIP file contains supplemetary material for the publication LHCb-PAPER-2018-024. The files are: Supplementary.pdf : An overview of the extra figures *.pdf, *.png, *.eps : The figures in various formats Fig1-S.pdf [15 KiB] HiDef png [232 KiB] Thumbnail [71 KiB] *C file Fig2a-S.pdf [45 KiB] HiDef png [454 KiB] Thumbnail [98 KiB] *C file Fig2b-S.pdf [46 KiB] HiDef png [260 KiB] Thumbnail [76 KiB] *C file Fig2c-S.pdf [45 KiB] HiDef png [454 KiB] Thumbnail [100 KiB] *C file Fig2d-S.pdf [46 KiB] HiDef png [269 KiB] Thumbnail [78 KiB] *C file Fig3a-S.pdf [29 KiB] HiDef png [480 KiB] Thumbnail [106 KiB] *C file Fig3b-S.pdf [43 KiB] HiDef png [389 KiB] Thumbnail [100 KiB] *C file Fig3c-S.pdf [28 KiB] HiDef png [427 KiB] Thumbnail [97 KiB] *C file Fig3d-S.pdf [43 KiB] HiDef png [370 KiB] Thumbnail [94 KiB] *C file Fig4a-S.pdf [34 KiB] HiDef png [253 KiB] Thumbnail [68 KiB] *C file Fig4b-S.pdf [82 KiB] HiDef png [361 KiB] Thumbnail [91 KiB] *C file Fig4c-S.pdf [57 KiB] HiDef png [352 KiB] Thumbnail [89 KiB] *C file

Created on 16 February 2019.Citation count from INSPIRE on 22 February 2019.