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A precise measurement of the $B^0$ meson oscillation frequency

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Abstract

The oscillation frequency, $\Delta m_d$, of $B^0$ mesons is measured using semileptonic decays with a $D^-$ or $D^{*-}$ meson in the final state, in a data sample of $pp$ collisions collected by the LHCb detector corresponding to an integrated luminosity of 3.0$ fb^{-1}$. A combination of the two decay modes gives $\Delta m_d = (505.0 \pm 2.1 \pm 1.0) \rm ns^{-1}$, where the first uncertainty is statistical and the second is systematic. This is the most precise single measurement of this parameter. It is compatible with the current world average and has similar precision.

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Distribution of $m_{K\pi\pi}$ for the $ B ^0 \rightarrow D ^- \mu ^+ \nu _\mu X$ candidates in (left) 2011 and (right) 2012 data. Projections of the fit function are superimposed (blue continuous line) for the full PDF and its components: (red dashed line) signal $ D ^-$ from $ B ^0$ or $ B ^+$ decays and (filled yellow area) combinatorial background.

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Distributions of (top) $m_{K\pi}$ and (bottom) $\delta m$ for $ B ^0 \rightarrow D ^{*-} \mu ^+ \nu _\mu X$ candidates in (left) 2011 and (right) 2012 data. Projections of the fit function are superimposed for (blue continuous line) the full PDF and its components: (red dashed line) signal $ D ^{*-}$ from $ B ^0$ or $ B ^+$ decays, (black dashed-dotted line) $\overline{ D }{} {}^0$ from $ B $ and (filled yellow area) combinatorial backgrounds.

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Fits to the output of the $ B ^+$ veto BDT for (top four plots) $ B ^0 \rightarrow D ^- \mu ^+ \nu _\mu X$ and (bottom four plots) $ B ^0 \rightarrow D ^{*-} \mu ^+ \nu _\mu X$ in 2012 data, for each tagging category. The filled red histogram, the dashed green line, and the continuous blue line correspond to background, signal, and total templates, respectively. The average mistag fraction per category increases when going from (a) to (d), and (e) to (h).

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Decay time distributions for (left) $ B ^0 \rightarrow D ^- \mu ^+ \nu _\mu X$ and (right) $ B ^0 \rightarrow D ^{*-} \mu ^+ \nu _\mu X$ in the category with lowest mistag in 2012 data.

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Mixing asymmetry projections in the four tagging categories for (top plots) $ B ^0 \rightarrow D ^- \mu ^+ \nu _\mu X$ and (bottom plots) $ B ^0 \rightarrow D ^{*-} \mu ^+ \nu _\mu X$ for 2011 data. The average mistag per category increases when going from (a) to (d), and from (e) to (h).

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Mixing asymmetry projections in the four tagging categories for (top plots) $ B ^0 \rightarrow D ^- \mu ^+ \nu _\mu X$ and (bottom plots) $ B ^0 \rightarrow D ^{*-} \mu ^+ \nu _\mu X$ for 2012 data. The average mistag per category increases when going from (a) to (d), and from (e) to (h).

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The $k$-factor distribution and the average $k$-factor (black points) as a function of the visible mass of the $ B$ candidate, in samples of simulated (top) $ B ^0 \rightarrow D ^- \mu ^+ \nu _\mu X$ and (bottom) $ B ^0 \rightarrow D ^{*-} \mu ^+ \nu _\mu X$ decays. Polynomial fits to the average $k$-factor are also shown as a solid (red) line.

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Tables and captions

Results for $\Delta m_{ d }$ measured in each mode for 2011 and 2012 data separately, for the total sample, and for the combination of the two modes. The quoted uncertainties for the separate samples are statistical only. For the total samples and the combination, they refer to statistical and total systematic uncertainties, respectively.

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Sources of systematic uncertainties on $\Delta m_{ d }$ , separated into those that are correlated and uncorrelated between the two decay channels $ B ^0 \rightarrow D ^- \mu ^+ \nu _\mu X$ and $ B ^0 \rightarrow D ^{*-} \mu ^+ \nu _\mu X$ .

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Created on 19 October 2019.