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Measurement of the branching fraction of the $B^{0}\rightarrow D_{s}^{+}\pi^{-}$ decay

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Abstract

A branching fraction measurement of the $B^{0}\rightarrow D_{s}^{+}\pi^{-}$ decay is presented using proton-proton collision data collected with the LHCb experiment, corresponding to an integrated luminosity of $5.0 $fb$^{-1}$. The branching fraction is found to be ${\mathcal{B}(B^{0}\rightarrow D_{s}^{+}\pi^{-}) = (19.4 \pm 1.8\pm 1.3 \pm 1.2)\times 10^{-6}}$, where the first uncertainty is statistical, the second systematic and the third is due to the uncertainty on the $B^0 \to D^{-}\pi^{+}$, $D_{s}^{+}\rightarrow K^{+}K^{-}\pi^{+}$ and $D^{-}\rightarrow K^{+}\pi^{-}\pi^{-}$ branching fractions. This is the most precise single measurement of this quantity to date. As this decay proceeds through a single amplitude involving a $b \to u$ charged-current transition, the result provides information on non-factorisable strong interaction effects and the magnitude of the Cabibbo-Kobayashi-Maskawa matrix element $V_{ub}$. Additionally, the collision energy dependence of the hadronisation-fraction ratio $f_s/f_d$ is measured through $\bar{B}{}_{s}^{0}\rightarrow D_{s}^{+}\pi^{-}$ and $B^0 \to D^{-}\pi^{+}$ decays.

Figures and captions

Tree diagram of the $ B ^0 \rightarrow D ^+_ s \pi ^- $ decay, in which a $ B ^0$ meson decays through the weak interaction to a $ D ^+_ s $ meson and a charged pion. This diagram represents the only (leading order) process contributing to this decay. Strong interaction between the $ D ^+_ s $ meson and the pion lead to a non-factorisable contribution to the decay amplitude.

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Bd2DsPi_diagram.png

The invariant mass distributions of normalisation $ B ^0 \rightarrow D ^- \pi ^+ $ candidates, for (left) Run 1 and (right) Run 2 data samples. Overlaid are the fit projections along with the signal and background contributions.

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mass_Bd2DPi_BeautyMass_kpipi_both_run1_log_run1run2_PaperDraft_Paper.pdf
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mass_Bd2DPi_BeautyMass_kpipi_both_20152016_log_run1run2_PaperDraft_PaperNoLeg.pdf

The (top) $ D ^+_ s \pi ^- $ and (bottom) $ K ^+ K ^- \pi ^+ $ invariant mass distributions of signal $ B ^0 \rightarrow D ^+_ s \pi ^- $ candidates, for (left) Run 1 and (right) Run 2 data samples. Overlaid are the fit projections along with the signal and background contributions.

mass_B[..].pdf [71 KiB]
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mass_Bs2DsPi_BeautyMass_phipi_both_run1_log_run1run2_PaperDraft_Paper.pdf
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mass_Bs2DsPi_BeautyMass_phipi_both_20152016_log_run1run2_PaperDraft_PaperNoLeg.pdf
mass_B[..].pdf [74 KiB]
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mass_Bs2DsPi_CharmMass_phipi_both_run1_log_run1run2_PaperDraft_PaperNoLeg.pdf
mass_B[..].pdf [75 KiB]
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mass_Bs2DsPi_CharmMass_phipi_both_20152016_log_run1run2_PaperDraft_PaperNoLeg.pdf

Result of the determination of $|V_{ub}||a_{\text{NF}}|$. The blue line represents the result of this measurement, the vertical bands are the known exclusive and inclusive measurements of $|V_{ub}|$, which are $(3.70\pm 0.16)\times 10^{-3}$ and $(4.49\pm 0.28)\times 10^{-3}$, respectively [38]. The horizontal dashed line at $|a_{\text{NF}}|=1.0$ represents exact factorisation. The error bands represent an uncertainty of one standard deviation.

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Plot_aNF_Vub_result.png

Visualisation of the $pp$ collision energy dependence of the efficiency-corrected yield ratio of $\overline{ B } {}^0_ s \rightarrow D ^+_ s \pi ^- $ and $ B ^0 \rightarrow D ^- \pi ^+ $ decays, which scales with $f_{s}/f_{d}$. The inner error bars indicate the statistical uncertainty only, whereas the outer indicate the uncorrelated, including statistical, uncertainties. The correlated systematic uncertainty is not shown. The red dotted line represents a linear fit through the three values of $\mathcal{R}$ with uncorrelated, including statistical, uncertainties.

R_Ener[..].pdf [14 KiB]
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R_EnergyDependence.pdf

Animated gif made out of all figures.

PAPER-2020-021.gif
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Tables and captions

Relative systematic uncertainty $\sigma$ on the $ B ^0 \rightarrow D ^+_ s \pi ^- $ branching fraction measurement.

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Table_1.pdf

Relative systematic uncertainty $\sigma$ on the ratio of the efficiency-corrected $\overline{ B } {}^0_ s \rightarrow D ^+_ s \pi ^- $ and $ B ^0 \rightarrow D ^- \pi ^+ $ yield ratios. The ratios $\mathcal{R}_{13\text{ Te V} }/\mathcal{R}_{7\text{ Te V} }$ and $\mathcal{R}_{13\text{ Te V} }/\mathcal{R}_{8\text{ Te V} }$ are reported together as the difference of the systematic uncertainty for 7 and 8 $\text{ Te V}$ is negligible.

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Table_2.pdf

Results of $ B ^0 \rightarrow D ^+_ s \pi ^- $ and $ B ^0 \rightarrow D ^- \pi ^+ $ signal efficiencies and yields, as well as the branching fractions used as input for this measurement [38].

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Table_3.pdf

Supplementary Material [file]

Supplementary material full pdf

Supple[..].pdf [787 KiB]
Supplementary.pdf

This ZIP file contains supplemetary material for the publication LHCb-PAPER-2020-021. The files are: Supplementary.pdf : An overview of the extra figures supplementary.tex : LaTeX document with extra figures *.pdf, *.png, *.eps, *.C : The figures in variuous formats

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Created on 19 February 2021.