A branching fraction measurement of the $B^{0}\rightarrow D_{s}^{+}\pi^{}$ decay is presented using protonproton 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 $b \to u$ chargedcurrent transition, the result provides information on nonfactorisable strong interaction effects and the magnitude of the CabibboKobayashiMaskawa matrix element $V_{ub}$. Additionally, the collision energy dependence of the hadronisationfraction ratio $f_s/f_d$ is measured through $\bar{B}{}_{s}^{0}\rightarrow D_{s}^{+}\pi^{}$ and $B^0 \to D^{}\pi^{+}$ decays.
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 nonfactorisable contribution to the decay amplitude. 
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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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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. 
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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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Visualisation of the $pp$ collision energy dependence of the efficiencycorrected 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. 
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Animated gif made out of all figures. 
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Relative systematic uncertainty $\sigma$ on the $ B ^0 \rightarrow D ^+_ s \pi ^ $ branching fraction measurement. 
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Relative systematic uncertainty $\sigma$ on the ratio of the efficiencycorrected $\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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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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Supplementary material full pdf 
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This ZIP file contains supplemetary material for the publication LHCbPAPER2020021. 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.