A search for the rare decays $B_s^0\to\tau^+\tau^$ and $B^0\to\tau^+\tau^$ is performed using protonproton collision data collected with the LHCb detector. The data sample corresponds to an integrated luminosity of 3fb$^{1}$ collected in 2011 and 2012. The $\tau$ leptons are reconstructed through the decay $\tau^\to\pi^\pi^+\pi^\nu_{\tau}$. Assuming no contribution from $B^0\to\tau^+\tau^$ decays, an upper limit is set on the branching fraction $\mathcal{B}(B_s^0\to\tau^+\tau^) < 6.8\times 10^{3}$ at 95 confidence level. If instead no contribution from $B_s^0\to\tau^+\tau^$ decays is assumed, the limit is $\mathcal{B}(B^0\to\tau^+\tau^)< 2.1 \times 10^{3}$ at 95 confidence level. These results correspond to the first direct limit on $\mathcal{B}(B_s^0\to\tau^+\tau^)$ and the world's best limit on $\mathcal{B}(B^0\to\tau^+\tau^)$.
Twodimensional distribution of the invariant masses $m_{\pi ^+ \pi ^ }$ of the two oppositely charged twopion combinations for simulated $ B ^0_ s \rightarrow \tau ^+\tau ^ $ candidates. The distribution is symmetric by construction. The vertical and horizontal lines illustrate the sector boundaries. 
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(left) Normalised NN output distribution in the signal ($\widehat{\mathcal{N}}^{\text{SR}}_{\text{sim}}$) and control ($\widehat{\mathcal{N}}^{\text{CR}}_{\text{sim}}$) region for $ B ^0_ s \rightarrow \tau ^+\tau ^ $ simulated events. (right) Normalised NN output distribution in the data control region $\widehat{\mathcal{N}}^{\text{CR}}_{\text{data}}$. The uncertainties reflect the statistics of the (simulated) data. 
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Distribution of the NN output in the signal region $\mathcal{N}^{\text{SR}}_{\text{data}}$ (black points), with the total fit result (blue line) and the background component (green line). The fitted $ B ^0_ s \rightarrow \tau ^+\tau ^ $ signal component is negative and is therefore shown multiplied by $1$ (red line). For each bin of the signal and background component the combined statistical and systematic uncertainty on the template is shown as a lightcoloured band. The difference between data and fit divided by its uncertainty (pull) is shown underneath. 
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Invariant mass distribution of the reconstructed $ B ^0 \rightarrow D^D_s^{+}$ candidates in data (black points), together with the total fit result (blue line) used to determine the $ B ^0 \rightarrow D^D_s^{+}$ yield. The individual components are described in the text. 
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Distribution of the NN output in the signal region $\mathcal{N}^{\text{SR}}_{\text{data}}$ (black points), with the total fit result (blue line), and the background component (green line). Shown is the fit using the "background only" model. For each bin of the background component the combined statistical and systematic uncertainty is shown as a lightcoloured band. The difference between data and fit divided by its uncertainty (pull) is shown underneath. 
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Profile likelihood scan of the $ B ^0_ s \rightarrow \tau ^+\tau ^ $ signal yield. The intersections of the likelihood curve with the horizontal lines define the 68.3%, 95.4% and 99.7% likelihood intervals. 
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The $p$value derived with the CL$_{\text{s}}$ method as a function of $\mathcal{B} ( B ^0_ s \rightarrow \tau ^+\tau ^ )$. Expected (observed) values are shown by a dashed (full) black line. The green (yellow) band covers the regions of 68% and 95% confidence for the expected limit. The red horizontal line corresponds to the limit at 95% CL. 
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Normalised NN output distribution in the signal ($\widehat{\mathcal{N}}^{\text{SR}}_{\text{sim}}$) and control ($\widehat{\mathcal{N}}^{\text{CR}}_{\text{sim}}$) region for $ B ^0 \rightarrow \tau ^+\tau ^ $ simulated events. 
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Fit results for $ B ^0 \rightarrow \tau ^+\tau ^ $. Distribution $\mathcal{N}^{\text{SR}}_{\text{data}}$ (black points), overlaid with the total fit result (blue line), and background component (green line), assuming all signal events originate from $ B ^0 \rightarrow \tau ^+\tau ^ $ decays. The $ B ^0 \rightarrow \tau ^+\tau ^ $ signal component is also shown (red line), multiplied by $1$. For each bin of the signal and background component the combined statistical and systematic uncertainty is shown as a lightcoloured band. The difference between data and fit divided by its uncertainty (pull) is shown underneath. 
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The $p$value derived with the CL$_{\text{s}}$ method as a function of $\mathcal{B} ( B ^0 \rightarrow \tau ^+\tau ^ $). Expected (observed) values are shown by a dashed (full) black line. The green (yellow) band covers the regions of 68% and 95% confidence for the expected limit. The red horizontal line corresponds to the limit at 95% CL. 
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Animated gif made out of all figures. 
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Supplementary material full pdf 
supple[..].pdf [106 KiB] 

This ZIP file contains supplemetary material for the publication LHCbPAPER2017003. The files are: supplementary.pdf : An overview of the extra figures *.pdf, *.png, *.eps, *.C : The figures in various formats 
Fig1S.pdf [53 KiB] HiDef png [989 KiB] Thumbnail [678 KiB] *C file 
Created on 20 February 2021.