A search for $B^{0}_{s}\to\tau^{\pm}\mu^{\mp}$ and $B^{0}\to\tau^{\pm}\mu^{\mp}$ decays is performed using data corresponding to an integrated luminosity of 3 fb$^{1}$ of protonproton collisions, recorded with the LHCb detector in 2011 and 2012. For this search, the $\tau$ lepton is reconstructed in the $\tau^{}\to\pi^{}\pi^{+}\pi^{}\nu_{\tau}$ channel. No significant signal is observed. Assuming no contribution from $B^{0}\to\tau^{\pm}\mu^{\mp}$ decays, an upper limit is set on the $B^{0}_{s}\to\tau^{\pm}\mu^{\mp}$ branching fraction of $\mathcal{B}\left( B^{0}_{s}\to\tau^{\pm}\mu^{\mp}\right) < 4.2\times 10^{5}$ at $95\%$ confidence level. If instead no contribution from $B^{0}_{s}\to\tau^{\pm}\mu^{\mp}$ decays is assumed, a limit of $\mathcal{B}\left( B^{0}\to\tau^{\pm}\mu^{\mp}\right) < 1.4\times 10^{5}$ is obtained at $95\%$ confidence level. These are the first limit on $\mathcal{B}\left( B^{0}_{s}\to\tau^{\pm}\mu^{\mp}\right)$ and the world's best limit on $\mathcal{B}\left( B^{0}\to\tau^{\pm}\mu^{\mp}\right)$.
Distribution of the reconstructed $ B $ invariant mass for $ B ^0_ s \rightarrow \tau ^\pm ( \rightarrow \pi ^\pm \pi ^\mp \pi ^\pm \nu _\tau ) \mu ^\mp $ simulated decays and samesign candidates in data after initial selection (see text). 
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Final BDT output binned distributions for data and simulated signal samples. The markers are displaced horizontally to improve visibility. 
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Distributions of the reconstructed $ B $ invariantmass in data in the four final BDT bins with the projections of the fit for the $ B ^0_ s $ signalonly hypothesis overlaid. The lowerpart of each figure shows the normalised residuals. 
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The expected and observed pvalues derived with the CLs method as a function of the $ B ^0_ s \rightarrow \tau ^\pm \mu ^\mp $ branching fraction. 
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The expected and observed pvalues derived with the CLs method as a function of the $ B ^0 \rightarrow \tau ^\pm \mu ^\mp $ branching fraction. 
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Animated gif made out of all figures. 
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Expected and observed $90\%$ and $95\%$ CL limits on the $ B ^0_{( s )} \rightarrow \tau ^\pm \mu ^\mp $ branching fraction. 
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Created on 17 August 2019.Citation count from INSPIRE on 20 August 2019.