A study of the decays $B^0_s \rightarrow \mu ^+\mu ^-$ and $B^0 \rightarrow \mu ^+\mu ^-$ has been performed using data corresponding to an integrated luminosity of 25 fb$^{-1}$ of 7 and 8 TeV proton–proton collisions collected with the ATLAS detector during the LHC Run 1. For the $B^0$ dimuon decay, an upper limit on the branching fraction is set at $\mathcal{B}(B^0 \rightarrow \mu ^+\mu ^-) < 4.2 \times 10^{-10}$ at 95 % confidence level. For $B^0_s$ , the branching fraction $\mathcal{B}(B^0_s \rightarrow \mu ^+\mu ^-) = \left( 0.9^{+1.1-0.8} \right) \times 10^{-9}$ is measured. The results are consistent with the Standard Model expectation with a p value of 4.8 %, corresponding to 2.0 standard
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