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A search for the rare decays B-s(0) -> mu(+) mu(-) and B-s(0) -> mu(+) mu-is performed with data collected in 2011 and 2012 with the LHCb experiment at the Large Hadron Collider. The data samples comprise 1.1 fb(-1) of proton-proton collisions at root s = 8 TeV and 1.0 fb(-1) at root s = 7 TeV. We observe an excess of B-s(0) -> mu(+) mu-candidates with respect to the background expectation. The probability that the background could produce such an excess or larger is 5.3 x 10(-4) corresponding to a signal significance of 3.5 standard deviations. A maximum-likelihood fit gives a branching fraction of B(B-s(0) -> mu(+) mu(-)) = (3.2(-1.2)(+1.5)) x 10(-9), where the statistical uncertainty is 95% of the total uncertainty. This result is in agreement with the standard model expectation. The observed number of B-s(0) -> mu(+) mu-candidates is consistent with the background expectation, giving an upper limit of B(B-s(0) -> mu(+) mu(-)) < 9.4 x 10(-10) at 95% confidence level. DOI: 10.1103/PhysRevLett.110.021801
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