The differential branching fraction of B0 → K*(892)0 μ+ μ- decays is measured as a function of the squared invariant mass of the dimuon system. The data corresponds to 3/fb of integrated luminosity collected in 2011 and 2012 by the LHCb detector at the Large Hadron Collider at CERN. Integrated across squared dimuon invariant mass, and interpolated through excluded regions, the total branching fraction is found to be B[B0 → K*(892)0 μ+ μ-] = (1.058 +0.017-0.016 ± 0.013 ± 0.070) × 10**-6

In the theoretically favoured region of squared dimuon invariant mass, (1.1 < q² < 6) GeV²/c**4 , the differential branching fraction is found to be

dB[B0 → K*(892)0 μ+ μ-]/dq² = (0.402 +0.020-0.019 ± 0.008 ± 0.027) × 10**-7

In the two results above, the first uncertainty is statistical, the second systematic, and the third due to the uncertainty of the branching fraction of the normalisation channel. The differential branching fraction is in agreement with, although lower than, the Standard Model prediction of (0.49 ± 0.08) × 10**-7. As with the measurement of several decay modes including a quark-level b → sl+l- transition, the Standard Model predictions are consistently higher than the measured values.

In this analysis, for the first time, the fraction of S-wave in the Kπ system is measured and explicitly accounted for. Previous analyses had measured the branching fraction of both P- and S-wave components and compared to predictions for pure P-wave. In the same theoretically favoured region of (1.1 < q² < 6) GeV²/c**4 , and for the Kπ invariant mass range (796 < m[Kπ] < 996) MeV/c², the fraction of S-wave is found to be

F_S = 0.097 ± 0.016 ± 0.008,

where the first uncertainty is statistical, and the second is systematic. This value is somewhat larger than expected, although no concrete theoretical predictions exist.