An improved measurement of the decay B0s→μ+μ− and searches for the decays B0→μ+μ− and B0s→μ+μ−γ are performed at the LHCb experiment using data collected in proton-proton collisions at √s=7, 8 and 13 TeV, corresponding to integrated luminosities of 1, 2 and 6 fb−1, respectively. The B0s→μ+μ− branching fraction and effective lifetime are measured to be B(B0s→μ+μ−)=(3.09+0.46+0.15−0.43−0.11)×10−9 and τ(B0s→μ+μ−)=(2.07±0.29±0.03) ps, respectively, where the uncertainties include both statistical and systematic contributions. No significant signal for B0→μ+μ− and B0s→μ+μ−γ decays is found and the upper limits B(B0→μ+μ−)<2.6×10−10 and B(B0s→μ+μ−γ)<2.0×10−9 at 95% confidence level are determined, where the latter is limited to the range mμμ>4.9 GeV/c2. Additionally, the ratio between the B0→μ+μ− and B0s→μ+μ− branching fractions is measured to be Rμ+μ−<0.095 at 95% confidence level. The results are in agreement with the Standard Model predictions.10 MoreReceived 23 August 2021Accepted 8 December 2021DOI:https://doi.org/10.1103/PhysRevD.105.012010Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3.© 2022 CERN, for the LHCb CollaborationPhysics Subject Headings (PhySH)Research AreasBranching fractionFlavor changing neutral currentsRare decaysPhysical SystemsBottom mesonsParticles & Fields