We investigate the prospects for the discovery of neutral Higgs bosons with a
pair of muons by direct searches at the CERN Large Hadron Collider (LHC) as
well as by indirect searches in the rare decay Bs→μ+μ− at the
Fermilab Tevatron and the LHC. Promising results are found for the minimal
supersymmetric standard model, the minimal supergravity (mSUGRA) model, and
supergravity models with non-universal Higgs masses (NUHM SUGRA). For
tanβ≃50, we find that (i) the contours for a branching fraction
of B(Bs→μ+μ−)=1×10−8 in the parameter space are very
close to the 5σ contours for pp→bϕ0→bμ+μ−+X,ϕ0=h0,H0,A0 at the LHC with an integrated luminosity (L) of 30
fb−1, (ii) the regions covered by B(Bs→μ+μ−)≥5×10−9 and the discovery region for bϕ0→bμ+μ− with 300
fb−1 are complementary in the mSUGRA parameter space, (iii) in NUHM SUGRA
models, a discovery of B(Bs→μ+μ−)≃5×10−9 at the
LHC will cover regions of the parameter space beyond the direct search for
bϕ0→bμ+μ− with L=300 fb−1.Comment: The version to appear in Physics Letters